1 00:00:01,070 --> 00:00:03,410 The following content is provided under a Creative 2 00:00:03,410 --> 00:00:04,830 Commons license. 3 00:00:04,830 --> 00:00:07,040 Your support will help MIT OpenCourseWare 4 00:00:07,040 --> 00:00:11,130 continue to offer high-quality educational resources for free. 5 00:00:11,130 --> 00:00:13,670 To make a donation or to view additional materials 6 00:00:13,670 --> 00:00:17,630 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,630 --> 00:00:18,503 at ocw.mit.edu. 8 00:00:22,137 --> 00:00:23,470 GABRIEL SANCHEZ-MARTINEZ: Great. 9 00:00:23,470 --> 00:00:23,970 OK. 10 00:00:23,970 --> 00:00:28,660 So today's lecture is on transit service reliability. 11 00:00:28,660 --> 00:00:30,577 This is my penultimate lecture, because we 12 00:00:30,577 --> 00:00:31,660 have guest lecturers, too. 13 00:00:31,660 --> 00:00:36,250 So let's start out with what is reliable transit for you. 14 00:00:36,250 --> 00:00:39,430 What do you think of when you think of reliable transit? 15 00:00:39,430 --> 00:00:40,600 What does it mean for you? 16 00:00:44,730 --> 00:00:48,554 And I'll write a few videos on the board. 17 00:00:48,554 --> 00:00:51,928 [CHALK ON BLACKBOARD] 18 00:00:58,676 --> 00:01:00,010 [INAUDIBLE] 19 00:01:00,010 --> 00:01:03,432 AUDIENCE: Arrival at or close to scheduled arrival. 20 00:01:03,432 --> 00:01:04,819 GABRIEL SANCHEZ-MARTINEZ: OK. 21 00:01:04,819 --> 00:01:07,110 Low variance, OK, of-- 22 00:01:07,110 --> 00:01:08,830 there's a word for that. 23 00:01:08,830 --> 00:01:10,490 Punctuality, right? 24 00:01:10,490 --> 00:01:11,375 So let's use that. 25 00:01:16,800 --> 00:01:20,187 Just because it's hard to write on the board with chalk. 26 00:01:20,187 --> 00:01:22,020 It's hard to spell correctly, actually, when 27 00:01:22,020 --> 00:01:23,680 you're close up to the board. 28 00:01:23,680 --> 00:01:24,180 Emily. 29 00:01:26,940 --> 00:01:28,180 AUDIENCE: Lack of disruption. 30 00:01:28,180 --> 00:01:31,760 So it's the same service every weekday. 31 00:01:39,194 --> 00:01:41,610 GABRIEL SANCHEZ-MARTINEZ: And you kind of got two of them. 32 00:01:41,610 --> 00:01:43,450 Lack of disruptions is one of them 33 00:01:43,450 --> 00:01:45,540 and you said the same service, right? 34 00:01:45,540 --> 00:01:47,419 So I guess predictability. 35 00:01:54,270 --> 00:01:56,145 Great. 36 00:01:56,145 --> 00:01:57,780 AUDIENCE: The word legibility, which 37 00:01:57,780 --> 00:02:00,550 is that you sort of know where transit is going 38 00:02:00,550 --> 00:02:01,345 and it makes sense. 39 00:02:01,345 --> 00:02:03,470 GABRIEL SANCHEZ-MARTINEZ: You called it legibility? 40 00:02:03,470 --> 00:02:04,280 AUDIENCE: Legibility. 41 00:02:04,280 --> 00:02:05,488 GABRIEL SANCHEZ-MARTINEZ: OK. 42 00:02:05,488 --> 00:02:08,330 That's coining a new term there. 43 00:02:08,330 --> 00:02:09,840 AUDIENCE: Well, yeah. 44 00:02:09,840 --> 00:02:11,220 It's coining a new term. 45 00:02:14,867 --> 00:02:16,450 GABRIEL SANCHEZ-MARTINEZ: You had one. 46 00:02:16,450 --> 00:02:19,672 AUDIENCE: Oh, not in the US. 47 00:02:19,672 --> 00:02:20,172 [LAUGHTER] 48 00:02:20,172 --> 00:02:21,796 GABRIEL SANCHEZ-MARTINEZ: [INAUDIBLE].. 49 00:02:24,955 --> 00:02:26,850 I appreciate the humor, though. 50 00:02:26,850 --> 00:02:29,010 Any other ideas? 51 00:02:29,010 --> 00:02:31,680 AUDIENCE: Maybe the quality of the ride 52 00:02:31,680 --> 00:02:34,285 is always the same, like tables are clean. 53 00:02:34,285 --> 00:02:36,160 GABRIEL SANCHEZ-MARTINEZ: Consistent quality. 54 00:02:36,160 --> 00:02:36,784 AUDIENCE: Yeah. 55 00:02:39,450 --> 00:02:41,635 It's always possible to enter the car. 56 00:02:44,980 --> 00:02:46,110 Surrounding is consistent. 57 00:02:46,110 --> 00:02:48,026 GABRIEL SANCHEZ-MARTINEZ: Sufficient capacity. 58 00:02:56,059 --> 00:02:56,559 Actually. 59 00:02:56,559 --> 00:02:58,890 AUDIENCE: I think it also has to cover all the places 60 00:02:58,890 --> 00:03:00,305 you want to go in like a 90-- 61 00:03:00,305 --> 00:03:02,430 some kind of percentile of what you want to travel, 62 00:03:02,430 --> 00:03:05,540 so you're not getting a car [INAUDIBLE] or something. 63 00:03:05,540 --> 00:03:06,790 GABRIEL SANCHEZ-MARTINEZ: Yep. 64 00:03:06,790 --> 00:03:16,000 And so that includes [INAUDIBLE] coverage, which is spatial, 65 00:03:16,000 --> 00:03:22,200 and also span of service, right, which is the same thing 66 00:03:22,200 --> 00:03:24,282 but temporal. 67 00:03:24,282 --> 00:03:26,752 [WRITING ON BOARD] 68 00:03:35,150 --> 00:03:36,740 OK, these are some good ideas. 69 00:03:36,740 --> 00:03:38,010 AUDIENCE: I have a real-- 70 00:03:38,010 --> 00:03:38,420 GABRIEL SANCHEZ-MARTINEZ: Sorry? 71 00:03:38,420 --> 00:03:40,045 AUDIENCE: I said I have a real one now. 72 00:03:43,820 --> 00:03:46,132 Consistent fare structure or-- 73 00:03:46,132 --> 00:03:47,340 GABRIEL SANCHEZ-MARTINEZ: OK. 74 00:03:47,340 --> 00:03:49,030 That's usually consistent. 75 00:03:49,030 --> 00:03:50,870 Are you thinking of a particular example? 76 00:03:50,870 --> 00:03:54,200 AUDIENCE: I think of just when places where 77 00:03:54,200 --> 00:03:57,620 the price keeps rising often. 78 00:03:57,620 --> 00:03:59,500 GABRIEL SANCHEZ-MARTINEZ: OK. 79 00:03:59,500 --> 00:04:04,670 I'll say-- I don't know. 80 00:04:04,670 --> 00:04:07,070 AUDIENCE: [INAUDIBLE] transfers [INAUDIBLE] confusing. 81 00:04:07,070 --> 00:04:08,903 GABRIEL SANCHEZ-MARTINEZ: Good communication 82 00:04:08,903 --> 00:04:11,135 of fare policy, so a clear fare policy. 83 00:04:11,135 --> 00:04:11,760 AUDIENCE: Sure. 84 00:04:11,760 --> 00:04:13,239 GABRIEL SANCHEZ-MARTINEZ: Yeah. 85 00:04:13,239 --> 00:04:16,690 [WRITING ON BOARD] 86 00:04:22,600 --> 00:04:23,100 Eli. 87 00:04:23,100 --> 00:04:24,725 AUDIENCE: I feel like we haven't worked 88 00:04:24,725 --> 00:04:27,589 in maintenance of headways and high-frequency service in here. 89 00:04:27,589 --> 00:04:28,880 GABRIEL SANCHEZ-MARTINEZ: Sure. 90 00:04:28,880 --> 00:04:30,280 AUDIENCE: It's kind of covered by punctuality 91 00:04:30,280 --> 00:04:31,040 and predictability-- 92 00:04:31,040 --> 00:04:32,140 GABRIEL SANCHEZ-MARTINEZ: Right. 93 00:04:32,140 --> 00:04:33,306 But it's a little different. 94 00:04:33,306 --> 00:04:35,550 And we're going to talk a lot about that today. 95 00:04:35,550 --> 00:04:37,320 So let's add that in. 96 00:04:37,320 --> 00:04:39,916 So even headways? 97 00:04:39,916 --> 00:04:41,860 AUDIENCE: Yeah. 98 00:04:41,860 --> 00:04:43,570 You wouldn't say short headways. 99 00:04:43,570 --> 00:04:45,910 That's not necessarily part of the liability. 100 00:04:45,910 --> 00:04:48,076 AUDIENCE: Well, it seems like we're sort of actually 101 00:04:48,076 --> 00:04:50,410 expanding the traditional definition for liability here. 102 00:04:50,410 --> 00:04:52,284 GABRIEL SANCHEZ-MARTINEZ: Yeah, we have been. 103 00:04:52,284 --> 00:04:55,000 I'm not filtering too much out because-- 104 00:04:55,000 --> 00:04:57,940 I guess we'll stop here. 105 00:04:57,940 --> 00:04:59,620 The point I wanted to make is that-- 106 00:04:59,620 --> 00:05:01,570 I'll come back to this in lecture-- 107 00:05:01,570 --> 00:05:05,480 reliability means a lot of things to different people. 108 00:05:05,480 --> 00:05:08,390 And doing all these things can be difficult. 109 00:05:08,390 --> 00:05:11,170 So we're going to talk about some aspects. 110 00:05:11,170 --> 00:05:14,740 We're going to focus more on punctuality, lack 111 00:05:14,740 --> 00:05:19,540 of disruptions, predictability. 112 00:05:19,540 --> 00:05:23,200 We'll talk about common equality in system. 113 00:05:23,200 --> 00:05:25,435 That has to do with even headways. 114 00:05:25,435 --> 00:05:28,060 We're not going to talk so much about fair policy, or coverage, 115 00:05:28,060 --> 00:05:32,170 or span of service, or legibility. 116 00:05:32,170 --> 00:05:32,920 All right. 117 00:05:32,920 --> 00:05:34,230 So right. 118 00:05:34,230 --> 00:05:36,580 So impacts of unreliability, the causes 119 00:05:36,580 --> 00:05:39,340 of unreliability, how to measure unreliability 120 00:05:39,340 --> 00:05:42,800 or reliability, and then real-time control strategies. 121 00:05:42,800 --> 00:05:45,530 We've mentioned some of these topics before. 122 00:05:45,530 --> 00:05:49,030 Now let's focus on these things. 123 00:05:49,030 --> 00:05:51,474 OK, so passenger impacts. 124 00:05:51,474 --> 00:05:53,140 What happens when service is unreliable? 125 00:05:53,140 --> 00:05:55,910 We have longer waiting times, right? 126 00:05:55,910 --> 00:06:02,780 We have the need to have a longer reliability buffer. 127 00:06:02,780 --> 00:06:05,470 So have we talked about reliability buffer 128 00:06:05,470 --> 00:06:08,620 before in this course? 129 00:06:08,620 --> 00:06:09,880 No? 130 00:06:09,880 --> 00:06:14,044 So if your trip to-- 131 00:06:14,044 --> 00:06:16,460 we're going to talk more about it later than we will here. 132 00:06:16,460 --> 00:06:20,074 But if your trip to-- 133 00:06:20,074 --> 00:06:23,002 [WRITING ON BOARD] 134 00:06:28,380 --> 00:06:33,090 OK, so you know that running times are stochastic, right? 135 00:06:33,090 --> 00:06:38,710 So there's a distribution of running times. 136 00:06:38,710 --> 00:06:41,155 So this is running time, or in this case let's 137 00:06:41,155 --> 00:06:42,220 call it journey time. 138 00:06:47,360 --> 00:06:55,190 And this is a probability [INAUDIBLE],, right? 139 00:06:55,190 --> 00:06:58,610 So the schedule has to have a single intrinsic value. 140 00:06:58,610 --> 00:07:01,520 And you can go to your journey planner, 141 00:07:01,520 --> 00:07:03,490 and it will say your journey takes this long. 142 00:07:03,490 --> 00:07:06,170 You walk this much time, you wait this much time, 143 00:07:06,170 --> 00:07:07,200 you arrive at this time. 144 00:07:07,200 --> 00:07:10,360 So you add those components up and you have a specific time. 145 00:07:10,360 --> 00:07:15,110 That specific time may be close to the median, and may not. 146 00:07:15,110 --> 00:07:19,130 So if service is reliable, then there's 147 00:07:19,130 --> 00:07:22,790 little variance in this distribution, correct? 148 00:07:22,790 --> 00:07:23,860 So you might have-- 149 00:07:26,860 --> 00:07:30,800 I don't have much of another color here. 150 00:07:30,800 --> 00:07:31,820 That doesn't work. 151 00:07:31,820 --> 00:07:33,710 So I'll just write on white as well. 152 00:07:33,710 --> 00:07:34,410 Maybe a dot. 153 00:07:37,090 --> 00:07:40,190 So you might have one distribution of journeys 154 00:07:40,190 --> 00:07:41,375 that has lower variance. 155 00:07:48,150 --> 00:07:51,480 And therefore you need to budget less time to make your trip 156 00:07:51,480 --> 00:07:52,740 and arrive on time. 157 00:07:52,740 --> 00:07:53,850 Correct? 158 00:07:53,850 --> 00:07:56,040 So to the extent that the waiting is 159 00:07:56,040 --> 00:08:00,210 variable or your in-vehicle time is variable, then 160 00:08:00,210 --> 00:08:04,950 if you need to be at work or at school at 9:00 AM, 161 00:08:04,950 --> 00:08:08,790 that means that, even if on average it takes half an hour, 162 00:08:08,790 --> 00:08:11,160 you might have to budget for 45 minutes. 163 00:08:11,160 --> 00:08:14,530 So the extra 15 minutes of time that you budget, that's called 164 00:08:14,530 --> 00:08:16,920 the reliability buffer. 165 00:08:16,920 --> 00:08:18,100 It's a cost. 166 00:08:18,100 --> 00:08:21,060 You could monetize it if you wanted to. 167 00:08:21,060 --> 00:08:23,700 It means that people are budgeting, and in some cases 168 00:08:23,700 --> 00:08:25,740 wasting, that time. 169 00:08:25,740 --> 00:08:27,450 And we want to decrease that. 170 00:08:27,450 --> 00:08:31,440 So the need for trip time reliability buffer. 171 00:08:31,440 --> 00:08:32,520 Higher loads. 172 00:08:32,520 --> 00:08:35,909 So that means, of course, that vehicles 173 00:08:35,909 --> 00:08:38,020 have more people in them, and therefore rides 174 00:08:38,020 --> 00:08:39,870 are more uncomfortable for passengers. 175 00:08:39,870 --> 00:08:42,090 And they are also slower, because if a vehicle has 176 00:08:42,090 --> 00:08:44,150 more people in it, the bus stops more often 177 00:08:44,150 --> 00:08:46,202 and the process is slower. 178 00:08:46,202 --> 00:08:47,660 We know that from earlier lectures. 179 00:08:52,540 --> 00:08:58,350 We know from random incidents that from a passenger 180 00:08:58,350 --> 00:09:03,570 perspective, passengers will experience 181 00:09:03,570 --> 00:09:05,620 more crowded vehicles because they 182 00:09:05,620 --> 00:09:07,290 are more likely to board the vehicle 183 00:09:07,290 --> 00:09:09,232 where there are more people in it. 184 00:09:09,232 --> 00:09:11,190 It's a little bit of a chicken and egg problem. 185 00:09:11,190 --> 00:09:13,730 So even if, on average across the vehicles, 186 00:09:13,730 --> 00:09:16,200 your loads are right where they should be, 187 00:09:16,200 --> 00:09:18,810 most people are going to be on the more crowded vehicles. 188 00:09:18,810 --> 00:09:21,150 So that's that thing. 189 00:09:21,150 --> 00:09:25,590 In terms of agency impacts can increase costs, making, 190 00:09:25,590 --> 00:09:30,150 for example, you need a longer recovery time at the terminal. 191 00:09:30,150 --> 00:09:32,460 And therefore, you know that that translates 192 00:09:32,460 --> 00:09:38,610 to higher vehicle costs, higher crew costs, reduced ridership 193 00:09:38,610 --> 00:09:42,120 and revenue, reduced operator morale, a public 194 00:09:42,120 --> 00:09:43,570 and political problem. 195 00:09:43,570 --> 00:09:46,225 What do we mean by that? 196 00:09:46,225 --> 00:09:47,850 What happens when public transportation 197 00:09:47,850 --> 00:09:52,870 is unreliable in terms of politics? 198 00:09:52,870 --> 00:09:54,680 AUDIENCE: The public hates it. 199 00:09:54,680 --> 00:09:56,050 Public hates unreliability. 200 00:09:56,050 --> 00:09:57,341 GABRIEL SANCHEZ-MARTINEZ: Sure. 201 00:09:57,341 --> 00:09:59,000 AUDIENCE: It creates pressure. 202 00:09:59,000 --> 00:10:02,459 The forces against public transportation grows stronger. 203 00:10:02,459 --> 00:10:03,750 GABRIEL SANCHEZ-MARTINEZ: Sure. 204 00:10:03,750 --> 00:10:04,070 So-- 205 00:10:04,070 --> 00:10:05,190 AUDIENCE: [INAUDIBLE] funding, and then-- 206 00:10:05,190 --> 00:10:06,980 GABRIEL SANCHEZ-MARTINEZ: Yeah, so there's a funding, right? 207 00:10:06,980 --> 00:10:09,990 And we'll talk more about this in the last two lectures. 208 00:10:09,990 --> 00:10:12,570 So when public transportation is unreliable, 209 00:10:12,570 --> 00:10:15,180 sometimes governments are hesitant, 210 00:10:15,180 --> 00:10:17,740 or the public may be hesitant, to fund it more 211 00:10:17,740 --> 00:10:19,350 before they fix the problems. 212 00:10:19,350 --> 00:10:23,830 But fixing the problems might require some resources. 213 00:10:23,830 --> 00:10:26,250 So it's a vicious cycle. 214 00:10:26,250 --> 00:10:28,340 And then reduced effective capacity. 215 00:10:28,340 --> 00:10:31,010 And we'll show a real example here in Boston of that. 216 00:10:33,560 --> 00:10:34,060 All right. 217 00:10:34,060 --> 00:10:35,350 So what causes this? 218 00:10:35,350 --> 00:10:37,870 We can divide causes into external and internal causes. 219 00:10:37,870 --> 00:10:39,130 External causes. 220 00:10:39,130 --> 00:10:43,210 Traffic, demand-- demand variability in particular-- 221 00:10:43,210 --> 00:10:43,810 incidents. 222 00:10:43,810 --> 00:10:46,300 So a passenger may get sick. 223 00:10:46,300 --> 00:10:48,400 These things are external. 224 00:10:48,400 --> 00:10:51,160 The agency knows that they could happen, 225 00:10:51,160 --> 00:10:54,280 but there's not much you can do about them. 226 00:10:54,280 --> 00:10:57,100 Internal causes are in the control of the agency, 227 00:10:57,100 --> 00:10:58,520 at least a little more. 228 00:10:58,520 --> 00:11:01,954 So equipment failure, that's something that agency owns. 229 00:11:01,954 --> 00:11:04,120 Maybe you can't predict exactly when it will happen, 230 00:11:04,120 --> 00:11:05,830 but with some preventive maintenance 231 00:11:05,830 --> 00:11:09,300 they could reduce the chance of this happening. 232 00:11:09,300 --> 00:11:13,240 Insufficient resources, poor operations planning, 233 00:11:13,240 --> 00:11:16,370 lack of supervision and control, and human driver behavior. 234 00:11:16,370 --> 00:11:18,580 What do I mean by human driver behavior? 235 00:11:18,580 --> 00:11:21,165 How does that cause unreliability? 236 00:11:26,521 --> 00:11:27,020 Henry. 237 00:11:27,020 --> 00:11:30,620 AUDIENCE: The way that a driver drives can vary 238 00:11:30,620 --> 00:11:32,930 and that affects runtime. 239 00:11:32,930 --> 00:11:35,140 Or maybe some are more aggressive and some are less. 240 00:11:35,140 --> 00:11:35,570 GABRIEL SANCHEZ-MARTINEZ: Yes. 241 00:11:35,570 --> 00:11:37,550 Some drivers are slow, some drivers are fast. 242 00:11:37,550 --> 00:11:39,633 And then if you're running high-frequency service, 243 00:11:39,633 --> 00:11:40,390 they'll bunch up. 244 00:11:40,390 --> 00:11:42,230 And that could be the cause of bunching. 245 00:11:42,230 --> 00:11:48,272 Or maybe that fast driver is now running early, rolling 246 00:11:48,272 --> 00:11:49,480 a long headway service early. 247 00:11:49,480 --> 00:11:53,000 And that's really bad for waiting time, as we'll see. 248 00:11:53,000 --> 00:11:55,850 So if we think about transit, and look 249 00:11:55,850 --> 00:11:59,410 at the whole process of planning it and delivering it 250 00:11:59,410 --> 00:12:00,977 as if it were a business process, 251 00:12:00,977 --> 00:12:02,810 we know that we start with service planning, 252 00:12:02,810 --> 00:12:05,210 and move on to operations planning, 253 00:12:05,210 --> 00:12:06,430 and then actual operations. 