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GABRIEL SANCHEZ-MARTINEZ: Great.
OK.
So today's lecture is on transit service reliability.
This is my penultimate lecture, because we
have guest lecturers, too.
So let's start out with what is reliable transit for you.
What do you think of when you think of reliable transit?
What does it mean for you?
And I'll write a few videos on the board.
[CHALK ON BLACKBOARD]
[INAUDIBLE]
AUDIENCE: Arrival at or close to scheduled arrival.
GABRIEL SANCHEZ-MARTINEZ: OK.
Low variance, OK, of--
there's a word for that.
Punctuality, right?
So let's use that.
Just because it's hard to write on the board with chalk.
It's hard to spell correctly, actually, when
you're close up to the board.
Emily.
AUDIENCE: Lack of disruption.
So it's the same service every weekday.
GABRIEL SANCHEZ-MARTINEZ: And you kind of got two of them.
Lack of disruptions is one of them
and you said the same service, right?
So I guess predictability.
Great.
AUDIENCE: The word legibility, which
is that you sort of know where transit is going
and it makes sense.
GABRIEL SANCHEZ-MARTINEZ: You called it legibility?
AUDIENCE: Legibility.
GABRIEL SANCHEZ-MARTINEZ: OK.
That's coining a new term there.
AUDIENCE: Well, yeah.
It's coining a new term.
GABRIEL SANCHEZ-MARTINEZ: You had one.
AUDIENCE: Oh, not in the US.
[LAUGHTER]
GABRIEL SANCHEZ-MARTINEZ: [INAUDIBLE]..
I appreciate the humor, though.
Any other ideas?
AUDIENCE: Maybe the quality of the ride
is always the same, like tables are clean.
GABRIEL SANCHEZ-MARTINEZ: Consistent quality.
AUDIENCE: Yeah.
It's always possible to enter the car.
Surrounding is consistent.
GABRIEL SANCHEZ-MARTINEZ: Sufficient capacity.
Actually.
AUDIENCE: I think it also has to cover all the places
you want to go in like a 90--
some kind of percentile of what you want to travel,
so you're not getting a car [INAUDIBLE] or something.
GABRIEL SANCHEZ-MARTINEZ: Yep.
And so that includes [INAUDIBLE] coverage, which is spatial,
and also span of service, right, which is the same thing
but temporal.
[WRITING ON BOARD]
OK, these are some good ideas.
AUDIENCE: I have a real--
GABRIEL SANCHEZ-MARTINEZ: Sorry?
AUDIENCE: I said I have a real one now.
Consistent fare structure or--
GABRIEL SANCHEZ-MARTINEZ: OK.
That's usually consistent.
Are you thinking of a particular example?
AUDIENCE: I think of just when places where
the price keeps rising often.
GABRIEL SANCHEZ-MARTINEZ: OK.
I'll say-- I don't know.
AUDIENCE: [INAUDIBLE] transfers [INAUDIBLE] confusing.
GABRIEL SANCHEZ-MARTINEZ: Good communication
of fare policy, so a clear fare policy.
AUDIENCE: Sure.
GABRIEL SANCHEZ-MARTINEZ: Yeah.
[WRITING ON BOARD]
Eli.
AUDIENCE: I feel like we haven't worked
in maintenance of headways and high-frequency service in here.
GABRIEL SANCHEZ-MARTINEZ: Sure.
AUDIENCE: It's kind of covered by punctuality
and predictability--
GABRIEL SANCHEZ-MARTINEZ: Right.
But it's a little different.
And we're going to talk a lot about that today.
So let's add that in.
So even headways?
AUDIENCE: Yeah.
You wouldn't say short headways.
That's not necessarily part of the liability.
AUDIENCE: Well, it seems like we're sort of actually
expanding the traditional definition for liability here.
GABRIEL SANCHEZ-MARTINEZ: Yeah, we have been.
I'm not filtering too much out because--
I guess we'll stop here.
The point I wanted to make is that--
I'll come back to this in lecture--
reliability means a lot of things to different people.
And doing all these things can be difficult.
So we're going to talk about some aspects.
We're going to focus more on punctuality, lack
of disruptions, predictability.
We'll talk about common equality in system.
That has to do with even headways.
We're not going to talk so much about fair policy, or coverage,
or span of service, or legibility.
All right.
So right.
So impacts of unreliability, the causes
of unreliability, how to measure unreliability
or reliability, and then real-time control strategies.