254 00:12:06,430 --> 00:12:10,310 And each of these things, the output of one 255 00:12:10,310 --> 00:12:13,760 is the input to the next process, and so forth. 256 00:12:13,760 --> 00:12:16,460 The input to service policy, among them are 257 00:12:16,460 --> 00:12:18,530 is demand estimation. 258 00:12:18,530 --> 00:12:22,810 Then we bring in analysis of models or vehicle scheduling 259 00:12:22,810 --> 00:12:24,080 and crew scheduling. 260 00:12:24,080 --> 00:12:26,090 And during operations there's service control. 261 00:12:26,090 --> 00:12:29,090 We'll talk about service control, real-time control, 262 00:12:29,090 --> 00:12:33,000 too, as an input to operations, to make them more reliable. 263 00:12:33,000 --> 00:12:36,890 So there's also a feedback loop, because passengers 264 00:12:36,890 --> 00:12:40,040 might complain or somehow you have data collecting 265 00:12:40,040 --> 00:12:41,280 information on performance. 266 00:12:41,280 --> 00:12:44,600 And you can take that back to service planning or operations 267 00:12:44,600 --> 00:12:47,360 planning, or you could modify your service control 268 00:12:47,360 --> 00:12:50,120 to change the cycle. 269 00:12:50,120 --> 00:12:53,510 And here we have the key agents in each of these steps. 270 00:12:53,510 --> 00:12:55,910 So transit agency management, mostly 271 00:12:55,910 --> 00:12:57,740 taking care of service policy. 272 00:12:57,740 --> 00:13:00,110 Then you have some operational planning stuff, 273 00:13:00,110 --> 00:13:02,300 taking care of operations planning. 274 00:13:02,300 --> 00:13:06,650 And then the actual drivers and inspectors out in the field. 275 00:13:06,650 --> 00:13:10,520 So I guess one thing to take away 276 00:13:10,520 --> 00:13:14,360 from this is that there are many decisions across all 277 00:13:14,360 --> 00:13:17,610 of this process that affect reliability. 278 00:13:17,610 --> 00:13:22,550 And you can't really have reliable service if you-- 279 00:13:22,550 --> 00:13:24,170 there's many places where you could-- 280 00:13:24,170 --> 00:13:25,850 a cause on reliability. 281 00:13:25,850 --> 00:13:28,650 One of them might be your vehicles break down. 282 00:13:28,650 --> 00:13:30,500 So no matter what you do, if your fleet 283 00:13:30,500 --> 00:13:33,530 is old and having difficulty with maintenance, 284 00:13:33,530 --> 00:13:35,570 you might have the best service control 285 00:13:35,570 --> 00:13:38,930 policies, and all the supervision in the world, 286 00:13:38,930 --> 00:13:40,950 and you still have unreliable service. 287 00:13:40,950 --> 00:13:44,060 So it's a hard problem. 288 00:13:44,060 --> 00:13:45,830 It used to be very hard, actually, 289 00:13:45,830 --> 00:13:50,870 because, well, to ensure reliability you 290 00:13:50,870 --> 00:13:55,160 need to ensure the variability and things. 291 00:13:55,160 --> 00:13:57,980 So you know from data collection that if you 292 00:13:57,980 --> 00:14:00,920 want to measure the mean, you can calculate your sample size. 293 00:14:00,920 --> 00:14:02,540 Measuring the variance of something 294 00:14:02,540 --> 00:14:05,600 requires an even greater data collection effort. 295 00:14:05,600 --> 00:14:09,670 So things have gotten a lot easier with technology. 296 00:14:09,670 --> 00:14:13,400 And so we know that we have several data collection 297 00:14:13,400 --> 00:14:14,060 systems-- 298 00:14:14,060 --> 00:14:15,740 AVL, AFC, APC. 299 00:14:15,740 --> 00:14:19,640 That makes it a lot easier and cheaper to measure reliability. 300 00:14:19,640 --> 00:14:21,950 We'll give some examples. 301 00:14:21,950 --> 00:14:24,020 Then we have scheduling systems, which 302 00:14:24,020 --> 00:14:26,450 make it very easy to make an adjustment in the schedule. 303 00:14:26,450 --> 00:14:28,460 If we see that we've not scheduled enough time 304 00:14:28,460 --> 00:14:31,070 for this bus, we need to add some recovery 305 00:14:31,070 --> 00:14:35,270 time, that's going to increase the fleet size by one. 306 00:14:35,270 --> 00:14:38,330 With a program or scheduling software, 307 00:14:38,330 --> 00:14:41,330 you can do that quickly and react. 308 00:14:41,330 --> 00:14:46,270 And the best systems will actually read AVL data in, 309 00:14:46,270 --> 00:14:50,510 and you don't even have to manually analyze it. 310 00:14:50,510 --> 00:14:52,610 You can sort of use the program to analyze it. 311 00:14:52,610 --> 00:14:55,220 And the same program will help you schedule. 312 00:14:55,220 --> 00:14:57,800 And then there's improved communications technology, 313 00:14:57,800 --> 00:15:01,650 which makes it easy to communicate instructions. 314 00:15:01,650 --> 00:15:04,760 Hey, depart a little later from this stop, 315 00:15:04,760 --> 00:15:07,100 or from this terminal. 316 00:15:07,100 --> 00:15:12,040 Don't, you know, start running without passengers. 317 00:15:12,040 --> 00:15:14,960 And start operating in revenue service three 318 00:15:14,960 --> 00:15:19,550 stops down because we have a long gap. 319 00:15:19,550 --> 00:15:24,834 So you may have heard, you can't really have control-- 320 00:15:24,834 --> 00:15:26,500 there are so many ways of saying things, 321 00:15:26,500 --> 00:15:28,330 but you can't really do something about something 322 00:15:28,330 --> 00:15:29,380 until you measure it. 323 00:15:29,380 --> 00:15:32,140 So measuring it is important. 324 00:15:32,140 --> 00:15:34,870 We'll talk a little bit about reliability 325 00:15:34,870 --> 00:15:36,247 as a performance metric. 326 00:15:36,247 --> 00:15:38,330 And there are different key performance indicators 327 00:15:38,330 --> 00:15:39,967 you can calculate for reliability, 328 00:15:39,967 --> 00:15:41,050 and that's the first step. 329 00:15:41,050 --> 00:15:42,508 You want to measure it and you want 330 00:15:42,508 --> 00:15:44,500 to be able to track your reliability 331 00:15:44,500 --> 00:15:46,360 for particular routes or system wide, 332 00:15:46,360 --> 00:15:50,240 and then be able to change a policy, see what the effect is. 333 00:15:50,240 --> 00:15:53,290 So one thing about it is it's not 334 00:15:53,290 --> 00:15:55,450 the only thing that matters. 335 00:15:55,450 --> 00:15:56,770 Reliability is important. 336 00:15:56,770 --> 00:15:59,050 It would be a mistake not to measure it. 337 00:15:59,050 --> 00:16:01,570 Because you might have a very productive service, 338 00:16:01,570 --> 00:16:05,980 but you might have all of these problems that we identified. 339 00:16:05,980 --> 00:16:09,820 On the other hand, if you put too much focus on reliability, 340 00:16:09,820 --> 00:16:12,340 then it would come at a cost. 341 00:16:12,340 --> 00:16:15,910 If you want to make your schedule very reliable, 342 00:16:15,910 --> 00:16:19,150 then you can add a lot of recovery time. 343 00:16:19,150 --> 00:16:20,752 And you could add many timing points 344 00:16:20,752 --> 00:16:22,210 and make the buses hold everywhere, 345 00:16:22,210 --> 00:16:24,550 and that would slow service down. 346 00:16:24,550 --> 00:16:27,130 It would increase journey times. 347 00:16:27,130 --> 00:16:28,900 Even if they would be very predictable, 348 00:16:28,900 --> 00:16:32,140 they would be very long, and that could deteriorate service. 349 00:16:34,830 --> 00:16:38,670 So we make a distinction between reliability on low frequency 350 00:16:38,670 --> 00:16:41,624 service and reliability on high frequency service. 351 00:16:41,624 --> 00:16:42,540 What's the difference? 352 00:16:42,540 --> 00:16:45,120 We've talked about the waiting strategies 353 00:16:45,120 --> 00:16:46,830 for low and high frequency. 354 00:16:52,519 --> 00:16:54,310 We've talked about it several times before. 355 00:16:54,310 --> 00:16:55,224 [CHUCKLES] 356 00:16:55,224 --> 00:16:57,640 What's the difference between a service that runs every 20 357 00:16:57,640 --> 00:17:02,200 minutes and a service that runs every five minutes with regards 358 00:17:02,200 --> 00:17:05,660 to your strategy to take that service? 359 00:17:05,660 --> 00:17:07,970 AUDIENCE: It's more frequent and you can just walk up. 360 00:17:07,970 --> 00:17:09,350 GABRIEL SANCHEZ-MARTINEZ: OK, so high frequency service 361 00:17:09,350 --> 00:17:10,141 is walk-up service. 362 00:17:10,141 --> 00:17:11,690 AUDIENCE: No random arrivals. 363 00:17:11,690 --> 00:17:11,940 GABRIEL SANCHEZ-MARTINEZ: Right. 364 00:17:11,940 --> 00:17:13,540 The arrivals tend to be random. 365 00:17:13,540 --> 00:17:18,430 They don't actually have to be for this distinction 366 00:17:18,430 --> 00:17:19,260 to be valid. 367 00:17:19,260 --> 00:17:22,329 They have to be independent of the vehicle arrivals. 368 00:17:22,329 --> 00:17:23,569 AUDIENCE: [INAUDIBLE] 369 00:17:23,569 --> 00:17:24,310 GABRIEL SANCHEZ-MARTINEZ: Yes. 370 00:17:24,310 --> 00:17:25,400 Yes, we'll mention that. 371 00:17:25,400 --> 00:17:28,960 So with low frequency service, most people 372 00:17:28,960 --> 00:17:33,520 will time their arrival at stops so that they 373 00:17:33,520 --> 00:17:35,260 are with the schedule. 374 00:17:35,260 --> 00:17:38,500 So if vehicles are arriving on schedule, 375 00:17:38,500 --> 00:17:40,170 and passengers are arriving on schedule, 376 00:17:40,170 --> 00:17:42,680 people wait very little time. 377 00:17:42,680 --> 00:17:44,980 And if there's very little variability in that, 378 00:17:44,980 --> 00:17:46,780 if service is incredibly punctual, 379 00:17:46,780 --> 00:17:50,950 people would show up the minute before and wait almost nothing. 380 00:17:50,950 --> 00:17:53,530 If there's some variability, then people 381 00:17:53,530 --> 00:17:55,720 have to add some reliability buffer time. 382 00:17:55,720 --> 00:18:00,760 So even though it says it's going to come at 3:53, 383 00:18:00,760 --> 00:18:03,160 you might have to get there at 3:50. 384 00:18:03,160 --> 00:18:04,630 OK. 385 00:18:04,630 --> 00:18:06,730 So you then can set-- 386 00:18:06,730 --> 00:18:10,730 because you want to measure reliability, people-- 387 00:18:10,730 --> 00:18:13,040 especially in the US, we call that on-time performance, 388 00:18:13,040 --> 00:18:17,200 which is a long way of saying punctuality. 389 00:18:17,200 --> 00:18:19,280 You could have different wait threshold windows. 390 00:18:19,280 --> 00:18:22,060 And we've talked about performance measurement before. 391 00:18:22,060 --> 00:18:24,940 We're just here, so we're going back to specifically 392 00:18:24,940 --> 00:18:25,780 reliability. 393 00:18:25,780 --> 00:18:28,270 One way would be to say, any bus that 394 00:18:28,270 --> 00:18:30,940 departs this stop between one minute early and five minutes 395 00:18:30,940 --> 00:18:32,120 late is on time. 396 00:18:32,120 --> 00:18:34,950 And any bus outside of that window is not on time. 397 00:18:34,950 --> 00:18:37,570 And then you say, I am 90% reliable. 398 00:18:37,570 --> 00:18:41,094 This bus leaves that stop 90% of the time within that window. 399 00:18:41,094 --> 00:18:42,760 And then you could have tighter windows. 400 00:18:42,760 --> 00:18:45,430 You could say, not early and up to three minutes late, 401 00:18:45,430 --> 00:18:47,980 or not early and up to one minute late. 402 00:18:47,980 --> 00:18:50,450 Of course what happens-- 403 00:18:50,450 --> 00:18:52,047 well, let's start with the first one. 404 00:18:52,047 --> 00:18:53,380 What's wrong with the first one? 405 00:18:56,720 --> 00:18:58,730 What's different about the first one? 406 00:18:58,730 --> 00:19:00,620 You allow early departures. 407 00:19:00,620 --> 00:19:02,750 What's bad about early departures when you 408 00:19:02,750 --> 00:19:05,200 have a long headway service? 409 00:19:05,200 --> 00:19:06,700 AUDIENCE: People aren't expecting it 410 00:19:06,700 --> 00:19:08,020 and they miss their bus. 411 00:19:08,020 --> 00:19:08,280 GABRIEL SANCHEZ-MARTINEZ: Right. 412 00:19:08,280 --> 00:19:10,850 So if people are really timing their arrival at the stops 413 00:19:10,850 --> 00:19:16,680 according to the schedule, and it's 20-minute headway service, 414 00:19:16,680 --> 00:19:17,710 bus leaves early. 415 00:19:17,710 --> 00:19:19,057 You arrived a minute early. 416 00:19:19,057 --> 00:19:20,390 Now you have to wait 20 minutes. 417 00:19:20,390 --> 00:19:21,960 It's really bad. 418 00:19:21,960 --> 00:19:22,760 Really bad. 419 00:19:22,760 --> 00:19:25,790 This thing is a little-- 420 00:19:25,790 --> 00:19:29,040 real-time apps help with this, but not everyone has one. 421 00:19:29,040 --> 00:19:32,450 And if service tends to be reliable, 422 00:19:32,450 --> 00:19:37,500 and every now and then it isn't, then people might still have-- 423 00:19:37,500 --> 00:19:40,580 they're trying to show up to work on time. 424 00:19:40,580 --> 00:19:43,370 So there's not much the app can do unless there's 425 00:19:43,370 --> 00:19:45,862 a good warning ahead of time, this bus 426 00:19:45,862 --> 00:19:46,820 is going to come early. 427 00:19:46,820 --> 00:19:48,580 You'd better be there. 428 00:19:48,580 --> 00:19:50,660 So you have to rush to get ready. 429 00:19:50,660 --> 00:19:53,030 OK. 430 00:19:53,030 --> 00:19:57,110 So it's good to not allow early departures. 431 00:19:57,110 --> 00:19:58,940 What happens when you move to tighter 432 00:19:58,940 --> 00:20:04,220 bounds on the late side? 433 00:20:04,220 --> 00:20:05,620 Two things happen. 434 00:20:05,620 --> 00:20:06,820 AUDIENCE: Harder to meet it. 435 00:20:06,820 --> 00:20:08,861 GABRIEL SANCHEZ-MARTINEZ: So it's harder to meet. 436 00:20:08,861 --> 00:20:11,320 And that means that your reported reliability 437 00:20:11,320 --> 00:20:12,860 comes down. 438 00:20:12,860 --> 00:20:15,490 So you can imagine, internally, a pressure on the agency 439 00:20:15,490 --> 00:20:18,160 to have a little more slack, to say that you 440 00:20:18,160 --> 00:20:19,930 have higher reliability. 441 00:20:19,930 --> 00:20:22,060 What happens in terms of performance, 442 00:20:22,060 --> 00:20:25,671 or in terms of waiting time, benefit for the passenger? 443 00:20:28,440 --> 00:20:35,710 If the agency actually has a holding policy that prevents 444 00:20:35,710 --> 00:20:37,374 a bus from departing late-- 445 00:20:37,374 --> 00:20:39,790 more than five minutes late, more than three minutes late, 446 00:20:39,790 --> 00:20:40,840 more than one minute late-- 447 00:20:40,840 --> 00:20:42,923 from a stop in the middle of the route with people 448 00:20:42,923 --> 00:20:45,460 inside of it, what happens is you move to tighter windows. 449 00:20:47,435 --> 00:20:48,810 AUDIENCE: The driver will be less 450 00:20:48,810 --> 00:20:52,161 lenient in holding the bus for people running after it? 451 00:20:52,161 --> 00:20:54,160 GABRIEL SANCHEZ-MARTINEZ: Especially if you're-- 452 00:20:54,160 --> 00:20:56,110 right, tighter window on the early side, more holding. 453 00:20:56,110 --> 00:20:57,440 AUDIENCE: Like, sorry, we've got to go. 454 00:20:57,440 --> 00:20:58,731 GABRIEL SANCHEZ-MARTINEZ: Yeah. 455 00:21:01,130 --> 00:21:04,800 So how do you make the bus not be late? 456 00:21:04,800 --> 00:21:07,011 What's the strategy for that? 457 00:21:07,011 --> 00:21:08,937 AUDIENCE: You schedule in more-- 458 00:21:08,937 --> 00:21:11,270 GABRIEL SANCHEZ-MARTINEZ: You don't schedule for median. 459 00:21:11,270 --> 00:21:14,090 You schedule for a higher percentile. 460 00:21:14,090 --> 00:21:15,570 So now it's easy, piece of cake. 461 00:21:15,570 --> 00:21:19,760 You schedule it for 80 percentile, only 20% 462 00:21:19,760 --> 00:21:21,770 of the time will you be-- 463 00:21:21,770 --> 00:21:22,880 OK, but what happens? 464 00:21:22,880 --> 00:21:25,910 That means that 80% of the time you're arriving early, 465 00:21:25,910 --> 00:21:27,220 so you have to hold. 466 00:21:27,220 --> 00:21:29,610 So as you make that window tighter, 467 00:21:29,610 --> 00:21:31,370 it means that you're probably going to be 468 00:21:31,370 --> 00:21:33,054 setting your percentile higher. 469 00:21:33,054 --> 00:21:34,970 And it means that you'll be holding more often 470 00:21:34,970 --> 00:21:36,110 and slowing service down. 471 00:21:36,110 --> 00:21:39,620 And holding is very frustrating for passengers. 472 00:21:39,620 --> 00:21:42,100 So you shouldn't hold always and for a long time. 473 00:21:47,840 --> 00:21:49,910 And in general, I guess one other comment is 474 00:21:49,910 --> 00:21:55,010 like any kind of window, especially on the later side, 475 00:21:55,010 --> 00:21:57,415 the benefits of going from five to three to one minutes 476 00:21:57,415 --> 00:21:59,290 are going to be marginal in terms of waiting. 477 00:21:59,290 --> 00:22:01,160 And they can be substantial in terms 478 00:22:01,160 --> 00:22:02,690 of how often you'll have to hold it 479 00:22:02,690 --> 00:22:04,297 and how slow the service will be. 480 00:22:04,297 --> 00:22:05,130 AUDIENCE: I'm sorry. 481 00:22:05,130 --> 00:22:07,830 Why is holding more often if you're-- 482 00:22:07,830 --> 00:22:10,720 GABRIEL SANCHEZ-MARTINEZ: If you have a tighter window. 483 00:22:10,720 --> 00:22:12,180 AUDIENCE: [INAUDIBLE] 484 00:22:12,180 --> 00:22:13,670 GABRIEL SANCHEZ-MARTINEZ: So if you have a tighter window-- 485 00:22:13,670 --> 00:22:16,280 if your vehicle must depart between zero minutes early 486 00:22:16,280 --> 00:22:19,010 and one minute late, it's a very tight window, right? 487 00:22:19,010 --> 00:22:22,370 So how can you guarantee that that vehicle departs 488 00:22:22,370 --> 00:22:23,580 that stop in the window? 489 00:22:26,610 --> 00:22:32,560 You have to schedule it such that it almost always arrives-- 490 00:22:36,080 --> 00:22:39,200 you have to allow a lot of time on the schedule 491 00:22:39,200 --> 00:22:42,620 so that almost always it can arrive, 492 00:22:42,620 --> 00:22:44,420 and it's not arriving one minute late. 493 00:22:44,420 --> 00:22:44,603 AUDIENCE: Ah, all right. 494 00:22:44,603 --> 00:22:45,230 [INAUDIBLE] time. 495 00:22:45,230 --> 00:22:45,730 So you're-- 496 00:22:45,730 --> 00:22:47,020 [INTERPOSING VOICES] 497 00:22:47,020 --> 00:22:49,270 GABRIEL SANCHEZ-MARTINEZ: So you control the late side 498 00:22:49,270 --> 00:22:51,020 by scheduling more time. 499 00:22:51,020 --> 00:22:53,660 And then what happens on the early side? 500 00:22:53,660 --> 00:22:55,610 On the early side, if you arrive early, you-- 501 00:22:55,610 --> 00:22:56,670 AUDIENCE: You just sit there. 502 00:22:56,670 --> 00:22:58,730 GABRIEL SANCHEZ-MARTINEZ: You have to sit there. 503 00:22:58,730 --> 00:22:59,330 OK. 504 00:22:59,330 --> 00:23:05,824 So in long headway service, or low frequency service, 505 00:23:05,824 --> 00:23:08,240 there is a little interaction between successive vehicles, 506 00:23:08,240 --> 00:23:12,359 so bunching is not a normal thing. 507 00:23:12,359 --> 00:23:14,900 So we'll talk about bunching in the context of high frequency 508 00:23:14,900 --> 00:23:16,280 service. 509 00:23:16,280 --> 00:23:19,100 And then, of course, real time information is changing this. 510 00:23:19,100 --> 00:23:21,060 So now you have an app. 511 00:23:21,060 --> 00:23:26,240 And your app, as you're doing your breakfast, phone vibrates 512 00:23:26,240 --> 00:23:27,840 and says, here's the time. 513 00:23:27,840 --> 00:23:29,100 Here's my predicted time. 514 00:23:29,100 --> 00:23:31,760 So you rush. 515 00:23:31,760 --> 00:23:34,710 Maybe you'll skip something on breakfast or you'll-- 516 00:23:34,710 --> 00:23:36,290 I don't know. 517 00:23:36,290 --> 00:23:38,840 So that is very poorly understood 518 00:23:38,840 --> 00:23:40,880 from a research standpoint. 519 00:23:40,880 --> 00:23:45,830 We don't really know how exactly that happens, 520 00:23:45,830 --> 00:23:51,770 what percentage of people are actually changing when they 521 00:23:51,770 --> 00:23:55,280 would arrive based on the app. 522 00:23:55,280 --> 00:23:57,740 And we don't really know what the implications are. 523 00:23:57,740 --> 00:24:00,470 Because you can't just say-- 524 00:24:00,470 --> 00:24:05,075 imagine if everybody had an app, and everybody used that app. 525 00:24:05,075 --> 00:24:07,640 And you're running 20-minute headway service. 526 00:24:07,640 --> 00:24:09,430 Now you say, well, everybody is going 527 00:24:09,430 --> 00:24:12,110 to show up to time the arrival at the stop. 528 00:24:12,110 --> 00:24:14,930 So let's not worry at all about reliability. 529 00:24:14,930 --> 00:24:17,870 It doesn't matter when vehicles come because people know 530 00:24:17,870 --> 00:24:19,880 and they time their arrivals. 531 00:24:19,880 --> 00:24:21,950 So now we can speed up service. 532 00:24:21,950 --> 00:24:25,640 But there is some sense of convenience of knowing 533 00:24:25,640 --> 00:24:27,920 that it runs every 20 minutes. 534 00:24:27,920 --> 00:24:32,240 The availability of service every 20 minutes 535 00:24:32,240 --> 00:24:36,050 is a factor that wouldn't be considered if you did that. 536 00:24:36,050 --> 00:24:39,380 So in some way, it is still important 537 00:24:39,380 --> 00:24:41,480 even if people can time their arrival at stops, 538 00:24:41,480 --> 00:24:46,380 to keep service as scheduled when it's long headway. 539 00:24:46,380 --> 00:24:47,420 And we don't really-- 540 00:24:47,420 --> 00:24:48,420 how do you measure that? 541 00:24:48,420 --> 00:24:52,490 How you quantify that convenience, that coverage? 542 00:24:52,490 --> 00:24:55,560 All questions for researchers. 543 00:24:55,560 --> 00:24:58,510 AUDIENCE: So is there-- 544 00:24:58,510 --> 00:25:03,950 for this time window, is there a defined threshold 545 00:25:03,950 --> 00:25:09,790 to define something that is a very tight time frame? 546 00:25:09,790 --> 00:25:14,480 Like median, long, and tight time frame for this? 547 00:25:14,480 --> 00:25:16,330 And when does it matter? 548 00:25:16,330 --> 00:25:19,590 Because obviously, tight is different in the mornings 549 00:25:19,590 --> 00:25:21,355 when you have [INAUDIBLE]. 550 00:25:25,006 --> 00:25:27,380 GABRIEL SANCHEZ-MARTINEZ: This is-- that decisions are up 551 00:25:27,380 --> 00:25:28,070 to the agency? 552 00:25:28,070 --> 00:25:29,070 AUDIENCE: It's up to the agency. 553 00:25:29,070 --> 00:25:29,630 GABRIEL SANCHEZ-MARTINEZ: Yeah. 554 00:25:29,630 --> 00:25:31,171 And usually there's a trade-off where 555 00:25:31,171 --> 00:25:33,850 you want to set a goal that is attainable. 556 00:25:33,850 --> 00:25:36,440 You don't want to be reporting 30% reliability. 557 00:25:36,440 --> 00:25:40,370 So it's a bar that moves according to the abilities 558 00:25:40,370 --> 00:25:42,750 of the agency, usually. 559 00:25:42,750 --> 00:25:45,027 That's what happens in practice. 560 00:25:45,027 --> 00:25:47,360 If there are no more questions on low frequency service, 561 00:25:47,360 --> 00:25:49,210 let's move to high frequency service. 562 00:25:49,210 --> 00:25:50,342 A little more interesting. 563 00:25:50,342 --> 00:25:51,300 Do you have a question? 564 00:25:51,300 --> 00:25:51,470 AUDIENCE: Yeah. 565 00:25:51,470 --> 00:25:53,060 What's the cut off there between high frequency 566 00:25:53,060 --> 00:25:53,990 and low frequency? 567 00:25:53,990 --> 00:25:55,656 GABRIEL SANCHEZ-MARTINEZ: Good question. 568 00:25:55,656 --> 00:25:56,570 So what do you think? 569 00:25:59,310 --> 00:26:01,220 [INTERPOSING VOICES] 570 00:26:01,220 --> 00:26:03,240 That is a good point. 571 00:26:03,240 --> 00:26:05,870 He said it depends which country you're in. 572 00:26:05,870 --> 00:26:09,240 That's a very legitimate observation. 573 00:26:09,240 --> 00:26:11,880 So it's not just US and non-US. 574 00:26:11,880 --> 00:26:12,380 It's-- 575 00:26:12,380 --> 00:26:14,392 [INTERPOSING VOICES] 576 00:26:14,392 --> 00:26:15,350 AUDIENCE: Urban, rural. 577 00:26:15,350 --> 00:26:16,520 GABRIEL SANCHEZ-MARTINEZ: Here in the US, 578 00:26:16,520 --> 00:26:18,530 here in Boston, what would you consider 579 00:26:18,530 --> 00:26:22,372 to be high frequency service? 580 00:26:22,372 --> 00:26:23,830 AUDIENCE: Up to 10-minute headways. 581 00:26:23,830 --> 00:26:24,290 GABRIEL SANCHEZ-MARTINEZ: 10 minutes? 582 00:26:24,290 --> 00:26:25,414 AUDIENCE: Up to 10 minutes. 583 00:26:25,414 --> 00:26:27,620 AUDIENCE: Yeah, certainly not more than that. 584 00:26:27,620 --> 00:26:28,420 GABRIEL SANCHEZ-MARTINEZ: If it's 12 minutes, 585 00:26:28,420 --> 00:26:29,675 do you look at the schedule? 586 00:26:29,675 --> 00:26:30,300 AUDIENCE: Yeah. 587 00:26:30,300 --> 00:26:30,883 AUDIENCE: Yes. 588 00:26:30,883 --> 00:26:33,020 GABRIEL SANCHEZ-MARTINEZ: OK. 589 00:26:33,020 --> 00:26:33,530 All right. 590 00:26:33,530 --> 00:26:35,780 AUDIENCE: [INAUDIBLE] divides it as 15 and [INAUDIBLE] 591 00:26:35,780 --> 00:26:36,900 going up to 16 and 17. 592 00:26:36,900 --> 00:26:42,410 GABRIEL SANCHEZ-MARTINEZ: So yeah, some agencies say 15. 593 00:26:42,410 --> 00:26:44,120 In London, I think it's 12. 594 00:26:44,120 --> 00:26:46,530 I think that's the cutoff. 595 00:26:46,530 --> 00:26:49,970 Now, if you go to Chile and you say 596 00:26:49,970 --> 00:26:51,530 that you're running 10 minute, they 597 00:26:51,530 --> 00:26:55,970 think of that as long headway service-- very long. 598 00:26:55,970 --> 00:26:58,230 Because they have buses that run every minute. 599 00:26:58,230 --> 00:27:03,500 So that's high frequency, and seven minutes is low frequency. 600 00:27:03,500 --> 00:27:06,500 So that's a distinction, at least 601 00:27:06,500 --> 00:27:09,110 from an operational standpoint, that people make differently 602 00:27:09,110 --> 00:27:09,870 in every country. 603 00:27:09,870 --> 00:27:13,260 But in terms of waiting time strategy, 604 00:27:13,260 --> 00:27:17,000 I think it still holds that it's somewhere between 10 and 15. 605 00:27:17,000 --> 00:27:18,770 Maybe between 8 and 15. 606 00:27:18,770 --> 00:27:20,000 We don't know. 607 00:27:20,000 --> 00:27:22,360 Obviously, there's a continuum. 608 00:27:22,360 --> 00:27:25,520 It's not like everybody switches at exactly some threshold. 609 00:27:25,520 --> 00:27:28,090 It depends on the person, and what technology they have, 610 00:27:28,090 --> 00:27:29,930 and what service they're taking. 611 00:27:29,930 --> 00:27:33,710 Between those 8 and 15 minutes, or even 12 minutes, 612 00:27:33,710 --> 00:27:36,890 there's going to be a transition from one strategy to the other. 613 00:27:36,890 --> 00:27:39,410 And you know that when you're well in the high frequency 614 00:27:39,410 --> 00:27:43,610 zone, your models of random, or at least independent, 615 00:27:43,610 --> 00:27:46,250 arrivals of passengers at stops hold. 616 00:27:46,250 --> 00:27:51,530 Whereas as you move towards 15 and longer, they stop holding 617 00:27:51,530 --> 00:27:53,780 and you shouldn't be measuring waiting time like this. 618 00:27:53,780 --> 00:27:55,070 AUDIENCE: I was asking that because, even 619 00:27:55,070 --> 00:27:57,260 with 10 minutes, which is considered high frequency, 620 00:27:57,260 --> 00:28:00,546 I still want to schedule myself for when I'm 621 00:28:00,546 --> 00:28:01,755 going to get to the bus stop. 622 00:28:01,755 --> 00:28:04,045 I'm not just like, oh, let me just walk to the bus stop 623 00:28:04,045 --> 00:28:04,900 and I'll wait. 624 00:28:04,900 --> 00:28:06,358 GABRIEL SANCHEZ-MARTINEZ: So for 10 625 00:28:06,358 --> 00:28:08,970 minutes, do you actually consult the schedule? 626 00:28:08,970 --> 00:28:12,230 AUDIENCE: Well, I consult the app for 10 minutes. 627 00:28:12,230 --> 00:28:13,730 GABRIEL SANCHEZ-MARTINEZ: But do you 628 00:28:13,730 --> 00:28:16,940 plan to take the 9:10 train? 629 00:28:16,940 --> 00:28:21,560 Or-- you see, there's a distinction, like the day 630 00:28:21,560 --> 00:28:23,510 before, you know I'm going to take the 9:10 631 00:28:23,510 --> 00:28:25,300 AUDIENCE: If they were running clock-based, consistent 632 00:28:25,300 --> 00:28:25,900 10-minute headways, then I would. 633 00:28:25,900 --> 00:28:26,980 GABRIEL SANCHEZ-MARTINEZ: Then you would show up. 634 00:28:26,980 --> 00:28:27,210 AUDIENCE: Yeah. 635 00:28:27,210 --> 00:28:27,410 Yeah. 636 00:28:27,410 --> 00:28:28,099 But they're not. 637 00:28:28,099 --> 00:28:29,640 GABRIEL SANCHEZ-MARTINEZ: So for you, 638 00:28:29,640 --> 00:28:34,220 10 is right there on the fence between the two, it seems. 639 00:28:34,220 --> 00:28:37,340 More on the scheduled side, on the high frequency side, 640 00:28:37,340 --> 00:28:38,210 perhaps. 641 00:28:38,210 --> 00:28:38,900 AUDIENCE: Yeah. 642 00:28:38,900 --> 00:28:40,108 GABRIEL SANCHEZ-MARTINEZ: OK. 643 00:28:42,130 --> 00:28:44,030 But let's say that it's five minutes. 644 00:28:44,030 --> 00:28:46,940 So now we're clear on that vague area. 645 00:28:46,940 --> 00:28:50,820 So now you're in a zone where most people will 646 00:28:50,820 --> 00:28:53,202 time their arrivals at stops-- sorry, will not 647 00:28:53,202 --> 00:28:54,410 time their arrivals at stops. 648 00:28:54,410 --> 00:28:56,240 They will show up when convenient. 649 00:28:56,240 --> 00:28:58,929 And they expect to wait about half of the headway. 650 00:28:58,929 --> 00:29:00,720 You know that if the headways are variable, 651 00:29:00,720 --> 00:29:03,200 you're going to have that waiting time increasing. 652 00:29:03,200 --> 00:29:05,930 So there's going to be a reliability buffer time 653 00:29:05,930 --> 00:29:07,555 calculation that you can do. 654 00:29:07,555 --> 00:29:10,850 And it's going to be the coefficient variation 655 00:29:10,850 --> 00:29:13,500 of headway, will sort of affect. 656 00:29:13,500 --> 00:29:17,190 That's the factor that sort of increases the expected waiting 657 00:29:17,190 --> 00:29:17,690 time. 658 00:29:20,750 --> 00:29:23,390 Punctuality is not as critical for the passengers. 659 00:29:23,390 --> 00:29:25,710 They don't really care if every train 660 00:29:25,710 --> 00:29:27,966 is five minutes late, as long as they 661 00:29:27,966 --> 00:29:29,090 come in every five minutes. 662 00:29:29,090 --> 00:29:32,360 It doesn't really matter that they're all five minutes late. 663 00:29:32,360 --> 00:29:34,250 So really, what matters for a passenger 664 00:29:34,250 --> 00:29:36,560 is bunching and long gaps. 665 00:29:36,560 --> 00:29:38,720 We've talked about that before. 666 00:29:38,720 --> 00:29:41,720 We know that in high frequency service, 667 00:29:41,720 --> 00:29:45,740 there is a lot of vehicle interaction. 668 00:29:45,740 --> 00:29:47,720 We can maybe review it quickly. 669 00:29:54,140 --> 00:29:56,860 Think of this as a bus route. 670 00:29:56,860 --> 00:29:58,430 And here's a vehicle. 671 00:30:01,760 --> 00:30:04,960 Each of these are vehicles. 672 00:30:04,960 --> 00:30:07,480 And there's a random arrival process. 673 00:30:07,480 --> 00:30:10,950 Passengers are arriving randomly at the different stops. 674 00:30:10,950 --> 00:30:16,330 So what happens when vehicles are not evenly spaced in time, 675 00:30:16,330 --> 00:30:17,840 not in space. 676 00:30:17,840 --> 00:30:20,990 So what happens when they're not evenly spaced? 677 00:30:20,990 --> 00:30:23,810 AUDIENCE: The one that's close to the next one picks up less? 678 00:30:23,810 --> 00:30:27,550 GABRIEL SANCHEZ-MARTINEZ: OK, so this vehicle 679 00:30:27,550 --> 00:30:31,760 has a smaller gap ahead of it. 680 00:30:31,760 --> 00:30:33,800 And therefore, because people are arriving 681 00:30:33,800 --> 00:30:37,520 at some rate, in that time, for that rate, 682 00:30:37,520 --> 00:30:40,370 fewer passengers will be taking this bus. 683 00:30:40,370 --> 00:30:42,910 And that means that real times are shorter. 684 00:30:42,910 --> 00:30:44,490 Vehicle catches up. 685 00:30:44,490 --> 00:30:45,920 So now you have a bunch. 686 00:30:45,920 --> 00:30:49,340 Eventually this vehicle will catch up to this one. 687 00:30:49,340 --> 00:30:52,790 If this vehicle, the one ahead of it, 688 00:30:52,790 --> 00:30:56,150 has a long headway ahead of it, the opposite happens. 689 00:30:56,150 --> 00:30:59,480 More people than average arrive, and then that vehicle 690 00:30:59,480 --> 00:31:00,970 has many more people in it. 691 00:31:00,970 --> 00:31:02,340 The loads increase. 692 00:31:02,340 --> 00:31:03,420 It slows down. 693 00:31:03,420 --> 00:31:06,395 So those two effects work together to create bunching. 694 00:31:06,395 --> 00:31:07,700 And we've talked about that. 695 00:31:07,700 --> 00:31:11,375 And with bunching, the counterpart is long gaps. 696 00:31:11,375 --> 00:31:13,250 You usually have a bunch and then a long gap. 697 00:31:13,250 --> 00:31:16,110 Or a long gap preceding a bunch. 698 00:31:16,110 --> 00:31:19,130 So you'll hear passengers complaining, 699 00:31:19,130 --> 00:31:23,190 I've been waiting 15 minutes, and now three buses arrive, 700 00:31:23,190 --> 00:31:24,320 as if that were ironic. 701 00:31:24,320 --> 00:31:29,231 But that's actually exactly why it happens. 702 00:31:29,231 --> 00:31:31,730 AUDIENCE: So what's the best strategy to deal with bunching? 703 00:31:31,730 --> 00:31:34,063 GABRIEL SANCHEZ-MARTINEZ: We'll talk about many of them. 704 00:31:34,063 --> 00:31:35,180 Yeah. 705 00:31:35,180 --> 00:31:38,900 OK, so one observation is that some high frequency 706 00:31:38,900 --> 00:31:40,520 routes have branches. 707 00:31:40,520 --> 00:31:42,950 So they're only high frequency in the trunk, 708 00:31:42,950 --> 00:31:46,760 and the individual branches are actually long headway. 709 00:31:46,760 --> 00:31:52,120 And there, you have to run scheduled service 710 00:31:52,120 --> 00:31:52,930 on the branches. 711 00:31:52,930 --> 00:31:54,790 And then you have to, I guess, try 712 00:31:54,790 --> 00:31:57,160 to run scheduled service on the trunk. 713 00:31:57,160 --> 00:31:58,870 There might be some hybrid strategies, 714 00:31:58,870 --> 00:32:01,750 but that's still the subject of research. 715 00:32:01,750 --> 00:32:04,030 And of course, schedule control is much easier 716 00:32:04,030 --> 00:32:06,040 than headway control. 717 00:32:06,040 --> 00:32:07,584 You can do it without technology. 718 00:32:07,584 --> 00:32:09,250 You can print a schedule, and the driver 719 00:32:09,250 --> 00:32:11,630 can have the schedule in the vehicle. 720 00:32:11,630 --> 00:32:13,590 And you can tell drivers, don't leave early. 721 00:32:13,590 --> 00:32:17,390 And if they follow instructions, they won't leave early. 722 00:32:17,390 --> 00:32:19,580 So if you want to control headways, 723 00:32:19,580 --> 00:32:22,200 and you want to keep the vehicles evenly spaced, 724 00:32:22,200 --> 00:32:24,460 now you need all this technology infrastructure 725 00:32:24,460 --> 00:32:27,580 to detect where vehicles are, to predict the running 726 00:32:27,580 --> 00:32:33,160 times between them, and to communicate instructions 727 00:32:33,160 --> 00:32:38,060 to those vehicles so that the headways can be adjusted. 728 00:32:38,060 --> 00:32:39,920 Here's a little reliability buffer time. 729 00:32:39,920 --> 00:32:44,350 So let's talk about how to actually calculate it 730 00:32:44,350 --> 00:32:47,240 in a high frequency, closed fare system. 