We've mentioned some of these topics before.
Now let's focus on these things.
OK, so passenger impacts.
What happens when service is unreliable?
We have longer waiting times, right?
We have the need to have a longer reliability buffer.
So have we talked about reliability buffer
before in this course?
No?
So if your trip to--
we're going to talk more about it later than we will here.
But if your trip to--
[WRITING ON BOARD]
OK, so you know that running times are stochastic, right?
So there's a distribution of running times.
So this is running time, or in this case let's
call it journey time.
And this is a probability [INAUDIBLE],, right?
So the schedule has to have a single intrinsic value.
And you can go to your journey planner,
and it will say your journey takes this long.
You walk this much time, you wait this much time,
you arrive at this time.
So you add those components up and you have a specific time.
That specific time may be close to the median, and may not.
So if service is reliable, then there's
little variance in this distribution, correct?
So you might have--
I don't have much of another color here.
That doesn't work.
So I'll just write on white as well.
Maybe a dot.
So you might have one distribution of journeys
that has lower variance.
And therefore you need to budget less time to make your trip
and arrive on time.
Correct?
So to the extent that the waiting is
variable or your in-vehicle time is variable, then
if you need to be at work or at school at 9:00 AM,
that means that, even if on average it takes half an hour,
you might have to budget for 45 minutes.
So the extra 15 minutes of time that you budget, that's called
the reliability buffer.
It's a cost.
You could monetize it if you wanted to.
It means that people are budgeting, and in some cases
wasting, that time.
And we want to decrease that.
So the need for trip time reliability buffer.
Higher loads.
So that means, of course, that vehicles
have more people in them, and therefore rides
are more uncomfortable for passengers.
And they are also slower, because if a vehicle has
more people in it, the bus stops more often
and the process is slower.
We know that from earlier lectures.
We know from random incidents that from a passenger
perspective, passengers will experience
more crowded vehicles because they
are more likely to board the vehicle
where there are more people in it.
It's a little bit of a chicken and egg problem.
So even if, on average across the vehicles,
your loads are right where they should be,
most people are going to be on the more crowded vehicles.
So that's that thing.
In terms of agency impacts can increase costs, making,
for example, you need a longer recovery time at the terminal.
And therefore, you know that that translates
to higher vehicle costs, higher crew costs, reduced ridership
and revenue, reduced operator morale, a public
and political problem.
What do we mean by that?
What happens when public transportation
is unreliable in terms of politics?
AUDIENCE: The public hates it.
Public hates unreliability.
GABRIEL SANCHEZ-MARTINEZ: Sure.
AUDIENCE: It creates pressure.
The forces against public transportation grows stronger.
GABRIEL SANCHEZ-MARTINEZ: Sure.
So--
AUDIENCE: [INAUDIBLE] funding, and then--
GABRIEL SANCHEZ-MARTINEZ: Yeah, so there's a funding, right?
And we'll talk more about this in the last two lectures.
So when public transportation is unreliable,
sometimes governments are hesitant,
or the public may be hesitant, to fund it more
before they fix the problems.
But fixing the problems might require some resources.
So it's a vicious cycle.
And then reduced effective capacity.
And we'll show a real example here in Boston of that.
All right.
So what causes this?
We can divide causes into external and internal causes.
External causes.
Traffic, demand-- demand variability in particular--
incidents.
So a passenger may get sick.
These things are external.
The agency knows that they could happen,
but there's not much you can do about them.
Internal causes are in the control of the agency,
at least a little more.
So equipment failure, that's something that agency owns.
Maybe you can't predict exactly when it will happen,
but with some preventive maintenance
they could reduce the chance of this happening.
Insufficient resources, poor operations planning,
lack of supervision and control, and human driver behavior.
What do I mean by human driver behavior?
How does that cause unreliability?
Henry.
AUDIENCE: The way that a driver drives can vary
and that affects runtime.
Or maybe some are more aggressive and some are less.
GABRIEL SANCHEZ-MARTINEZ: Yes.
Some drivers are slow, some drivers are fast.
And then if you're running high-frequency service,
they'll bunch up.
And that could be the cause of bunching.
Or maybe that fast driver is now running early, rolling
a long headway service early.
And that's really bad for waiting time, as we'll see.
So if we think about transit, and look
at the whole process of planning it and delivering it
as if it were a business process,
we know that we start with service planning,
and move on to operations planning,
and then actual operations.
And each of these things, the output of one
is the input to the next process, and so forth.
The input to service policy, among them are
is demand estimation.
Then we bring in analysis of models or vehicle scheduling
and crew scheduling.
And during operations there's service control.
We'll talk about service control, real-time control,
too, as an input to operations, to make them more reliable.
So there's also a feedback loop, because passengers
might complain or somehow you have data collecting
information on performance.
And you can take that back to service planning or operations
planning, or you could modify your service control
to change the cycle.
And here we have the key agents in each of these steps.
So transit agency management, mostly
taking care of service policy.
Then you have some operational planning stuff,
taking care of operations planning.
And then the actual drivers and inspectors out in the field.
So I guess one thing to take away
from this is that there are many decisions across all
of this process that affect reliability.
And you can't really have reliable service if you--
there's many places where you could--
a cause on reliability.
One of them might be your vehicles break down.
So no matter what you do, if your fleet
is old and having difficulty with maintenance,
you might have the best service control
policies, and all the supervision in the world,
and you still have unreliable service.
So it's a hard problem.
It used to be very hard, actually,
because, well, to ensure reliability you
need to ensure the variability and things.
So you know from data collection that if you
want to measure the mean, you can calculate your sample size.
Measuring the variance of something
requires an even greater data collection effort.
So things have gotten a lot easier with technology.
And so we know that we have several data collection
systems--
AVL, AFC, APC.
That makes it a lot easier and cheaper to measure reliability.
We'll give some examples.
Then we have scheduling systems, which
make it very easy to make an adjustment in the schedule.
If we see that we've not scheduled enough time
for this bus, we need to add some recovery
time, that's going to increase the fleet size by one.
With a program or scheduling software,
you can do that quickly and react.
And the best systems will actually read AVL data in,
and you don't even have to manually analyze it.
You can sort of use the program to analyze it.
And the same program will help you schedule.
And then there's improved communications technology,
which makes it easy to communicate instructions.
Hey, depart a little later from this stop,
or from this terminal.
Don't, you know, start running without passengers.
And start operating in revenue service three
stops down because we have a long gap.
So you may have heard, you can't really have control--
there are so many ways of saying things,
but you can't really do something about something
until you measure it.
So measuring it is important.
We'll talk a little bit about reliability
as a performance metric.
And there are different key performance indicators
you can calculate for reliability,
and that's the first step.
You want to measure it and you want
to be able to track your reliability
for particular routes or system wide,
and then be able to change a policy, see what the effect is.
So one thing about it is it's not
the only thing that matters.
Reliability is important.
It would be a mistake not to measure it.
Because you might have a very productive service,
but you might have all of these problems that we identified.
On the other hand, if you put too much focus on reliability,
then it would come at a cost.
If you want to make your schedule very reliable,
then you can add a lot of recovery time.
And you could add many timing points
and make the buses hold everywhere,
and that would slow service down.
It would increase journey times.
Even if they would be very predictable,
they would be very long, and that could deteriorate service.
So we make a distinction between reliability on low frequency
service and reliability on high frequency service.
What's the difference?
We've talked about the waiting strategies
for low and high frequency.
We've talked about it several times before.
[CHUCKLES]
What's the difference between a service that runs every 20
minutes and a service that runs every five minutes with regards
to your strategy to take that service?
AUDIENCE: It's more frequent and you can just walk up.
GABRIEL SANCHEZ-MARTINEZ: OK, so high frequency service
is walk-up service.
AUDIENCE: No random arrivals.
GABRIEL SANCHEZ-MARTINEZ: Right.
The arrivals tend to be random.
They don't actually have to be for this distinction
to be valid.
They have to be independent of the vehicle arrivals.
AUDIENCE: [INAUDIBLE]
GABRIEL SANCHEZ-MARTINEZ: Yes.
Yes, we'll mention that.
So with low frequency service, most people
will time their arrival at stops so that they
are with the schedule.
So if vehicles are arriving on schedule,
and passengers are arriving on schedule,
people wait very little time.
And if there's very little variability in that,
if service is incredibly punctual,
people would show up the minute before and wait almost nothing.
If there's some variability, then people
have to add some reliability buffer time.
So even though it says it's going to come at 3:53,
you might have to get there at 3:50.
OK.