731 00:32:47,240 --> 00:32:49,540 So think of the London Tube. 732 00:32:49,540 --> 00:32:54,010 You tap in the station, and then you tap out when you leave. 733 00:32:54,010 --> 00:32:59,170 So you can measure the probability distribution 734 00:32:59,170 --> 00:33:02,320 of travel time, or of journey time, from tap-in time 735 00:33:02,320 --> 00:33:04,270 to tap-out time. 736 00:33:04,270 --> 00:33:07,870 And we define the reliability buffer time 737 00:33:07,870 --> 00:33:10,405 as the difference between the 95th percentile 738 00:33:10,405 --> 00:33:13,180 and the 50th percentile of that journey time. 739 00:33:13,180 --> 00:33:17,530 So again, if this distribution were much narrower, 740 00:33:17,530 --> 00:33:23,140 then people would not have to budget that difference as they 741 00:33:23,140 --> 00:33:27,220 plan to make a trip, to arrive at a certain time at work 742 00:33:27,220 --> 00:33:27,720 or school. 743 00:33:32,922 --> 00:33:34,380 Something interesting about this is 744 00:33:34,380 --> 00:33:38,640 that London has somewhat recently started 745 00:33:38,640 --> 00:33:43,350 refunding fares if people's journeys exceed 746 00:33:43,350 --> 00:33:45,990 30 minutes of the expected. 747 00:33:45,990 --> 00:33:50,550 So they're not doing it by percentile, but they-- 748 00:33:50,550 --> 00:33:52,860 so here's an application in fare policy, 749 00:33:52,860 --> 00:33:55,770 which is not the most obvious one. 750 00:33:55,770 --> 00:33:58,370 But you can certainly measure this reliability 751 00:33:58,370 --> 00:33:59,160 of buffer time. 752 00:33:59,160 --> 00:34:00,040 Yes, question. 753 00:34:00,040 --> 00:34:01,400 AUDIENCE: Do you know how much it costs them? 754 00:34:01,400 --> 00:34:02,608 GABRIEL SANCHEZ-MARTINEZ: No. 755 00:34:04,160 --> 00:34:05,330 I don't think much. 756 00:34:05,330 --> 00:34:07,170 Well, it is a lot in total. 757 00:34:07,170 --> 00:34:08,239 AUDIENCE: [INAUDIBLE] 758 00:34:08,239 --> 00:34:09,989 GABRIEL SANCHEZ-MARTINEZ: I don't remember 759 00:34:09,989 --> 00:34:11,150 what percent of passengers. 760 00:34:11,150 --> 00:34:12,560 I think the percent is quite low, 761 00:34:12,560 --> 00:34:16,820 except if there's a big disruption it might be high. 762 00:34:16,820 --> 00:34:19,100 But because of the sheer size of the network, 763 00:34:19,100 --> 00:34:20,659 I'm sure that that adds up, too. 764 00:34:20,659 --> 00:34:21,159 Yeah. 765 00:34:21,159 --> 00:34:23,449 AUDIENCE: It's a good marketing strategy. 766 00:34:23,449 --> 00:34:24,100 GABRIEL SANCHEZ-MARTINEZ: Yeah. 767 00:34:24,100 --> 00:34:25,050 AUDIENCE: Builds confidence. 768 00:34:25,050 --> 00:34:26,300 GABRIEL SANCHEZ-MARTINEZ: London, they 769 00:34:26,300 --> 00:34:27,550 don't talk so much passengers. 770 00:34:27,550 --> 00:34:28,940 They talk about their customers. 771 00:34:28,940 --> 00:34:31,770 And they want to have customer service. 772 00:34:31,770 --> 00:34:36,897 And so they like to have that internal mentality. 773 00:34:36,897 --> 00:34:39,230 AUDIENCE: Well, how do they know someone wasn't dwelling 774 00:34:39,230 --> 00:34:41,540 at a station as a passenger? 775 00:34:41,540 --> 00:34:43,340 GABRIEL SANCHEZ-MARTINEZ: Because they 776 00:34:43,340 --> 00:34:47,690 can look at other people doing that same trip. 777 00:34:47,690 --> 00:34:49,969 So if somebody wants to hang out, 778 00:34:49,969 --> 00:34:51,469 they're not going to get a free trip 779 00:34:51,469 --> 00:34:52,835 just because they wanted to. 780 00:34:52,835 --> 00:34:53,960 AUDIENCE: It's interesting. 781 00:34:53,960 --> 00:34:56,000 In the daily metro, to prevent crowding, 782 00:34:56,000 --> 00:34:57,710 if you spend too much time in the system, 783 00:34:57,710 --> 00:35:00,694 they actually give you a penalty when you tap out. 784 00:35:00,694 --> 00:35:02,360 And so some of the journeys are so long, 785 00:35:02,360 --> 00:35:03,680 people actually have to rush to get out, 786 00:35:03,680 --> 00:35:05,120 or else they suffer a [INAUDIBLE].. 787 00:35:05,120 --> 00:35:07,286 GABRIEL SANCHEZ-MARTINEZ: Not very good reliability. 788 00:35:07,286 --> 00:35:09,730 We can add that to the list. 789 00:35:09,730 --> 00:35:10,290 Yeah. 790 00:35:10,290 --> 00:35:13,730 AUDIENCE: How do they determine the expected journey time? 791 00:35:13,730 --> 00:35:14,495 Is it median-- 792 00:35:14,495 --> 00:35:16,370 GABRIEL SANCHEZ-MARTINEZ: They look at this-- 793 00:35:16,370 --> 00:35:18,160 so they measure this. 794 00:35:18,160 --> 00:35:19,790 And I'll show you the next slide. 795 00:35:19,790 --> 00:35:21,290 Before we move on to the next slide, 796 00:35:21,290 --> 00:35:24,110 any other questions on this one? 797 00:35:24,110 --> 00:35:26,270 I saw several hands raised. 798 00:35:26,270 --> 00:35:26,910 OK. 799 00:35:26,910 --> 00:35:30,440 So they look at good days and bad days, 800 00:35:30,440 --> 00:35:31,670 to answer your question. 801 00:35:31,670 --> 00:35:34,910 So they pick some baseline of days 802 00:35:34,910 --> 00:35:38,540 that have no major disruptions, service is running well. 803 00:35:41,190 --> 00:35:43,360 It's the amount that they expect. 804 00:35:43,360 --> 00:35:45,650 And then they'll measure reliability buffer time 805 00:35:45,650 --> 00:35:47,300 on those days. 806 00:35:47,300 --> 00:35:49,730 So that is an amount that they say 807 00:35:49,730 --> 00:35:53,660 is sort of inherent to the operation 808 00:35:53,660 --> 00:35:56,660 and not much under their control, unless they invest 809 00:35:56,660 --> 00:36:01,220 in better signaling systems or things like this. 810 00:36:01,220 --> 00:36:04,550 Anything in excess of that, if you look at, 811 00:36:04,550 --> 00:36:08,330 now, all days together, will be something 812 00:36:08,330 --> 00:36:10,320 that they could have avoided. 813 00:36:10,320 --> 00:36:11,400 That's the idea. 814 00:36:11,400 --> 00:36:15,170 This distinction between the baseline buffer time 815 00:36:15,170 --> 00:36:17,060 and the access buffer time. 816 00:36:17,060 --> 00:36:21,290 So if that x as buffer time exceeds some amount, 817 00:36:21,290 --> 00:36:25,940 you can then say, well, we have a problem. 818 00:36:25,940 --> 00:36:30,060 Passengers were taking much longer than we scheduled for, 819 00:36:30,060 --> 00:36:32,830 or that we thought they could take, and therefore 820 00:36:32,830 --> 00:36:36,870 let's refund the fare, because it was bad service. 821 00:36:36,870 --> 00:36:39,323 AUDIENCE: This is for [INAUDIBLE] on the Victoria 822 00:36:39,323 --> 00:36:39,823 Line? 823 00:36:42,900 --> 00:36:44,150 GABRIEL SANCHEZ-MARTINEZ: Yes. 824 00:36:44,150 --> 00:36:44,660 Northbound? 825 00:36:44,660 --> 00:36:45,527 You mean this graph? 826 00:36:45,527 --> 00:36:46,110 AUDIENCE: Mhm. 827 00:36:46,110 --> 00:36:46,220 GABRIEL SANCHEZ-MARTINEZ: Yeah. 828 00:36:46,220 --> 00:36:47,553 So northbound, southbound, yeah. 829 00:36:52,720 --> 00:36:54,380 And the reference is right here. 830 00:36:54,380 --> 00:36:57,580 David Uniman, 2009, so you can check it out in the library 831 00:36:57,580 --> 00:36:59,170 if you're interested. 832 00:36:59,170 --> 00:37:02,530 OK, so what happens when it's low frequency. 833 00:37:02,530 --> 00:37:06,720 Now people are not arriving necessarily 834 00:37:06,720 --> 00:37:08,102 to randomly or independent now. 835 00:37:08,102 --> 00:37:10,060 They might actually be scheduling their arrival 836 00:37:10,060 --> 00:37:11,830 to meet a particular train. 837 00:37:11,830 --> 00:37:14,800 But of course, trains may not be running on schedule. 838 00:37:14,800 --> 00:37:17,470 So you have this space-time diagram here. 839 00:37:17,470 --> 00:37:20,980 We have time on the horizontal and space, or the stations, 840 00:37:20,980 --> 00:37:22,330 on the vertical. 841 00:37:22,330 --> 00:37:25,690 And you see that there is some degree 842 00:37:25,690 --> 00:37:27,710 of variability in timing. 843 00:37:27,710 --> 00:37:30,520 And if these vehicles were on time, maybe 844 00:37:30,520 --> 00:37:32,300 they would be more evenly spaced. 845 00:37:32,300 --> 00:37:34,810 So we have taps. 846 00:37:34,810 --> 00:37:38,290 Here, there's a touch in at 8:00. 847 00:37:38,290 --> 00:37:40,810 And so what we do is that we look at what's the next train? 848 00:37:45,090 --> 00:37:51,170 When does that tap in aboard, and that's 849 00:37:51,170 --> 00:37:52,730 how much they waited. 850 00:37:52,730 --> 00:37:56,190 You're comparing to scheduled departure, 851 00:37:56,190 --> 00:37:58,270 which is in this case 8:06. 852 00:37:58,270 --> 00:38:04,760 So because the train-- 853 00:38:04,760 --> 00:38:07,280 I don't know if I'm explaining this clearly. 854 00:38:07,280 --> 00:38:13,120 So you can match the tap-in time to the closest 855 00:38:13,120 --> 00:38:17,440 scheduled departure that follows that tap in. 856 00:38:17,440 --> 00:38:21,160 And that's the train that the person intends to board. 857 00:38:21,160 --> 00:38:23,590 And that's how much the person intends-- 858 00:38:23,590 --> 00:38:26,470 the difference between those two times is the amount of time 859 00:38:26,470 --> 00:38:29,260 that the person intends to wait or expects to wait. 860 00:38:29,260 --> 00:38:32,450 Any waiting time beyond that is excess waiting time. 861 00:38:35,470 --> 00:38:39,910 And then you're going to do the same for the in-vehicle time. 862 00:38:39,910 --> 00:38:43,690 That's where [INAUDIBLE] and that's 863 00:38:43,690 --> 00:38:45,940 how you get reliability buffer time. 864 00:38:45,940 --> 00:38:53,650 So you're now considering the waiting strategy is different. 865 00:38:53,650 --> 00:38:55,320 And here's the reference. 866 00:38:55,320 --> 00:38:58,340 2010, another thesis. 867 00:38:58,340 --> 00:39:00,150 For bus, there's another challenge. 868 00:39:03,420 --> 00:39:04,750 Well, there's two challenges. 869 00:39:04,750 --> 00:39:06,540 The first one is we need to distinguish 870 00:39:06,540 --> 00:39:10,050 between the performance of the contractor, 871 00:39:10,050 --> 00:39:13,970 if it's a private operator and you're paying the bus 872 00:39:13,970 --> 00:39:16,450 company to run service for you, and the performance 873 00:39:16,450 --> 00:39:17,990 as the passenger sees it. 874 00:39:17,990 --> 00:39:21,780 So as it says on the bottom, if service is unreliable, 875 00:39:21,780 --> 00:39:24,930 the passenger doesn't care why it's unreliable. 876 00:39:24,930 --> 00:39:27,930 But the operator needs to know if it's 877 00:39:27,930 --> 00:39:30,630 the fault of the operator or if it 878 00:39:30,630 --> 00:39:32,790 was an external reason that was not 879 00:39:32,790 --> 00:39:34,560 under the control of the operator. 880 00:39:34,560 --> 00:39:36,090 Why? 881 00:39:36,090 --> 00:39:38,276 Why is that important? 882 00:39:41,608 --> 00:39:44,470 Henry. 883 00:39:44,470 --> 00:39:49,450 AUDIENCE: If there is traffic, then there could likely 884 00:39:49,450 --> 00:39:52,780 be traffic downstream, as well. 885 00:39:52,780 --> 00:39:56,785 And you would continue to be on the line 886 00:39:56,785 --> 00:39:58,120 for the remainder of the trip. 887 00:39:58,120 --> 00:39:58,530 GABRIEL SANCHEZ-MARTINEZ: OK. 888 00:39:58,530 --> 00:40:00,540 But you're thinking of a specific trip. 889 00:40:00,540 --> 00:40:03,150 Because I'm thinking more generally. 890 00:40:03,150 --> 00:40:06,260 So why would the agency want to distinguish 891 00:40:06,260 --> 00:40:13,140 between bad performance that can be assigned or blamed 892 00:40:13,140 --> 00:40:18,090 on the operator versus bad performance that is exogenous. 893 00:40:18,090 --> 00:40:19,590 AUDIENCE: Because if the bad service 894 00:40:19,590 --> 00:40:22,740 is due to some act of God, then the agency maybe 895 00:40:22,740 --> 00:40:25,640 can't hold the contractor accountable. 896 00:40:25,640 --> 00:40:28,830 But if the contract and service provider did something wrong, 897 00:40:28,830 --> 00:40:31,344 then there can be some kind of punishment. 898 00:40:31,344 --> 00:40:32,760 GABRIEL SANCHEZ-MARTINEZ: OK, yes. 899 00:40:32,760 --> 00:40:36,510 And in this case, a punishment under the contract 900 00:40:36,510 --> 00:40:38,430 might be a penalty. 901 00:40:38,430 --> 00:40:41,760 So they might withhold some-- if there's a performance bonus, 902 00:40:41,760 --> 00:40:44,175 maybe the operator does not get that bonus 903 00:40:44,175 --> 00:40:47,511 when there might be actually provisions for a penalty. 904 00:40:47,511 --> 00:40:51,010 Or a discount on the payment. 905 00:40:51,010 --> 00:40:53,850 And it doesn't have to be an act of God. 906 00:40:53,850 --> 00:40:58,620 It can be normal traffic. 907 00:40:58,620 --> 00:41:04,530 And the variability in travel times 908 00:41:04,530 --> 00:41:06,900 that is expected because of traffic 909 00:41:06,900 --> 00:41:09,630 that is not under the control of the operator. 910 00:41:09,630 --> 00:41:14,910 But what if the operator is not maintaining his buses 911 00:41:14,910 --> 00:41:17,060 and some vehicles have to be put out of service? 912 00:41:17,060 --> 00:41:21,010 So the operator drops trips and now performance is not as good. 913 00:41:21,010 --> 00:41:24,330 That is very clearly the fault of the operator, 914 00:41:24,330 --> 00:41:27,570 and you want to penalize the operator. 915 00:41:27,570 --> 00:41:29,830 So that's one challenge. 916 00:41:29,830 --> 00:41:31,350 So you have to measure reliability, 917 00:41:31,350 --> 00:41:34,050 but you might have to assign its sources. 918 00:41:34,050 --> 00:41:36,690 You might have to calculate the sources of those 919 00:41:36,690 --> 00:41:41,260 and sort of assign cost codes to whatever you measure. 920 00:41:41,260 --> 00:41:42,930 And there might be a mix. 921 00:41:42,930 --> 00:41:47,370 The other challenge is that typically, buses are only 922 00:41:47,370 --> 00:41:49,230 tap on and not tap off. 923 00:41:49,230 --> 00:41:51,280 So you have to-- 924 00:41:51,280 --> 00:41:54,090 journey time includes the in-vehicle portion. 925 00:41:54,090 --> 00:41:55,800 So now you have to figure out where 926 00:41:55,800 --> 00:41:58,830 this person alights to figure out the in-vehicle component. 927 00:41:58,830 --> 00:42:01,530 And waiting time is another portion of this, 928 00:42:01,530 --> 00:42:04,290 and the passenger doesn't tap in until they 929 00:42:04,290 --> 00:42:05,540 have finished waiting. 930 00:42:05,540 --> 00:42:08,160 So you have to go back and calculate, how long did they 931 00:42:08,160 --> 00:42:08,910 wait? 932 00:42:08,910 --> 00:42:12,300 So those are two minor challenges. 933 00:42:12,300 --> 00:42:13,530 Here's a strategy. 934 00:42:13,530 --> 00:42:16,170 For destinations, we have ODX. 935 00:42:16,170 --> 00:42:18,790 So we can look at their next tap in. 936 00:42:18,790 --> 00:42:21,610 We can do trip chaining, as we discussed previously, 937 00:42:21,610 --> 00:42:24,810 and infer the destination for that person. 938 00:42:24,810 --> 00:42:26,610 And for some people that will fail, 939 00:42:26,610 --> 00:42:28,890 but we can scale up in probability. 940 00:42:28,890 --> 00:42:32,970 We can say, well, if this person didn't have a next tap, 941 00:42:32,970 --> 00:42:35,080 let's look at the distribution of passengers 942 00:42:35,080 --> 00:42:36,720 who do have an next tap and let's 943 00:42:36,720 --> 00:42:40,920 assume that these other people have destinations 944 00:42:40,920 --> 00:42:42,800 that are in proportion-- 945 00:42:42,800 --> 00:42:44,820 distributed in the same way as people 946 00:42:44,820 --> 00:42:46,650 who have destinations inferred. 947 00:42:46,650 --> 00:42:49,710 And then from AVL, we can sort of do the same trick 948 00:42:49,710 --> 00:42:51,690 that we did for rail. 949 00:42:51,690 --> 00:42:56,940 We can assume that there is some process by which passengers 950 00:42:56,940 --> 00:42:58,810 arrive at stops. 951 00:42:58,810 --> 00:43:00,600 So if it's high-frequency bus service, 952 00:43:00,600 --> 00:43:03,870 we say it's some arrival rate. 953 00:43:03,870 --> 00:43:05,400 If it's low frequency service, we 954 00:43:05,400 --> 00:43:11,940 say they arrive on time to match the schedule. 955 00:43:11,940 --> 00:43:15,147 And then we can compare that with actual vehicle times. 956 00:43:15,147 --> 00:43:16,730 So if we have an assumption about when 957 00:43:16,730 --> 00:43:20,580 the passenger arrived, then we can calculate the difference 958 00:43:20,580 --> 00:43:23,100 and measure the waiting time. 959 00:43:23,100 --> 00:43:24,660 So it's more stochastic because we 960 00:43:24,660 --> 00:43:26,940 don't know exactly when this person arrived. 961 00:43:26,940 --> 00:43:29,730 But in probability, you know that in aggregate, 962 00:43:29,730 --> 00:43:33,300 across all passengers, any one person arrived 963 00:43:33,300 --> 00:43:35,430 between this bus and that bus. 964 00:43:35,430 --> 00:43:37,470 So yeah. 965 00:43:37,470 --> 00:43:43,250 Questions about this process for measuring journey time 966 00:43:43,250 --> 00:43:44,327 reliability? 967 00:43:48,620 --> 00:43:49,752 Comments? 968 00:43:49,752 --> 00:43:51,960 AUDIENCE: One man complained about waiting time, it's 969 00:43:51,960 --> 00:43:53,005 like with the bus. 970 00:43:53,005 --> 00:43:54,040 Like, oh, with the scheduled bus, 971 00:43:54,040 --> 00:43:56,130 if the person only waits one minute, that's great. 972 00:43:56,130 --> 00:43:59,730 But if I'm waiting at my desk for eight minutes, 973 00:43:59,730 --> 00:44:01,030 I actually was-- 974 00:44:01,030 --> 00:44:02,530 GABRIEL SANCHEZ-MARTINEZ: So that it 975 00:44:02,530 --> 00:44:04,850 goes back to the discussion about apps 976 00:44:04,850 --> 00:44:06,880 that we had just a few minutes ago, 977 00:44:06,880 --> 00:44:10,890 that you can't just say that because there are apps, 978 00:44:10,890 --> 00:44:13,720 then we can just run service unreliably 979 00:44:13,720 --> 00:44:15,030 if it's long headway. 980 00:44:15,030 --> 00:44:16,114 AUDIENCE: Yeah. 981 00:44:16,114 --> 00:44:18,280 GABRIEL SANCHEZ-MARTINEZ: So if it's high frequency, 982 00:44:18,280 --> 00:44:20,070 you probably won't care. 983 00:44:20,070 --> 00:44:22,130 You'll just still go. 984 00:44:22,130 --> 00:44:25,230 Or you'll be timing it, but you would have arrived randomly, 985 00:44:25,230 --> 00:44:27,870 anyway, to some extent, i.e. your intention 986 00:44:27,870 --> 00:44:31,080 to begin the trip is random, or at least independent 987 00:44:31,080 --> 00:44:33,730 of the schedule. 988 00:44:33,730 --> 00:44:37,110 But if it's long headway service, then yes, 989 00:44:37,110 --> 00:44:41,520 you maybe stay at your desk or get a cup of coffee. 990 00:44:41,520 --> 00:44:43,260 But you're still inconvenienced. 991 00:44:43,260 --> 00:44:44,720 And so there's a penalty for it. 992 00:44:44,720 --> 00:44:45,060 AUDIENCE: Right. 993 00:44:45,060 --> 00:44:45,990 GABRIEL SANCHEZ-MARTINEZ: And we need to figure out 994 00:44:45,990 --> 00:44:46,740 how to measure it. 995 00:44:46,740 --> 00:44:49,560 And one way is to assume that people still arrive, 996 00:44:49,560 --> 00:44:53,099 or want to arrive, on time. 997 00:44:53,099 --> 00:44:55,390 And that's what we've been doing because that's what we 998 00:44:55,390 --> 00:44:57,460 used to do, and kind of works. 999 00:44:57,460 --> 00:45:01,117 But it's slightly different. 1000 00:45:01,117 --> 00:45:03,200 AUDIENCE: So how do you use the stochastic process 1001 00:45:03,200 --> 00:45:05,070 to estimate wait time? 1002 00:45:05,070 --> 00:45:06,361 GABRIEL SANCHEZ-MARTINEZ: Yeah. 1003 00:45:06,361 --> 00:45:16,260 So let's-- another timeline. 1004 00:45:16,260 --> 00:45:20,300 So in this case it's a timeline, not a space line. 1005 00:45:20,300 --> 00:45:32,140 So let's say that there's a tap at that time. 1006 00:45:32,140 --> 00:45:39,270 And the buses are arriving here, here, here. 1007 00:45:39,270 --> 00:45:39,770 Sorry. 1008 00:45:39,770 --> 00:45:43,460 Well, the tap has to be when the bus arrives, 1009 00:45:43,460 --> 00:45:44,510 or very close to it. 1010 00:45:44,510 --> 00:45:47,780 Because the person is tapping in at the bus. 1011 00:45:47,780 --> 00:45:50,060 So what you know for this person, 1012 00:45:50,060 --> 00:45:52,490 assuming that this bus isn't full, 1013 00:45:52,490 --> 00:45:56,120 is that that person arrived as late 1014 00:45:56,120 --> 00:45:58,160 as exactly when that vehicle arrived, 1015 00:45:58,160 --> 00:45:59,930 and as early as this vehicle. 1016 00:45:59,930 --> 00:46:04,640 So you know that the arrival time 1017 00:46:04,640 --> 00:46:08,150 of that person and the time at which they began waiting, 1018 00:46:08,150 --> 00:46:13,070 is a stochastic variable with a uniform distribution 1019 00:46:13,070 --> 00:46:13,820 on that range. 1020 00:46:17,730 --> 00:46:19,530 And you know the mean of that distribution 1021 00:46:19,530 --> 00:46:20,363 is half the headway. 1022 00:46:23,670 --> 00:46:27,960 So if the bus arrivals are high frequency 1023 00:46:27,960 --> 00:46:29,460 and the person is arriving randomly, 1024 00:46:29,460 --> 00:46:32,160 then this is certainly true. 1025 00:46:32,160 --> 00:46:38,760 If it's long headway service, then you 1026 00:46:38,760 --> 00:46:42,300 have to then consider what the scheduled times were. 1027 00:46:42,300 --> 00:46:44,820 So now you have to do a process similar to what 1028 00:46:44,820 --> 00:46:47,970 we did for rail, where-- 1029 00:46:50,940 --> 00:46:53,340 let me just draw it here. 1030 00:46:53,340 --> 00:47:00,789 So if this bus was meant to arrive here, 1031 00:47:00,789 --> 00:47:02,330 then maybe you say, well, this person 1032 00:47:02,330 --> 00:47:04,750 must have been wanting to get on that bus. 1033 00:47:04,750 --> 00:47:06,590 And so you made them wait some extra time. 1034 00:47:09,810 --> 00:47:18,290 And then if this bus was scheduled to depart here, 1035 00:47:18,290 --> 00:47:21,140 then you know that bus was early. 1036 00:47:21,140 --> 00:47:23,296 So that means that some of the people that end up 1037 00:47:23,296 --> 00:47:28,270 tapping in here were probably trying to get on this bus 1038 00:47:28,270 --> 00:47:30,650 and they missed it. 1039 00:47:30,650 --> 00:47:34,060 Because they arrived between this and this time-- 1040 00:47:34,060 --> 00:47:38,070 between the actual and the departed time. 1041 00:47:38,070 --> 00:47:40,230 So those are the people who suffer the most. 1042 00:47:40,230 --> 00:47:42,060 And that's more difficult to calculate. 1043 00:47:42,060 --> 00:47:44,760 You might have to assume some proportion of the people 1044 00:47:44,760 --> 00:47:45,630 you see here. 1045 00:47:45,630 --> 00:47:47,770 You could compare to a typical load 1046 00:47:47,770 --> 00:47:52,020 and see if there's an excess, and assume 1047 00:47:52,020 --> 00:47:56,130 that that excess would have been on the previous bus, 1048 00:47:56,130 --> 00:47:58,290 if that bus had departed on time. 1049 00:47:58,290 --> 00:48:01,070 So you have to use more assumptions. 1050 00:48:05,300 --> 00:48:07,110 OK. 1051 00:48:07,110 --> 00:48:11,026 So we understand how to measure reliability for rail tap ins 1052 00:48:11,026 --> 00:48:15,300 and tap outs, long headway, short headway, and for bus. 1053 00:48:15,300 --> 00:48:18,040 So strategies. 1054 00:48:18,040 --> 00:48:21,074 So the question Eli had earlier was, what do we do about it? 1055 00:48:21,074 --> 00:48:21,990 Now we can measure it. 1056 00:48:21,990 --> 00:48:24,130 So if you can measure something, you do something about it. 1057 00:48:24,130 --> 00:48:25,180 What can we do about it? 1058 00:48:25,180 --> 00:48:27,000 So two kinds of things. 1059 00:48:27,000 --> 00:48:31,470 We can use preventive strategies and corrective strategies. 1060 00:48:31,470 --> 00:48:34,710 Preventive strategies are aimed at maintaining normal service 1061 00:48:34,710 --> 00:48:36,870 and having some robust operations plans that 1062 00:48:36,870 --> 00:48:41,650 can handle unreliability without having a domino effect, 1063 00:48:41,650 --> 00:48:44,730 where everything cascades into unreliability. 1064 00:48:44,730 --> 00:48:47,100 And that it reduces the probability 1065 00:48:47,100 --> 00:48:48,930 that problems occur. 1066 00:48:48,930 --> 00:48:52,890 Corrective strategies are you know, 1067 00:48:52,890 --> 00:48:55,960 you're monitoring the system, you see unreliability, 1068 00:48:55,960 --> 00:48:59,700 and you do something to the system at that time to fix it, 1069 00:48:59,700 --> 00:49:02,580 to make it more reliable and to minimize 1070 00:49:02,580 --> 00:49:03,840 the impact on passengers. 1071 00:49:03,840 --> 00:49:05,340 So examples of preventive strategies 1072 00:49:05,340 --> 00:49:07,560 are having reserve fleet of drivers and vehicles. 1073 00:49:07,560 --> 00:49:10,810 If a driver is sick, you have another driver 1074 00:49:10,810 --> 00:49:11,970 and you send that driver. 1075 00:49:11,970 --> 00:49:16,470 Vehicle is not operating, you have another vehicle. 1076 00:49:16,470 --> 00:49:18,390 Having exclusive bus lanes. 1077 00:49:18,390 --> 00:49:20,460 So if you have great separation, you 1078 00:49:20,460 --> 00:49:22,200 get rid of some of the unreliability that 1079 00:49:22,200 --> 00:49:23,095 comes from traffic. 1080 00:49:26,190 --> 00:49:28,440 Traffic signal priority-- sorry, that 1081 00:49:28,440 --> 00:49:31,200 should be transit signal priority. 1082 00:49:31,200 --> 00:49:35,260 We talked about that in our previous lecture. 1083 00:49:35,260 --> 00:49:36,970 There are route design strategies. 1084 00:49:36,970 --> 00:49:37,980 So we know. 1085 00:49:37,980 --> 00:49:41,040 We've seen that longer routes are more reliable because they 1086 00:49:41,040 --> 00:49:47,040 have more time between recovery time, between layovers, 1087 00:49:47,040 --> 00:49:48,300 essentially. 1088 00:49:48,300 --> 00:49:50,200 They have fewer stops. 1089 00:49:50,200 --> 00:49:55,860 So there's less of a dwell time unreliability effect. 1090 00:49:55,860 --> 00:50:03,480 You can make schedules that have a good amount of recovery 1091 00:50:03,480 --> 00:50:04,420 at the end. 1092 00:50:04,420 --> 00:50:06,090 So you look at the percentiles and you 1093 00:50:06,090 --> 00:50:08,780 make sure that you're not picking the average 1094 00:50:08,780 --> 00:50:10,930 to calculate your cycle times. 1095 00:50:10,930 --> 00:50:14,190 And you set the timing points at good percentiles. 1096 00:50:14,190 --> 00:50:17,760 Maybe it's the median, maybe it's the 40th percentile. 1097 00:50:17,760 --> 00:50:19,380 And of course, hiring supervisors 1098 00:50:19,380 --> 00:50:22,380 to make sure that your people are showing up 1099 00:50:22,380 --> 00:50:26,460 and they're leaving on time rather than whenever they want, 1100 00:50:26,460 --> 00:50:27,750 et cetera. 1101 00:50:27,750 --> 00:50:31,050 So it's schedules. 1102 00:50:31,050 --> 00:50:36,120 So two critical decisions-- the cycle time, we know about that. 1103 00:50:36,120 --> 00:50:39,800 We know that it impacts cost and the reliability of departure 1104 00:50:39,800 --> 00:50:40,930 time of the terminal. 1105 00:50:40,930 --> 00:50:42,450 And you're very familiar with that, 1106 00:50:42,450 --> 00:50:45,480 I think, by now, so I don't have to spend as much time 1107 00:50:45,480 --> 00:50:46,470 discussing it. 1108 00:50:46,470 --> 00:50:48,190 Timing points is another. 1109 00:50:48,190 --> 00:50:54,700 So you can, in the middle of a bus route, have timing points. 1110 00:50:54,700 --> 00:51:00,060 So we know that there might be a terminal here 1111 00:51:00,060 --> 00:51:02,650 and a terminal here. 1112 00:51:02,650 --> 00:51:06,840 And whenever a bus arrives at the end to be, 1113 00:51:06,840 --> 00:51:09,990 they then have a layover to catch up. 1114 00:51:09,990 --> 00:51:12,080 We know that from assignment one, even. 1115 00:51:12,080 --> 00:51:16,050 But you can actually have points in the middle 1116 00:51:16,050 --> 00:51:19,890 where buses are also not allowed to leave early. 1117 00:51:19,890 --> 00:51:25,890 And so if you schedule the times of these in some way, 1118 00:51:25,890 --> 00:51:29,040 then buses might hold more or hold less, 1119 00:51:29,040 --> 00:51:31,920 and they will depart those points on time. 1120 00:51:31,920 --> 00:51:36,830 Where should you put those timing points, if at all? 1121 00:51:36,830 --> 00:51:38,650 AUDIENCE: Inter-transfers? 1122 00:51:38,650 --> 00:51:39,858 GABRIEL SANCHEZ-MARTINEZ: OK. 1123 00:51:39,858 --> 00:51:47,370 So one idea is that if there's a big train station here 1124 00:51:47,370 --> 00:51:50,580 or another bus line that also runs-- 1125 00:51:50,580 --> 00:51:53,070 especially for low frequency service-- 1126 00:51:53,070 --> 00:51:55,470 and people want to connect, they need to transfer, 1127 00:51:55,470 --> 00:51:56,730 and they want to connect. 1128 00:51:56,730 --> 00:51:59,720 You might actually have a timing point for both routes 1129 00:51:59,720 --> 00:52:04,210 there so the vehicles meet and people can switch vehicles. 1130 00:52:04,210 --> 00:52:05,400 So that's one idea. 1131 00:52:05,400 --> 00:52:06,380 What else? 1132 00:52:06,380 --> 00:52:09,581 AUDIENCE: Maybe after a high variability section, like after 1133 00:52:09,581 --> 00:52:10,080 [INAUDIBLE]? 1134 00:52:10,080 --> 00:52:11,288 GABRIEL SANCHEZ-MARTINEZ: OK. 1135 00:52:11,288 --> 00:52:16,470 So maybe this lane has a lot of traffic 1136 00:52:16,470 --> 00:52:24,400 and it's causing a lot of unreliability. 1137 00:52:24,400 --> 00:52:28,570 So you want to take care of it there instead 1138 00:52:28,570 --> 00:52:35,320 of letting it cascade into more variable headways, for example. 1139 00:52:35,320 --> 00:52:37,095 What else? 1140 00:52:37,095 --> 00:52:38,679 AUDIENCE: High demand, those stations. 1141 00:52:38,679 --> 00:52:40,636 GABRIEL SANCHEZ-MARTINEZ: High-demand stations. 1142 00:52:40,636 --> 00:52:41,240 OK. 1143 00:52:41,240 --> 00:52:42,400 So what about demand? 1144 00:52:42,400 --> 00:52:45,370 Demand is important, but what exactly? 1145 00:52:49,500 --> 00:52:54,380 AUDIENCE: I mean, if the bus is reliable at that stations, then 1146 00:52:54,380 --> 00:52:55,800 the passengers-- 1147 00:52:55,800 --> 00:52:56,400 GABRIEL SANCHEZ-MARTINEZ: What do you mean? 1148 00:52:56,400 --> 00:52:58,770 For example, a lot of people getting off from this bus 1149 00:52:58,770 --> 00:53:02,184 to take that station, or to enter that train station, or-- 1150 00:53:02,184 --> 00:53:04,600 AUDIENCE: People are getting onto the bus at that station. 1151 00:53:04,600 --> 00:53:05,808 GABRIEL SANCHEZ-MARTINEZ: OK. 1152 00:53:05,808 --> 00:53:11,160 So right upstream of sections where there are many boardings. 1153 00:53:11,160 --> 00:53:14,400 That's a very important thing because that's 1154 00:53:14,400 --> 00:53:16,830 where most people benefit. 1155 00:53:16,830 --> 00:53:17,700 And what else? 1156 00:53:17,700 --> 00:53:20,240 What else about passengers? 1157 00:53:20,240 --> 00:53:21,740 Where would you not want to do this? 1158 00:53:24,711 --> 00:53:25,210 Harry. 1159 00:53:25,210 --> 00:53:26,540 AUDIENCE: When the bus is full? 1160 00:53:26,540 --> 00:53:28,498 GABRIEL SANCHEZ-MARTINEZ: When the bus is full. 1161 00:53:28,498 --> 00:53:31,350 So if your load profile looks-- 1162 00:53:31,350 --> 00:53:32,460 I don't know. 1163 00:53:32,460 --> 00:53:34,380 A lot of people get on here. 1164 00:53:34,380 --> 00:53:38,470 And they're mostly not getting off. 1165 00:53:38,470 --> 00:53:41,362 And they sort of come down like that. 1166 00:53:41,362 --> 00:53:43,890 Do you want timing points on that bus route? 1167 00:53:43,890 --> 00:53:45,105 You don't. 1168 00:53:45,105 --> 00:53:47,880 You don't want timing points because most people are 1169 00:53:47,880 --> 00:53:53,250 getting on here and they don't want to be held here and here. 1170 00:53:53,250 --> 00:53:59,010 And very few people might be boarding in this section. 1171 00:53:59,010 --> 00:54:02,020 So if you hold a timing point, you're 1172 00:54:02,020 --> 00:54:05,610 going to benefit few passengers and penalize, 1173 00:54:05,610 --> 00:54:10,290 by longer and more frustrating vehicle rides, many passengers. 1174 00:54:10,290 --> 00:54:13,650 So what if there's a big transfer station here, 1175 00:54:13,650 --> 00:54:19,200 and a lot of people transfer, and then 1176 00:54:19,200 --> 00:54:23,280 here there's another station and a lot of people get on. 1177 00:54:23,280 --> 00:54:28,830 So then this is a good place to have a timing point, 1178 00:54:28,830 --> 00:54:34,170 right before a lot of people board 1179 00:54:34,170 --> 00:54:36,880 and when you don't have many people on the bus. 1180 00:54:36,880 --> 00:54:39,700 The flow profile is low. 1181 00:54:39,700 --> 00:54:42,140 AUDIENCE: [INAUDIBLE] liability before that [INAUDIBLE].. 1182 00:54:42,140 --> 00:54:43,556 GABRIEL SANCHEZ-MARTINEZ: Exactly. 1183 00:54:43,556 --> 00:54:47,750 So you want to maximize the segment of the population that 1184 00:54:47,750 --> 00:54:49,844 will benefit from the strategy and minimize 1185 00:54:49,844 --> 00:54:51,260 the segment of the population that 1186 00:54:51,260 --> 00:54:56,230 will be hurt by the strategy, i.e. people in the bus. 1187 00:54:56,230 --> 00:54:58,130 OK. 1188 00:54:58,130 --> 00:55:02,480 So that's a word about number and location of timing points. 1189 00:55:02,480 --> 00:55:04,460 And then the schedule at each timing point. 1190 00:55:04,460 --> 00:55:09,200 What should you set the percentile at? 1191 00:55:09,200 --> 00:55:11,960 Should this be the median? 1192 00:55:11,960 --> 00:55:13,730 Should they be 80 percentile? 1193 00:55:13,730 --> 00:55:18,110 Should they be 30 percentile? 1194 00:55:18,110 --> 00:55:19,460 AUDIENCE: The median realm. 1195 00:55:19,460 --> 00:55:21,740 GABRIEL SANCHEZ-MARTINEZ: So what happens if you-- 1196 00:55:21,740 --> 00:55:24,674 how many vehicles will have to be held? 1197 00:55:24,674 --> 00:55:26,090 What percent of vehicles will have 1198 00:55:26,090 --> 00:55:28,380 to be held if you set it to 80th percentile? 1199 00:55:28,380 --> 00:55:29,180 AUDIENCE: Oh, 80%. 1200 00:55:29,180 --> 00:55:30,170 GABRIEL SANCHEZ-MARTINEZ: 80%. 1201 00:55:30,170 --> 00:55:30,670 OK. 1202 00:55:30,670 --> 00:55:36,100 So 80% of vehicles would be sort of getting here and waiting. 1203 00:55:36,100 --> 00:55:40,280 That may be acceptable if, again, very few people are here 1204 00:55:40,280 --> 00:55:42,410 and a lot of people are boarding. 1205 00:55:42,410 --> 00:55:45,266 What if it's more of a mix? 1206 00:55:45,266 --> 00:55:46,640 Then you want to bring that down. 1207 00:55:46,640 --> 00:55:48,620 You dial it down. 1208 00:55:48,620 --> 00:55:53,030 So some people say set the half cycle 1209 00:55:53,030 --> 00:55:55,250 to somewhere between 90% and 95%-- 1210 00:55:55,250 --> 00:55:59,690 we've done that-- and then set timing points at 65. 1211 00:55:59,690 --> 00:56:03,690 I actually prefer that the timing points are below 50. 1212 00:56:06,480 --> 00:56:09,300 Because then you can advertise to your passengers. 1213 00:56:09,300 --> 00:56:13,690 You're essentially lying to people and saying-- 1214 00:56:13,690 --> 00:56:16,920 you're motivating people to arrive earlier than, most 1215 00:56:16,920 --> 00:56:20,010 often, the vehicle arrives. 1216 00:56:20,010 --> 00:56:22,140 So their probability of arriving and missing 1217 00:56:22,140 --> 00:56:26,080 a vehicle that departed early is lower 1218 00:56:26,080 --> 00:56:29,080 because you're telling them, expect an early departure, 1219 00:56:29,080 --> 00:56:29,999 essentially. 1220 00:56:29,999 --> 00:56:31,290 Except you don't call it early. 1221 00:56:31,290 --> 00:56:33,165 You say that's when it's scheduled to arrive. 1222 00:56:35,760 --> 00:56:39,150 So essentially you can control this 1223 00:56:39,150 --> 00:56:43,010 by scheduling a certain way, and then on the other side 1224 00:56:43,010 --> 00:56:44,020 by controlling it. 1225 00:56:44,020 --> 00:56:45,230 AUDIENCE: But the pushback when people are like, 1226 00:56:45,230 --> 00:56:46,930 oh, the bus is always running late. 1227 00:56:46,930 --> 00:56:48,410 GABRIEL SANCHEZ-MARTINEZ: Yeah. 1228 00:56:48,410 --> 00:56:49,680 Yeah, so it affects-- 1229 00:56:49,680 --> 00:56:50,520 there's a balance. 1230 00:56:50,520 --> 00:56:55,560 I'm not saying, schedule it 10th percentile. 1231 00:56:55,560 --> 00:57:00,540 But I think a little below 50 is a good strategy. 1232 00:57:00,540 --> 00:57:03,300 Because then you would minimize holding. 1233 00:57:03,300 --> 00:57:04,700 You would only hold vehicles that 1234 00:57:04,700 --> 00:57:08,526 are really early, essentially. 1235 00:57:08,526 --> 00:57:09,650 And holding is frustrating. 1236 00:57:09,650 --> 00:57:12,880 You don't want to be doing it all the time. 1237 00:57:12,880 --> 00:57:15,180 So by scheduling at a lower percentile, 1238 00:57:15,180 --> 00:57:17,340 you don't hold as often. 1239 00:57:17,340 --> 00:57:21,570 And you don't hold for as long times. 1240 00:57:21,570 --> 00:57:22,854 All right. 1241 00:57:22,854 --> 00:57:24,520 You have to be careful when you do this, 1242 00:57:24,520 --> 00:57:25,870 when you have timing points. 1243 00:57:25,870 --> 00:57:29,170 Because then your AVL data will come in, 1244 00:57:29,170 --> 00:57:31,970 and you're going to say, what's the running time? 1245 00:57:31,970 --> 00:57:36,460 Well, if people are following your instructions, 1246 00:57:36,460 --> 00:57:39,490 the minimum running time will be whatever 1247 00:57:39,490 --> 00:57:40,630 your timing points are. 1248 00:57:40,630 --> 00:57:49,050 So maybe your distribution would look like this. 1249 00:57:49,050 --> 00:57:50,900 But because you have timing points, 1250 00:57:50,900 --> 00:57:53,100 you've chopped off the early portion. 1251 00:57:53,100 --> 00:57:58,440 And now it looks more like this. 1252 00:57:58,440 --> 00:58:01,020 And now your 95th percentile is more to the right 1253 00:58:01,020 --> 00:58:04,100 than it used to be, maybe. 1254 00:58:04,100 --> 00:58:04,780 Maybe not. 1255 00:58:04,780 --> 00:58:06,829 Maybe it stays where it is. 1256 00:58:06,829 --> 00:58:08,370 But you have to be careful with this. 1257 00:58:08,370 --> 00:58:12,160 Your average will certainly move to the right. 1258 00:58:12,160 --> 00:58:16,590 So just be careful about that. 1259 00:58:16,590 --> 00:58:23,730 One strategy is to distinguish holding from running, 1260 00:58:23,730 --> 00:58:27,720 but that's a little difficult with AVL sometimes. 1261 00:58:27,720 --> 00:58:31,849 Another strategy is to run a month without timing points, 1262 00:58:31,849 --> 00:58:33,390 essentially instruct your drivers not 1263 00:58:33,390 --> 00:58:36,540 to use timing points, and collect data for a month, 1264 00:58:36,540 --> 00:58:38,320 and then use that for planning. 1265 00:58:38,320 --> 00:58:42,330 So just the things we can do. 1266 00:58:42,330 --> 00:58:43,870 OK, now corrective strategies. 1267 00:58:43,870 --> 00:58:46,020 So obviously, supervision. 1268 00:58:46,020 --> 00:58:49,730 Having supervisors, having an operations control practice 1269 00:58:49,730 --> 00:58:51,136 is important. 1270 00:58:51,136 --> 00:58:53,900 There's different strategies. 1271 00:58:53,900 --> 00:58:55,860 This is one of my favorite topics in transit. 1272 00:58:55,860 --> 00:59:01,520 So holding-- you can do holding to schedule or to headway. 1273 00:59:01,520 --> 00:59:03,860 So what is holding to schedule? 1274 00:59:03,860 --> 00:59:06,260 That's a simple one. 1275 00:59:06,260 --> 00:59:08,540 We've mentioned it a dozen times, 1276 00:59:08,540 --> 00:59:09,860 and even in this lecture. 1277 00:59:09,860 --> 00:59:12,710 You don't allow a vehicle to depart early from a timing 1278 00:59:12,710 --> 00:59:14,420 point or from a terminal. 1279 00:59:14,420 --> 00:59:19,490 So if a vehicle arrives a minute early at a timing point, 1280 00:59:19,490 --> 00:59:24,380 you instruct that driver to hold one minute. 1281 00:59:24,380 --> 00:59:26,720 Even though that bus is able to move on, 1282 00:59:26,720 --> 00:59:30,140 that bus holds for one minute. 1283 00:59:30,140 --> 00:59:32,140 TSP we talked about. 1284 00:59:32,140 --> 00:59:34,481 What's deadheading? 1285 00:59:34,481 --> 00:59:36,230 AUDIENCE: Just moving a bus from one place 1286 00:59:36,230 --> 00:59:40,662 to another that's not a revenue [INAUDIBLE].. 1287 00:59:40,662 --> 00:59:41,870 GABRIEL SANCHEZ-MARTINEZ: OK. 1288 00:59:41,870 --> 00:59:58,880 So let's say that you have buses here, 1289 00:59:58,880 --> 01:00:00,710 and this is your terminal. 1290 01:00:00,710 --> 01:00:03,980 And there's a bus that you are about to depart. 1291 01:00:03,980 --> 01:00:08,420 And your headway, the scheduled headway is more like this. 1292 01:00:08,420 --> 01:00:11,750 So you were supposed to have a bus here, but you didn't. 1293 01:00:11,750 --> 01:00:14,890 Something happened and the bus wasn't there. 1294 01:00:14,890 --> 01:00:22,060 And now you have two buses there instead of one. 1295 01:00:22,060 --> 01:00:23,810 Maybe there was a bunching on the way back 1296 01:00:23,810 --> 01:00:27,110 and the bunch arrived late, as it usually happens. 1297 01:00:27,110 --> 01:00:30,950 So one strategy that you can use is to take the first one 1298 01:00:30,950 --> 01:00:35,090 and instruct a deadhead to somewhere around here. 1299 01:00:35,090 --> 01:00:38,460 So this bus would run without its head sign 1300 01:00:38,460 --> 01:00:41,590 on, not allowing anybody to board-- 1301 01:00:41,590 --> 01:00:44,450 and that's why it's called a deadhead-- 1302 01:00:44,450 --> 01:00:46,030 to this stop. 1303 01:00:48,800 --> 01:00:50,870 And then this bus departs immediately, 1304 01:00:50,870 --> 01:00:52,550 but it remains in service. 1305 01:00:52,550 --> 01:00:56,300 So if that deadhead can happen quickly, maybe not even 1306 01:00:56,300 --> 01:00:58,140 following the streets or the bus, 1307 01:00:58,140 --> 01:00:59,960 maybe there's a faster way. 1308 01:00:59,960 --> 01:01:02,660 And you inject it downstream. 1309 01:01:02,660 --> 01:01:06,830 You can speed things up, you can balance the headways. 1310 01:01:06,830 --> 01:01:08,043 What's expressing? 1311 01:01:11,001 --> 01:01:12,603 AUDIENCE: Skipping stops? 1312 01:01:12,603 --> 01:01:15,186 GABRIEL SANCHEZ-MARTINEZ: That's one way of doing expressions. 1313 01:01:18,232 --> 01:01:19,940 Expressing can be done from the terminal. 1314 01:01:22,770 --> 01:01:25,410 So the distinction between expressing and deadheading 1315 01:01:25,410 --> 01:01:29,050 is that expressing them with people inside. 1316 01:01:29,050 --> 01:01:32,820 So in this case, you could have allowed people 1317 01:01:32,820 --> 01:01:35,940 to board at the terminal and then said, 1318 01:01:35,940 --> 01:01:37,250 we're going to run express. 1319 01:01:37,250 --> 01:01:38,624 You tell people who are boarding, 1320 01:01:38,624 --> 01:01:40,140 we're going to run express. 1321 01:01:40,140 --> 01:01:43,520 So if you're getting off anywhere between here and here, 1322 01:01:43,520 --> 01:01:44,340 don't board. 1323 01:01:44,340 --> 01:01:49,680 And the vehicle then skips stops, but with people inside. 1324 01:01:49,680 --> 01:01:53,100 So I don't think I need to do a drawing for this one. 1325 01:01:53,100 --> 01:01:55,240 Expressing can also be done halfway through. 1326 01:01:55,240 --> 01:02:04,590 So if you have this situation, then you 1327 01:02:04,590 --> 01:02:09,000 could say these people might have boarded, not 1328 01:02:09,000 --> 01:02:11,422 knowing that this bus was going to be expressed, 1329 01:02:11,422 --> 01:02:12,380 but something happened. 1330 01:02:12,380 --> 01:02:14,400 Maybe the driver was slow. 1331 01:02:14,400 --> 01:02:18,870 Maybe there was some traffic accident and there were delays. 1332 01:02:18,870 --> 01:02:22,410 So you can then announce this bus is being expressed, 1333 01:02:22,410 --> 01:02:24,109 or this train is being expressed, 1334 01:02:24,109 --> 01:02:26,150 and we're going to skip the following three stops 1335 01:02:26,150 --> 01:02:28,000 and arrive somewhere. 1336 01:02:28,000 --> 01:02:32,520 So if you're getting off before the express, 1337 01:02:32,520 --> 01:02:34,440 you have to decide, are you going 1338 01:02:34,440 --> 01:02:36,300 to stay and then walk back? 1339 01:02:36,300 --> 01:02:39,190 Are you going to stay and then take transit the opposite way? 1340 01:02:39,190 --> 01:02:41,130 Or are you going to get off right now 1341 01:02:41,130 --> 01:02:42,910 and wait for the next vehicle? 1342 01:02:42,910 --> 01:02:44,770 So it's a higher penalty for passengers. 1343 01:02:47,264 --> 01:02:48,180 What about short term? 1344 01:02:48,180 --> 01:02:50,880 We've talked about all of these, but in the context of planning. 1345 01:02:50,880 --> 01:02:54,250 And now we're using them for real time control. 1346 01:02:54,250 --> 01:02:57,486 So this is deadheading. 1347 01:02:57,486 --> 01:03:00,438 [WRITING ON BOARD] 1348 01:03:13,151 --> 01:03:13,650 Right. 1349 01:03:13,650 --> 01:03:17,616 And then yeah, so short term. 1350 01:03:17,616 --> 01:03:20,508 [WRITING ON BOARD] 1351 01:03:26,780 --> 01:03:27,860 Here's the situation. 1352 01:03:27,860 --> 01:03:38,280 You have-- this doesn't happen often, but it does happen. 1353 01:03:43,170 --> 01:03:45,600 You have a bunch in one direction 1354 01:03:45,600 --> 01:03:48,400 and a very long gap in the other direction. 1355 01:03:48,400 --> 01:03:50,960 And what happens with bunching? 1356 01:03:50,960 --> 01:03:54,060 The bus behind is usually not very full. 1357 01:03:54,060 --> 01:03:58,660 So you stop these buses and say stop. 1358 01:03:58,660 --> 01:04:03,730 And you tell the people here to move to the bus ahead. 1359 01:04:03,730 --> 01:04:04,510 Get off the bus. 1360 01:04:04,510 --> 01:04:05,343 We're in short term. 1361 01:04:05,343 --> 01:04:07,720 We're going to terminate the trip here. 1362 01:04:07,720 --> 01:04:11,680 And those people will have to transfer to the next bus. 1363 01:04:11,680 --> 01:04:13,190 If you don't allow this to happen, 1364 01:04:13,190 --> 01:04:15,210 then it's really onerous for passengers 1365 01:04:15,210 --> 01:04:18,430 because they have to get off and wait for the next one. 1366 01:04:18,430 --> 01:04:20,830 So it's better if you coordinate it this way. 1367 01:04:20,830 --> 01:04:24,850 And then this bus gets sent here and begins operating 1368 01:04:24,850 --> 01:04:28,091 in the opposite direction. 1369 01:04:28,091 --> 01:04:30,090 AUDIENCE: How much of this is done automatically 1370 01:04:30,090 --> 01:04:31,667 versus a person looking at this-- 1371 01:04:31,667 --> 01:04:33,750 GABRIEL SANCHEZ-MARTINEZ: I don't know of any case 1372 01:04:33,750 --> 01:04:36,540 where this is done automatically. 1373 01:04:36,540 --> 01:04:40,500 There has been researchers here at MIT and elsewhere, including 1374 01:04:40,500 --> 01:04:44,820 me, who have tried to write algorithms that 1375 01:04:44,820 --> 01:04:46,780 detect these opportunities. 1376 01:04:46,780 --> 01:04:50,160 But I don't know of any real implementation. 1377 01:04:50,160 --> 01:04:53,620 London buses does this, or at least they used to. 1378 01:04:53,620 --> 01:04:55,620 I think they still do. 1379 01:04:55,620 --> 01:05:00,600 But they really try to coordinate this. 1380 01:05:00,600 --> 01:05:06,070 They very rarely curtail trips without coordinating 1381 01:05:06,070 --> 01:05:07,187 in a bunch. 1382 01:05:07,187 --> 01:05:09,270 Because then people have to wait for the next one. 1383 01:05:09,270 --> 01:05:10,935 AUDIENCE: [INAUDIBLE] as well. 1384 01:05:10,935 --> 01:05:11,280 GABRIEL SANCHEZ-MARTINEZ: Pardon? 1385 01:05:11,280 --> 01:05:12,300 AUDIENCE: The train systems [INAUDIBLE].. 1386 01:05:12,300 --> 01:05:12,680 GABRIEL SANCHEZ-MARTINEZ: Yeah. 1387 01:05:12,680 --> 01:05:13,350 Yes. 1388 01:05:13,350 --> 01:05:14,830 So in trains, it's more common. 1389 01:05:14,830 --> 01:05:19,170 But it's usually a person in a control center determining 1390 01:05:19,170 --> 01:05:20,742 that they want to do this. 1391 01:05:20,742 --> 01:05:23,200 AUDIENCE: What's stopping them from [INAUDIBLE] algorithms? 1392 01:05:23,200 --> 01:05:26,827 Is it that the algorithms are not good enough or-- 1393 01:05:26,827 --> 01:05:28,660 GABRIEL SANCHEZ-MARTINEZ: That's part of it. 1394 01:05:28,660 --> 01:05:30,727 And then yeah. 1395 01:05:30,727 --> 01:05:32,310 I think I would say that's part of it. 1396 01:05:32,310 --> 01:05:33,870 The other is maybe a lack of interest 1397 01:05:33,870 --> 01:05:38,694 or a lack of faith in the computer. 1398 01:05:38,694 --> 01:05:39,870 There's a system in place. 1399 01:05:39,870 --> 01:05:42,100 It's just, you know, it's hard. 1400 01:05:42,100 --> 01:05:44,560 AUDIENCE: But there are two elements to this problem. 1401 01:05:44,560 --> 01:05:47,730 One is that you have to detect a problem in one direction. 1402 01:05:47,730 --> 01:05:49,230 And the other thing is that you have 1403 01:05:49,230 --> 01:05:51,330 to detect an opportunity in the other direction. 1404 01:05:51,330 --> 01:05:53,190 GABRIEL SANCHEZ-MARTINEZ: So this doesn't happen very often. 1405 01:05:53,190 --> 01:05:54,790 AUDIENCE: There are two parts here 1406 01:05:54,790 --> 01:05:56,790 that are completely independent from each other. 1407 01:05:56,790 --> 01:05:57,375 GABRIEL SANCHEZ-MARTINEZ: They're not independent, 1408 01:05:57,375 --> 01:05:59,100 though. 1409 01:05:59,100 --> 01:06:01,860 If the route is long you actually have-- 1410 01:06:01,860 --> 01:06:04,260 even though in a short route, in any given segment, 1411 01:06:04,260 --> 01:06:05,634 the probability of this happening 1412 01:06:05,634 --> 01:06:08,890 is low, if you have a long route it's much higher. 1413 01:06:08,890 --> 01:06:13,560 It's like the point you brought up with Professor Fritz' 1414 01:06:13,560 --> 01:06:16,980 lecture, you said, oh, the chances of a bus benefiting 1415 01:06:16,980 --> 01:06:19,110 from this are very small. 1416 01:06:19,110 --> 01:06:21,330 And then you said, well, what if it's a long route 1417 01:06:21,330 --> 01:06:22,870 and there are 20 signals? 1418 01:06:22,870 --> 01:06:24,640 Same thing applies here. 1419 01:06:24,640 --> 01:06:27,160 You might have a long route with many windows, 1420 01:06:27,160 --> 01:06:30,270 and the chances that there is one window at any given 1421 01:06:30,270 --> 01:06:34,500 time in the rush hour is actually pretty high. 1422 01:06:34,500 --> 01:06:37,150 AUDIENCE: And then the other thing is, as the controller-- 1423 01:06:37,150 --> 01:06:39,940 suppose I'm the controller, I have the algorithm. 1424 01:06:39,940 --> 01:06:43,110 And my computer starts beeping and gets all excited. 1425 01:06:43,110 --> 01:06:44,640 I have to respond quickly to this, 1426 01:06:44,640 --> 01:06:48,210 because that opportunity will pass. 1427 01:06:48,210 --> 01:06:51,210 GABRIEL SANCHEZ-MARTINEZ: And getting back 1428 01:06:51,210 --> 01:06:54,080 to algorithms and anticipation, what's 1429 01:06:54,080 --> 01:06:57,150 sort of neat about algorithms is that you 1430 01:06:57,150 --> 01:07:00,390 can try to predict that this will happen rather than waiting 1431 01:07:00,390 --> 01:07:02,290 until it happens to react. 1432 01:07:02,290 --> 01:07:04,106 And if you can do that early enough, 1433 01:07:04,106 --> 01:07:05,480 you might actually instruct a bus 1434 01:07:05,480 --> 01:07:09,937 that is departing the terminal to short term later on. 1435 01:07:09,937 --> 01:07:12,020 And if you do that, then you can set the head sign 1436 01:07:12,020 --> 01:07:14,770 on the bus to the short version. 1437 01:07:14,770 --> 01:07:16,470 And people who are boarding it are 1438 01:07:16,470 --> 01:07:17,640 going to know that it's going to be 1439 01:07:17,640 --> 01:07:19,390 short term so you won't have to coordinate 1440 01:07:19,390 --> 01:07:21,650 with the bus next to it. 1441 01:07:21,650 --> 01:07:24,570 You don't have to have a bunch, in other words. 1442 01:07:24,570 --> 01:07:26,280 So you can then minimize the problem 1443 01:07:26,280 --> 01:07:28,500 to finding a long gap here and predicting 1444 01:07:28,500 --> 01:07:31,902 when that gap will meet the next bus that's being dispatched. 1445 01:07:31,902 --> 01:07:33,110 You need algorithms for that. 1446 01:07:33,110 --> 01:07:34,710 It's very difficult to do it. 1447 01:07:34,710 --> 01:07:36,460 AUDIENCE: What do you tell the passengers? 1448 01:07:36,460 --> 01:07:38,670 Do you tell the passengers, listen, guys, this bus 1449 01:07:38,670 --> 01:07:40,550 might get short termed, just so you know. 1450 01:07:40,550 --> 01:07:40,720 GABRIEL SANCHEZ-MARTINEZ: No. 1451 01:07:40,720 --> 01:07:41,780 You change the head sign. 1452 01:07:41,780 --> 01:07:46,170 And you say this bus is running to Central Square instead 1453 01:07:46,170 --> 01:07:47,500 of Harvard. 1454 01:07:47,500 --> 01:07:48,272 AUDIENCE: Yeah. 1455 01:07:48,272 --> 01:07:49,980 AUDIENCE: Wouldn't you know this is going 1456 01:07:49,980 --> 01:07:51,271 to happen during commute hours? 1457 01:07:51,271 --> 01:07:52,800 Like the red line-- 1458 01:07:52,800 --> 01:07:55,380 I mean, I suppose for trains, the red line is so long. 1459 01:07:55,380 --> 01:07:59,280 But if you know your [?OE?] are mainly in the downtown area, 1460 01:07:59,280 --> 01:08:02,070 wouldn't you know beforehand that you want to just have 1461 01:08:02,070 --> 01:08:03,630 higher frequency on this one branch? 1462 01:08:03,630 --> 01:08:05,130 GABRIEL SANCHEZ-MARTINEZ: That would 1463 01:08:05,130 --> 01:08:07,410 be a service planning, short terming strategy, not 1464 01:08:07,410 --> 01:08:08,716 a real-time control strategy. 1465 01:08:08,716 --> 01:08:09,840 So we make the distinction. 1466 01:08:09,840 --> 01:08:12,690 Both are short terming, but this is something 1467 01:08:12,690 --> 01:08:17,260 that you decide in real time to bring the service that you 1468 01:08:17,260 --> 01:08:20,640 are delivering more close to what you plan to deliver. 1469 01:08:20,640 --> 01:08:23,729 Which is different from strategy in service planning, where 1470 01:08:23,729 --> 01:08:26,609 you identify when we talked about rider or quarter 1471 01:08:26,609 --> 01:08:27,134 strategies. 1472 01:08:27,134 --> 01:08:29,550 There might be a core of your route that has higher demand 1473 01:08:29,550 --> 01:08:32,990 and you have short terms to have frequency higher at that point. 1474 01:08:32,990 --> 01:08:35,869 Very different reasons and horizons 1475 01:08:35,869 --> 01:08:37,410 for planning and all sorts of things. 1476 01:08:40,350 --> 01:08:44,130 OK, use of reserve vehicles, this happens more with rail 1477 01:08:44,130 --> 01:08:44,773 than bus. 1478 01:08:44,773 --> 01:08:46,439 You could have it with bus, too, though. 1479 01:08:46,439 --> 01:08:49,380 I know that in South America they do it with bus. 1480 01:08:49,380 --> 01:08:53,130 So you have some buses stationed somewhere 1481 01:08:53,130 --> 01:08:55,229 in the city near key routes. 1482 01:08:55,229 --> 01:08:59,670 And they're just waiting there for an opportunity. 1483 01:08:59,670 --> 01:09:01,740 [LAUGHTER] 1484 01:09:01,740 --> 01:09:03,600 [CHATTER] 1485 01:09:03,600 --> 01:09:05,279 Right. 1486 01:09:05,279 --> 01:09:10,707 So then someone in a control center sees a long gap 1487 01:09:10,707 --> 01:09:13,290 and they call that bus and say, there's a big, long gap there. 1488 01:09:13,290 --> 01:09:13,800 Rush. 1489 01:09:13,800 --> 01:09:18,160 Go into that corridor and start operating Route X. So 1490 01:09:18,160 --> 01:09:20,670 they can inject a vehicle. 1491 01:09:20,670 --> 01:09:23,930 And you can do that with rail, too, if you have pocket tracks. 1492 01:09:23,930 --> 01:09:26,570 So you might have pocket tracks somewhere and sort of insert 1493 01:09:26,570 --> 01:09:28,100 a train. 1494 01:09:28,100 --> 01:09:30,880 Ari knows something about that. 1495 01:09:30,880 --> 01:09:33,920 OK, so mostly, if you do holding, 1496 01:09:33,920 --> 01:09:37,359 holding's the best strategy for keeping service on track. 1497 01:09:37,359 --> 01:09:41,216 You don't usually want to do the more aggressive strategies 1498 01:09:41,216 --> 01:09:43,090 because they hurt passengers and they require 1499 01:09:43,090 --> 01:09:44,649 much more coordination effort. 1500 01:09:44,649 --> 01:09:46,880 But if you have a major disruption, 1501 01:09:46,880 --> 01:09:47,880 sometimes you need them. 1502 01:09:47,880 --> 01:09:51,180 Holding by itself won't cut it. 1503 01:09:51,180 --> 01:09:53,500 Holding can be done in a bunch of different ways. 1504 01:09:53,500 --> 01:09:55,160 You can hold to schedule adherence. 1505 01:09:55,160 --> 01:09:56,760 We've spoken about that. 1506 01:09:56,760 --> 01:09:58,630 For headway, we've kind of brushed it off 1507 01:09:58,630 --> 01:09:59,920 and said headway adherence. 1508 01:09:59,920 --> 01:10:02,128 Well, there's actually a lot of ways you can do that. 1509 01:10:02,128 --> 01:10:04,090 So one of them is to look at the schedule 1510 01:10:04,090 --> 01:10:06,430 and realize that the time between scheduled trips 1511 01:10:06,430 --> 01:10:07,660 is five minutes. 1512 01:10:07,660 --> 01:10:09,130 So now instead of actually trying 1513 01:10:09,130 --> 01:10:11,410 to stick to the actual times, you 1514 01:10:11,410 --> 01:10:14,210 want to stick to a separation of five minutes between vehicles, 1515 01:10:14,210 --> 01:10:16,570 because that's the time that was scheduled. 1516 01:10:16,570 --> 01:10:19,240 So that would be scheduled headway adherence. 1517 01:10:19,240 --> 01:10:21,770 The next-- and these are in order of sophistication. 1518 01:10:21,770 --> 01:10:25,850 So the next one is threshold headway adherence. 1519 01:10:25,850 --> 01:10:28,780 So if you think about it, there's 1520 01:10:28,780 --> 01:10:34,000 no reason why the scheduled difference between departure 1521 01:10:34,000 --> 01:10:38,560 times is the best threshold that you should use for holding. 1522 01:10:38,560 --> 01:10:42,310 There might be one that is a minute less or a minute higher 1523 01:10:42,310 --> 01:10:45,200 that results in better performance. 1524 01:10:45,200 --> 01:10:47,792 Why not? 1525 01:10:47,792 --> 01:10:49,750 What physical reason is there for the scheduled 1526 01:10:49,750 --> 01:10:51,190 time being the best one. 1527 01:10:51,190 --> 01:10:52,060 There isn't any. 1528 01:10:52,060 --> 01:10:57,880 So if you optimize the threshold, 1529 01:10:57,880 --> 01:10:59,820 you can get better performance. 1530 01:10:59,820 --> 01:11:02,290 And usually the optimal threshold is below, 1531 01:11:02,290 --> 01:11:05,020 it's shorter than the schedule. 1532 01:11:05,020 --> 01:11:07,660 So you hold less often. 1533 01:11:07,660 --> 01:11:10,350 The problem with headway adherence 1534 01:11:10,350 --> 01:11:13,640 is that you hold too much, essentially. 1535 01:11:13,640 --> 01:11:16,277 So then there's headway regularity. 1536 01:11:16,277 --> 01:11:17,860 Don't worry about the schedule at all, 1537 01:11:17,860 --> 01:11:20,650 or about any predetermined headway. 1538 01:11:20,650 --> 01:11:23,470 You have a separation between vehicles. 1539 01:11:23,470 --> 01:11:29,440 And I know that if I have vehicles, 1540 01:11:29,440 --> 01:11:32,690 I want my vehicles spaced this way. 1541 01:11:32,690 --> 01:11:37,850 But instead, I have this situation. 1542 01:11:37,850 --> 01:11:42,990 So I want this vehicle to hold until it is here. 1543 01:11:42,990 --> 01:11:46,090 Or rather, what will really happen 1544 01:11:46,090 --> 01:11:47,590 is this vehicle will stay there. 1545 01:11:47,590 --> 01:11:49,570 You will ask it to stay there. 1546 01:11:49,570 --> 01:11:52,030 And you want this vehicle to move on 1547 01:11:52,030 --> 01:11:55,090 and this vehicle to move on to these positions. 1548 01:11:55,090 --> 01:11:56,530 And now they're even, and then you 1549 01:11:56,530 --> 01:11:58,230 let that vehicle go at that point. 1550 01:11:58,230 --> 01:11:59,564 So that's even headway holding. 1551 01:11:59,564 --> 01:12:01,480 AUDIENCE: That seems pretty easy to implement. 1552 01:12:01,480 --> 01:12:02,140 How often is it-- 1553 01:12:02,140 --> 01:12:02,890 GABRIEL SANCHEZ-MARTINEZ: Now it is. 1554 01:12:02,890 --> 01:12:04,580 It used to be very hard. 1555 01:12:04,580 --> 01:12:09,070 So how would you implement targeted headway holding 1556 01:12:09,070 --> 01:12:10,775 without technology? 1557 01:12:10,775 --> 01:12:11,650 AUDIENCE: [INAUDIBLE] 1558 01:12:11,650 --> 01:12:13,650 GABRIEL SANCHEZ-MARTINEZ: No, but how would you? 1559 01:12:13,650 --> 01:12:14,320 You can't do it. 1560 01:12:14,320 --> 01:12:14,890 AUDIENCE: You need a supervisor [INAUDIBLE].. 1561 01:12:14,890 --> 01:12:16,890 GABRIEL SANCHEZ-MARTINEZ: You need a supervisor. 1562 01:12:16,890 --> 01:12:19,036 So in London there was actually a time 1563 01:12:19,036 --> 01:12:20,410 when you didn't need a supervisor 1564 01:12:20,410 --> 01:12:23,440 because you had the driver getting off the bus, 1565 01:12:23,440 --> 01:12:27,100 and hitting a button on a post, and it starts a timer, 1566 01:12:27,100 --> 01:12:28,720 and then the driver leaves. 1567 01:12:28,720 --> 01:12:31,210 The next bus comes along and it sees the time. 1568 01:12:31,210 --> 01:12:34,620 So it knows, like, ah, OK, this is when I have to leave. 1569 01:12:34,620 --> 01:12:37,750 So you can do that, even without wireless communication. 1570 01:12:37,750 --> 01:12:39,700 Even in headway you can't do that. 1571 01:12:39,700 --> 01:12:41,290 You need communication. 1572 01:12:41,290 --> 01:12:44,080 Somebody needs to know the vehicle before, 1573 01:12:44,080 --> 01:12:46,750 the vehicle after, that means they communicated. 1574 01:12:46,750 --> 01:12:50,916 So it's much more of a recent strategy in terms of-- 1575 01:12:50,916 --> 01:12:52,290 AUDIENCE: Oh, so in this strategy 1576 01:12:52,290 --> 01:12:54,392 you're not necessarily trying to maintain a certain headway. 1577 01:12:54,392 --> 01:12:55,660 GABRIEL SANCHEZ-MARTINEZ: No certain headway. 1578 01:12:55,660 --> 01:12:57,900 It's often when it emerges from the system. 1579 01:12:57,900 --> 01:12:58,581 AUDIENCE: OK. 1580 01:12:58,581 --> 01:12:59,830 GABRIEL SANCHEZ-MARTINEZ: Yep. 1581 01:12:59,830 --> 01:13:01,990 And that's actually-- if we want to split hairs, 1582 01:13:01,990 --> 01:13:04,710 there's different kinds of ways of doing unit headway. 1583 01:13:04,710 --> 01:13:06,770 And let's not get into it. 1584 01:13:06,770 --> 01:13:11,010 Then the most sophisticated class is optimization. 1585 01:13:11,010 --> 01:13:14,120 And there's something called rolling horizon optimization. 1586 01:13:14,120 --> 01:13:16,390 So what happens there is that you use a simulation 1587 01:13:16,390 --> 01:13:19,330 model, essentially, to predict how the system would 1588 01:13:19,330 --> 01:13:24,130 evolve if you're holding time for a certain configuration. 1589 01:13:24,130 --> 01:13:26,560 And you can test a bunch of different headway holding 1590 01:13:26,560 --> 01:13:28,600 configurations and pick the one that's 1591 01:13:28,600 --> 01:13:31,960 best at a given time based on those forecasts. 1592 01:13:31,960 --> 01:13:35,200 In other words, pick the holding time that maximizes performance 1593 01:13:35,200 --> 01:13:37,870 across forecasts. 1594 01:13:37,870 --> 01:13:42,889 And so what's neat about this is that they can trade off waiting 1595 01:13:42,889 --> 01:13:43,930 time and in-vehicle time. 1596 01:13:43,930 --> 01:13:48,970 When you hold, the people inside the vehicle are waiting more. 1597 01:13:48,970 --> 01:13:53,800 The winners of this strategy are people who would miss that bus 1598 01:13:53,800 --> 01:13:55,900 and have to wait for the following bus that 1599 01:13:55,900 --> 01:13:57,850 has a long headway ahead of it. 1600 01:13:57,850 --> 01:14:00,250 So by evening out the headways, you 1601 01:14:00,250 --> 01:14:02,325 make everybody wait about the same. 1602 01:14:02,325 --> 01:14:04,450 And that minimizes average waiting time and average 1603 01:14:04,450 --> 01:14:05,740 crowding, et cetera. 1604 01:14:05,740 --> 01:14:10,120 So optimization strategy can predict or keep 1605 01:14:10,120 --> 01:14:12,600 track of how many people are inside vehicles. 1606 01:14:12,600 --> 01:14:15,100 And it can know, well, I know this is the penalty. 1607 01:14:15,100 --> 01:14:16,750 I know this is the benefit. 1608 01:14:16,750 --> 01:14:20,630 Let's trade these off and let's hold the optimal amount of time 1609 01:14:20,630 --> 01:14:24,390 such that the total time is minimized. 1610 01:14:24,390 --> 01:14:26,500 And you can multiply by factors that 1611 01:14:26,500 --> 01:14:30,430 take into account this utility of waiting being higher 1612 01:14:30,430 --> 01:14:33,040 than the disutility of being inside the vehicle. 1613 01:14:33,040 --> 01:14:36,620 So what that does is it reduces excessive holding. 1614 01:14:36,620 --> 01:14:40,870 So if you know that you have a full vehicle, 1615 01:14:40,870 --> 01:14:45,136 you don't hold it, even if it's very close to the next one. 1616 01:14:45,136 --> 01:14:46,510 Why would you hold a vehicle that 1617 01:14:46,510 --> 01:14:50,700 is full, even if it's this one right here bunched 1618 01:14:50,700 --> 01:14:51,710 to the next one. 1619 01:14:51,710 --> 01:14:52,210 You don't. 1620 01:14:52,210 --> 01:14:53,920 You don't want to hold it. 1621 01:14:53,920 --> 01:14:56,120 What if the vehicle isn't full, but it will be full 1622 01:14:56,120 --> 01:14:59,590 five stops ahead, because demand is very high for some reason. 1623 01:14:59,590 --> 01:15:00,640 And you know that. 1624 01:15:00,640 --> 01:15:04,240 Then optimization algorithm will see that because it's 1625 01:15:04,240 --> 01:15:05,770 predicting for next hour. 1626 01:15:05,770 --> 01:15:10,360 So it'll be able to pick a strategy that 1627 01:15:10,360 --> 01:15:12,640 improves performance. 1628 01:15:12,640 --> 01:15:14,680 One challenge is drivers. 1629 01:15:14,680 --> 01:15:16,750 If you hold too much, then drivers 1630 01:15:16,750 --> 01:15:18,820 might be 20 minutes late for their shift, 1631 01:15:18,820 --> 01:15:20,440 for their meal break. 1632 01:15:20,440 --> 01:15:21,950 What do you do about that? 1633 01:15:21,950 --> 01:15:23,320 That's still a challenge. 1634 01:15:23,320 --> 01:15:25,060 And that's a challenge throughout. 1635 01:15:25,060 --> 01:15:27,880 But there is opportunity with optimization algorithms 1636 01:15:27,880 --> 01:15:32,350 to insert constraints that take those into account so 1637 01:15:32,350 --> 01:15:35,290 that your holding policy is something 1638 01:15:35,290 --> 01:15:36,601 that you can implement. 1639 01:15:36,601 --> 01:15:38,434 AUDIENCE: It seems like [INAUDIBLE] would be 1640 01:15:38,434 --> 01:15:40,650 to [INAUDIBLE] the algorithm. 1641 01:15:40,650 --> 01:15:42,930 If it's taking 45 minutes to come up 1642 01:15:42,930 --> 01:15:44,940 with this great solution, then [INAUDIBLE].. 1643 01:15:44,940 --> 01:15:47,356 GABRIEL SANCHEZ-MARTINEZ: So this problem is [INAUDIBLE].. 1644 01:15:47,356 --> 01:15:50,490 And if you crunched all the possibilities, 1645 01:15:50,490 --> 01:15:51,596 you would never finish. 1646 01:15:51,596 --> 01:15:52,970 So you need a very good algorithm 1647 01:15:52,970 --> 01:15:56,710 to find something fast. 1648 01:15:56,710 --> 01:15:57,420 Yeah. 1649 01:15:57,420 --> 01:16:00,780 So there's two different ways of doing rolling horizon 1650 01:16:00,780 --> 01:16:02,880 optimization. 1651 01:16:02,880 --> 01:16:06,060 One way is to have constant running times in demands 1652 01:16:06,060 --> 01:16:07,710 within the prediction horizon. 1653 01:16:07,710 --> 01:16:09,960 So imagine this blue window being your-- 1654 01:16:09,960 --> 01:16:12,180 this is the time right now, and you're predicting 1655 01:16:12,180 --> 01:16:13,690 over the next, say, hour. 1656 01:16:13,690 --> 01:16:15,446 And that's the blue window. 1657 01:16:15,446 --> 01:16:17,820 What is actually happening is that your running times are 1658 01:16:17,820 --> 01:16:19,670 going up slowly and gradually. 1659 01:16:19,670 --> 01:16:21,630 Your demand is going up slowly, gradually 1660 01:16:21,630 --> 01:16:24,150 because you're in the PND. 1661 01:16:24,150 --> 01:16:28,380 If you are using static input, you 1662 01:16:28,380 --> 01:16:32,380 have to say what the running time is for the whole horizon. 1663 01:16:32,380 --> 01:16:35,480 So what you might do is break up the day into periods. 1664 01:16:35,480 --> 01:16:39,120 And if you start at this time, anytime before this, 1665 01:16:39,120 --> 01:16:40,950 you set some average. 1666 01:16:40,950 --> 01:16:42,700 And then once you cross that threshold, 1667 01:16:42,700 --> 01:16:44,200 you set a different average. 1668 01:16:44,200 --> 01:16:46,530 But then you miss out on some information. 1669 01:16:46,530 --> 01:16:50,070 So I worked on a model that actually 1670 01:16:50,070 --> 01:16:53,940 takes some dynamic inputs, too, to consider 1671 01:16:53,940 --> 01:16:55,860 these transitions, essentially. 1672 01:16:55,860 --> 01:16:59,900 And the way it works is you have these dynamic functions 1673 01:16:59,900 --> 01:17:02,130 of running times and demand. 1674 01:17:02,130 --> 01:17:04,040 You can see the current system state. 1675 01:17:04,040 --> 01:17:06,030 You send that to a model. 1676 01:17:06,030 --> 01:17:10,530 The model passes on those inputs and some holding time 1677 01:17:10,530 --> 01:17:13,200 configuration to a performance model, which essentially 1678 01:17:13,200 --> 01:17:15,720 forecasts what the system would do, 1679 01:17:15,720 --> 01:17:18,440 how the vehicle would move, where passengers would board, 1680 01:17:18,440 --> 01:17:19,824 all those things. 1681 01:17:19,824 --> 01:17:21,990 And then that gets sent to a cost model, which says, 1682 01:17:21,990 --> 01:17:22,950 how much are people waiting? 1683 01:17:22,950 --> 01:17:24,290 How much are people in vehicles? 1684 01:17:24,290 --> 01:17:27,330 Let's add those up and figure out what the average is. 1685 01:17:27,330 --> 01:17:29,710 And then that gets sent back to the optimization model, 1686 01:17:29,710 --> 01:17:31,560 and the optimization model says, what 1687 01:17:31,560 --> 01:17:34,320 if we, instead of doing that, let's turn this knob 1688 01:17:34,320 --> 01:17:36,750 and increase that holding time and decrease this one, 1689 01:17:36,750 --> 01:17:38,080 go again. 1690 01:17:38,080 --> 01:17:40,830 So it can do that on a loop, essentially, 1691 01:17:40,830 --> 01:17:45,210 until it finds optimal times. 1692 01:17:45,210 --> 01:17:49,680 The objective function is the average time in the system. 1693 01:17:49,680 --> 01:17:53,440 So Wv is like extra time in the vehicle. 1694 01:17:53,440 --> 01:17:55,860 So it's the time that a person spends 1695 01:17:55,860 --> 01:17:58,890 at a stop in the vehicle, not moving because the vehicle is 1696 01:17:58,890 --> 01:18:00,780 being held. 1697 01:18:00,780 --> 01:18:02,580 So you're adding time to that person. 1698 01:18:02,580 --> 01:18:05,500 And then Ws is waiting time at the stop. 1699 01:18:05,500 --> 01:18:07,440 And we can multiply by some factor 1700 01:18:07,440 --> 01:18:10,360 because we know that waiting time is more onerous. 1701 01:18:10,360 --> 01:18:12,020 There's a bunch of constraints. 1702 01:18:12,020 --> 01:18:14,364 I'll skip the differences between static and dynamic. 1703 01:18:14,364 --> 01:18:15,780 Essentially it's that running time 1704 01:18:15,780 --> 01:18:18,810 so demand can be functions of time now. 1705 01:18:18,810 --> 01:18:20,290 Here's what happens. 1706 01:18:20,290 --> 01:18:25,840 So here we test four different strategies. 1707 01:18:25,840 --> 01:18:29,850 The first one here, TH, is threshold holding. 1708 01:18:29,850 --> 01:18:32,290 EH is even headway holding. 1709 01:18:32,290 --> 01:18:36,180 OS is optimization of static inputs, 1710 01:18:36,180 --> 01:18:39,000 and OD is optimization with dynamic inputs. 1711 01:18:39,000 --> 01:18:41,050 And then we tested-- 1712 01:18:41,050 --> 01:18:43,950 if we look at the bottom two sets of four, 1713 01:18:43,950 --> 01:18:46,950 these are cases where both of the men and the running times 1714 01:18:46,950 --> 01:18:48,030 are dynamic. 1715 01:18:48,030 --> 01:18:49,690 So they're both transient. 1716 01:18:49,690 --> 01:18:51,720 And we tested a case of low crowding 1717 01:18:51,720 --> 01:18:53,410 and a case of high crowding. 1718 01:18:53,410 --> 01:18:57,330 So what we see is that in all cases of low crowding-- 1719 01:18:57,330 --> 01:19:03,090 by the way, the bottom 2/3 sets of runs are cases where maybe 1720 01:19:03,090 --> 01:19:06,110 running times are dynamic but demand isn't, or demand is 1721 01:19:06,110 --> 01:19:08,260 dynamic and running times aren't. 1722 01:19:08,260 --> 01:19:12,080 So if you look at all the cases of low crowding, 1723 01:19:12,080 --> 01:19:14,960 the white ones here, there's very little difference 1724 01:19:14,960 --> 01:19:16,030 in performance. 1725 01:19:16,030 --> 01:19:17,640 So it means that you don't really 1726 01:19:17,640 --> 01:19:19,530 need the most sophisticated strategy. 1727 01:19:19,530 --> 01:19:22,380 And the benefit of a very sophisticated optimization 1728 01:19:22,380 --> 01:19:25,020 strategy with dynamic inputs is not really 1729 01:19:25,020 --> 01:19:26,940 going to bring you a lot of benefit. 1730 01:19:26,940 --> 01:19:30,690 If you look at the high crowding case, what you see 1731 01:19:30,690 --> 01:19:34,470 is that there is a pretty significant benefit 1732 01:19:34,470 --> 01:19:38,520 of even headway holding over even optimized threshold 1733 01:19:38,520 --> 01:19:40,200 holding. 1734 01:19:40,200 --> 01:19:43,530 But moving to the model with optimization 1735 01:19:43,530 --> 01:19:47,940 doesn't do much for you if there's 1736 01:19:47,940 --> 01:19:52,050 a lot of sort of dynamics and system potentially. 1737 01:19:52,050 --> 01:19:56,100 So part of that is because the static inputs high information 1738 01:19:56,100 --> 01:19:58,190 about when those vehicles will fill up. 1739 01:19:58,190 --> 01:20:00,450 And when you insert that information into the system, 1740 01:20:00,450 --> 01:20:03,910 then the optimizer can see more of what happens 1741 01:20:03,910 --> 01:20:06,500 and can improve performance. 1742 01:20:06,500 --> 01:20:10,320 Here to the left is lower cost and therefore better. 1743 01:20:13,710 --> 01:20:15,720 Yeah, there's more to parse here, 1744 01:20:15,720 --> 01:20:18,420 but we're running out of time, so I'm 1745 01:20:18,420 --> 01:20:22,150 going to skip a few slides. 1746 01:20:22,150 --> 01:20:26,550 So you have control problems, routine disturbances 1747 01:20:26,550 --> 01:20:30,192 where you lose speed adjustments and holding lightly. 1748 01:20:30,192 --> 01:20:31,650 Then there's short-term disruptions 1749 01:20:31,650 --> 01:20:34,397 that might last between five and 30 minutes. 1750 01:20:34,397 --> 01:20:35,980 And there you can apply the strategies 1751 01:20:35,980 --> 01:20:37,160 that we've discussed. 1752 01:20:37,160 --> 01:20:41,460 And then there's very long, much longer interruptions 1753 01:20:41,460 --> 01:20:44,430 in service for which you need to do something major, 1754 01:20:44,430 --> 01:20:48,210 like bringing out bus service to replace train service. 1755 01:20:48,210 --> 01:20:51,432 And so only holding, short terming, 1756 01:20:51,432 --> 01:20:53,640 expressing, deadheading, they're not going to cut it. 1757 01:20:53,640 --> 01:20:57,210 You have a much bigger problem to deal with. 1758 01:20:57,210 --> 01:21:00,930 Here's a situation in a rail operation 1759 01:21:00,930 --> 01:21:04,580 where there's a signal failure, or perhaps there's 1760 01:21:04,580 --> 01:21:08,220 a suicide attempt, and there's a person on the tracks. 1761 01:21:08,220 --> 01:21:12,640 And you have this train that's standing there and can't move. 1762 01:21:12,640 --> 01:21:15,690 So the first thing you should do is 1763 01:21:15,690 --> 01:21:17,580 hold the trains downstream, immediately 1764 01:21:17,580 --> 01:21:19,039 downstream of the blockage. 1765 01:21:19,039 --> 01:21:21,330 If you don't do that, they will run around and queue up 1766 01:21:21,330 --> 01:21:22,560 on the other end. 1767 01:21:22,560 --> 01:21:25,500 And the people entering these stations 1768 01:21:25,500 --> 01:21:28,120 are going to wait a long time. 1769 01:21:28,120 --> 01:21:30,226 and those stations are going to fill up. 1770 01:21:30,226 --> 01:21:32,850 The other thing you should do is these trains that are lined up 1771 01:21:32,850 --> 01:21:36,840 here should be expressed as soon as the blockage is 1772 01:21:36,840 --> 01:21:40,410 cleared up so that you can move those vehicles forward. 1773 01:21:40,410 --> 01:21:42,630 And the vehicles at the end of the queue 1774 01:21:42,630 --> 01:21:46,041 can begin normal operation. 1775 01:21:46,041 --> 01:21:47,070 Does that make sense? 1776 01:21:51,680 --> 01:21:53,690 A lot of the very sophisticated models 1777 01:21:53,690 --> 01:21:56,220 are not used in practice for a number of reasons. 1778 01:21:56,220 --> 01:21:59,795 Sometimes it's that the models are simplistic. 1779 01:22:02,410 --> 01:22:05,830 Sometimes it's sort of a lack of faith in models. 1780 01:22:05,830 --> 01:22:08,890 Often it has to do with the data in real time 1781 01:22:08,890 --> 01:22:11,484 about where vehicles are not being that good. 1782 01:22:11,484 --> 01:22:13,150 So actually detecting where vehicles are 1783 01:22:13,150 --> 01:22:15,520 could be a major challenge. 1784 01:22:15,520 --> 01:22:18,410 And you need that information to make the determination of what 1785 01:22:18,410 --> 01:22:20,080 the optimal strategy is. 1786 01:22:20,080 --> 01:22:25,330 Recently our lab did a pilot of a real experiment 1787 01:22:25,330 --> 01:22:28,720 with the Green Line holding two headways instead 1788 01:22:28,720 --> 01:22:31,000 of the schedule. 1789 01:22:31,000 --> 01:22:33,120 So right now they use paper sheets 1790 01:22:33,120 --> 01:22:35,140 and they have a schedule. 1791 01:22:35,140 --> 01:22:39,910 And Jeff Fabian, who's a student in the lab, 1792 01:22:39,910 --> 01:22:45,520 designed an app that has all the train and driver information. 1793 01:22:45,520 --> 01:22:49,510 And it also calculates the even headway departing time. 1794 01:22:49,510 --> 01:22:52,690 So that departure time which would cause an even headway. 1795 01:22:52,690 --> 01:22:56,920 And for two weeks we had the inspectors of the terminal 1796 01:22:56,920 --> 01:23:00,100 use that instead of the paper schedule. 1797 01:23:00,100 --> 01:23:03,280 And what happened-- here's a picture of the app. 1798 01:23:03,280 --> 01:23:05,890 So you have all the trains for the day. 1799 01:23:05,890 --> 01:23:07,430 There's color coding. 1800 01:23:07,430 --> 01:23:10,330 So green is coming up and you can see 1801 01:23:10,330 --> 01:23:11,600 all these times are different. 1802 01:23:11,600 --> 01:23:16,690 So 9:36, there's some extra holding there for the train 1803 01:23:16,690 --> 01:23:20,860 that had been scheduled at 9:34 so that the headways are even 1804 01:23:20,860 --> 01:23:23,640 coming out. 1805 01:23:23,640 --> 01:23:25,660 And here's what happened. 1806 01:23:25,660 --> 01:23:31,340 The variability decreased by about 40% in some cases, 1807 01:23:31,340 --> 01:23:33,460 if you look at the coefficient of variation. 1808 01:23:33,460 --> 01:23:37,000 And you only look at trains that were compliant. 1809 01:23:37,000 --> 01:23:39,640 What really happened overall was a mix of things. 1810 01:23:39,640 --> 01:23:42,340 There was some noncompliance with headway times, 1811 01:23:42,340 --> 01:23:46,210 some insistence in departing on time to the schedule, 1812 01:23:46,210 --> 01:23:49,930 and then sometimes a compliance to the [INAUDIBLE] headway 1813 01:23:49,930 --> 01:23:50,675 policy. 1814 01:23:50,675 --> 01:23:52,300 So here's the coefficient of variation. 1815 01:23:52,300 --> 01:23:53,860 You know what that is. 1816 01:23:53,860 --> 01:23:56,380 You know that lower is better and the Green Line is lower, 1817 01:23:56,380 --> 01:23:57,880 so it's better. 1818 01:23:57,880 --> 01:24:01,390 You can calculate the equivalent benefit 1819 01:24:01,390 --> 01:24:03,550 that you would get by adding trains 1820 01:24:03,550 --> 01:24:07,070 to service in terms of decreasing waiting time. 1821 01:24:07,070 --> 01:24:09,850 You can increase frequency by adding new trains. 1822 01:24:09,850 --> 01:24:12,840 So decrease in variability of headways 1823 01:24:12,840 --> 01:24:15,550 was equivalent to adding 1.7 trains. 1824 01:24:15,550 --> 01:24:18,350 Which is money. 1825 01:24:18,350 --> 01:24:20,850 AUDIENCE: Yeah, but if I'm not mistaken-- you can correct me 1826 01:24:20,850 --> 01:24:21,770 if I'm wrong. 1827 01:24:21,770 --> 01:24:23,440 There is a mechanism in this algorithm 1828 01:24:23,440 --> 01:24:26,274 that tries to go back gradually to the schedule. 1829 01:24:26,274 --> 01:24:27,940 GABRIEL SANCHEZ-MARTINEZ: No, I wouldn't 1830 01:24:27,940 --> 01:24:29,240 characterize it that way. 1831 01:24:29,240 --> 01:24:34,990 There are constraints to prevent situations where there aren't 1832 01:24:34,990 --> 01:24:38,950 enough trains to be departed. 1833 01:24:38,950 --> 01:24:42,310 And there are some constraints on how much holding 1834 01:24:42,310 --> 01:24:44,410 there can be, et cetera. 1835 01:24:44,410 --> 01:24:47,410 So yeah, there's an intention not 1836 01:24:47,410 --> 01:24:51,380 to have too much of a cascading holding throughout the day. 1837 01:24:51,380 --> 01:24:55,210 But it's not so much as a programmed linear trend 1838 01:24:55,210 --> 01:25:00,010 towards schedule or anything like that. 1839 01:25:00,010 --> 01:25:02,440 AUDIENCE: Because you're going off schedule, does-- 1840 01:25:02,440 --> 01:25:03,130 GABRIEL SANCHEZ-MARTINEZ: Slightly. 1841 01:25:03,130 --> 01:25:04,230 AUDIENCE: Slightly. 1842 01:25:04,230 --> 01:25:06,030 So would you ever run into issues 1843 01:25:06,030 --> 01:25:08,604 with communicating with the public? 1844 01:25:08,604 --> 01:25:11,020 GABRIEL SANCHEZ-MARTINEZ: Green Line, especially in peaks, 1845 01:25:11,020 --> 01:25:15,230 high frequency, not running very reliably, anyway. 1846 01:25:15,230 --> 01:25:18,610 So I don't know anyone that looks at the schedule. 1847 01:25:18,610 --> 01:25:20,807 Maybe very early in the morning, but I don't know. 1848 01:25:20,807 --> 01:25:22,390 Maybe late at night, but I don't know. 1849 01:25:22,390 --> 01:25:24,431 AUDIENCE: I've totally used Green Line's schedule 1850 01:25:24,431 --> 01:25:25,180 late at night. 1851 01:25:25,180 --> 01:25:25,840 GABRIEL SANCHEZ-MARTINEZ: Late at night. 1852 01:25:25,840 --> 01:25:27,714 Yeah, late at night, I think it would happen. 1853 01:25:27,714 --> 01:25:30,422 But I don't think that during the day it would happen. 1854 01:25:30,422 --> 01:25:32,130 And what happened with this late at night 1855 01:25:32,130 --> 01:25:33,754 is that the schedule is reliable enough 1856 01:25:33,754 --> 01:25:36,570 that the even headway times are the scheduled times, anyway. 1857 01:25:36,570 --> 01:25:37,820 So there's no issue with that. 1858 01:25:37,820 --> 01:25:41,170 AUDIENCE: So would there be an issue in terms of applying this 1859 01:25:41,170 --> 01:25:43,122 to a more robust system? 1860 01:25:43,122 --> 01:25:45,580 GABRIEL SANCHEZ-MARTINEZ: We learned a lot from this pilot. 1861 01:25:45,580 --> 01:25:50,350 And I think whoever implements the next rail system will 1862 01:25:50,350 --> 01:25:52,360 have to rejudge his thesis. 1863 01:25:52,360 --> 01:25:55,900 Because there's so much that we learned, about compliance, 1864 01:25:55,900 --> 01:25:59,030 about issues with data. 1865 01:25:59,030 --> 01:26:00,370 I recommend reading it. 1866 01:26:00,370 --> 01:26:01,080 Eli. 1867 01:26:01,080 --> 01:26:02,996 AUDIENCE: Can you explain how it's determining 1868 01:26:02,996 --> 01:26:04,570 the headway that it should be? 1869 01:26:04,570 --> 01:26:05,530 GABRIEL SANCHEZ-MARTINEZ: It's even headway. 1870 01:26:05,530 --> 01:26:06,550 AUDIENCE: It's just maintaining event. 1871 01:26:06,550 --> 01:26:07,592 It's not like optimizing. 1872 01:26:07,592 --> 01:26:09,341 GABRIEL SANCHEZ-MARTINEZ: No optimization. 1873 01:26:09,341 --> 01:26:11,350 It's a very simple even headway strategy. 1874 01:26:11,350 --> 01:26:13,360 Prediction of the time it takes this train 1875 01:26:13,360 --> 01:26:16,720 to reach the next one, prediction 1876 01:26:16,720 --> 01:26:18,430 of the time it takes the trailing train 1877 01:26:18,430 --> 01:26:20,860 to arrive at the terminal, and then 1878 01:26:20,860 --> 01:26:26,740 using those to calculate the headways, essentially. 1879 01:26:26,740 --> 01:26:28,720 And then determining the holding time 1880 01:26:28,720 --> 01:26:30,850 to keep that train the middle and then 1881 01:26:30,850 --> 01:26:34,610 adding some constraints to prevent excessive holding. 1882 01:26:34,610 --> 01:26:38,290 Also to prevent-- if there was a long gap, 1883 01:26:38,290 --> 01:26:41,200 you might want to not hold the second one too much. 1884 01:26:41,200 --> 01:26:45,010 Send those together. 1885 01:26:45,010 --> 01:26:46,260 Here's something interesting. 1886 01:26:46,260 --> 01:26:47,620 Here's a space-time graph. 1887 01:26:47,620 --> 01:26:49,450 Time horizontal. 1888 01:26:49,450 --> 01:26:54,250 Green here shows compliance and red shows non-compliance. 1889 01:26:54,250 --> 01:26:56,290 So the first thing we see is that when 1890 01:26:56,290 --> 01:27:00,450 there's a lot of green, those lines are nicely evenly spaced. 1891 01:27:00,450 --> 01:27:01,440 So that's good. 1892 01:27:01,440 --> 01:27:04,690 That's the lower coefficient to variation. 1893 01:27:04,690 --> 01:27:07,167 When you see red, you see some bunching later on. 1894 01:27:07,167 --> 01:27:08,500 That doesn't happen immediately. 1895 01:27:08,500 --> 01:27:09,520 And it's slight. 1896 01:27:09,520 --> 01:27:12,070 Notice how slight the deviations can be. 1897 01:27:12,070 --> 01:27:15,060 But you see the effects of the dwell time effect 1898 01:27:15,060 --> 01:27:16,750 and the crunching happening. 1899 01:27:16,750 --> 01:27:19,000 The other thing that happens is that they have someone 1900 01:27:19,000 --> 01:27:21,450 controlling at reservoir. 1901 01:27:21,450 --> 01:27:24,370 So they have someone stationed there holding trains, 1902 01:27:24,370 --> 01:27:27,050 keeping them evenly spaced, more or less. 1903 01:27:27,050 --> 01:27:30,285 And which trains are being held? 1904 01:27:34,060 --> 01:27:37,210 The ones that are not as green, right? 1905 01:27:37,210 --> 01:27:41,050 So you've sent a train that might be full of people. 1906 01:27:41,050 --> 01:27:42,840 And you've decided that you somehow 1907 01:27:42,840 --> 01:27:44,860 need it to depart a little bit earlier 1908 01:27:44,860 --> 01:27:46,360 than the algorithm said. 1909 01:27:46,360 --> 01:27:51,790 And then you wait till you fold to them and hold two minutes. 1910 01:27:51,790 --> 01:27:55,750 You could have avoided that by having left a little later 1911 01:27:55,750 --> 01:27:56,540 from the terminal. 1912 01:27:56,540 --> 01:27:58,636 AUDIENCE: They're never hold at Fenway? 1913 01:27:58,636 --> 01:27:59,950 Fenway seems to-- 1914 01:27:59,950 --> 01:28:01,160 GABRIEL SANCHEZ-MARTINEZ: No. 1915 01:28:01,160 --> 01:28:04,910 No, just long hold times. 1916 01:28:04,910 --> 01:28:08,320 So that's the end. 1917 01:28:08,320 --> 01:28:10,600 Sorry for being a few minutes late. 1918 01:28:10,600 --> 01:28:14,070 If you have questions on holding or real-time control, 1919 01:28:14,070 --> 01:28:15,640 let me know. 1920 01:28:15,640 --> 01:28:18,540 Next lecture is on fare policy.