So you then can set--
because you want to measure reliability, people--
especially in the US, we call that on-time performance,
which is a long way of saying punctuality.
You could have different wait threshold windows.
And we've talked about performance measurement before.
We're just here, so we're going back to specifically
reliability.
One way would be to say, any bus that
departs this stop between one minute early and five minutes
late is on time.
And any bus outside of that window is not on time.
And then you say, I am 90% reliable.
This bus leaves that stop 90% of the time within that window.
And then you could have tighter windows.
You could say, not early and up to three minutes late,
or not early and up to one minute late.
Of course what happens--
well, let's start with the first one.
What's wrong with the first one?
What's different about the first one?
You allow early departures.
What's bad about early departures when you
have a long headway service?
AUDIENCE: People aren't expecting it
and they miss their bus.
GABRIEL SANCHEZ-MARTINEZ: Right.
So if people are really timing their arrival at the stops
according to the schedule, and it's 20-minute headway service,
bus leaves early.
You arrived a minute early.
Now you have to wait 20 minutes.
It's really bad.
Really bad.
This thing is a little--
real-time apps help with this, but not everyone has one.
And if service tends to be reliable,
and every now and then it isn't, then people might still have--
they're trying to show up to work on time.
So there's not much the app can do unless there's
a good warning ahead of time, this bus
is going to come early.
You'd better be there.
So you have to rush to get ready.
OK.
So it's good to not allow early departures.
What happens when you move to tighter
bounds on the late side?
Two things happen.
AUDIENCE: Harder to meet it.
GABRIEL SANCHEZ-MARTINEZ: So it's harder to meet.
And that means that your reported reliability
comes down.
So you can imagine, internally, a pressure on the agency
to have a little more slack, to say that you
have higher reliability.
What happens in terms of performance,
or in terms of waiting time, benefit for the passenger?
If the agency actually has a holding policy that prevents
a bus from departing late--
more than five minutes late, more than three minutes late,
more than one minute late--
from a stop in the middle of the route with people
inside of it, what happens is you move to tighter windows.
AUDIENCE: The driver will be less
lenient in holding the bus for people running after it?
GABRIEL SANCHEZ-MARTINEZ: Especially if you're--
right, tighter window on the early side, more holding.
AUDIENCE: Like, sorry, we've got to go.
GABRIEL SANCHEZ-MARTINEZ: Yeah.
So how do you make the bus not be late?
What's the strategy for that?
AUDIENCE: You schedule in more--
GABRIEL SANCHEZ-MARTINEZ: You don't schedule for median.
You schedule for a higher percentile.
So now it's easy, piece of cake.
You schedule it for 80 percentile, only 20%
of the time will you be--
OK, but what happens?
That means that 80% of the time you're arriving early,
so you have to hold.
So as you make that window tighter,
it means that you're probably going to be
setting your percentile higher.
And it means that you'll be holding more often
and slowing service down.
And holding is very frustrating for passengers.
So you shouldn't hold always and for a long time.
And in general, I guess one other comment is
like any kind of window, especially on the later side,
the benefits of going from five to three to one minutes
are going to be marginal in terms of waiting.
And they can be substantial in terms
of how often you'll have to hold it
and how slow the service will be.
AUDIENCE: I'm sorry.
Why is holding more often if you're--
GABRIEL SANCHEZ-MARTINEZ: If you have a tighter window.
AUDIENCE: [INAUDIBLE]
GABRIEL SANCHEZ-MARTINEZ: So if you have a tighter window--
if your vehicle must depart between zero minutes early
and one minute late, it's a very tight window, right?
So how can you guarantee that that vehicle departs
that stop in the window?
You have to schedule it such that it almost always arrives--
you have to allow a lot of time on the schedule
so that almost always it can arrive,
and it's not arriving one minute late.
AUDIENCE: Ah, all right.
[INAUDIBLE] time.
So you're--
[INTERPOSING VOICES]
GABRIEL SANCHEZ-MARTINEZ: So you control the late side
by scheduling more time.
And then what happens on the early side?
On the early side, if you arrive early, you--
AUDIENCE: You just sit there.
GABRIEL SANCHEZ-MARTINEZ: You have to sit there.
OK.
So in long headway service, or low frequency service,
there is a little interaction between successive vehicles,
so bunching is not a normal thing.
So we'll talk about bunching in the context of high frequency
service.
And then, of course, real time information is changing this.
So now you have an app.
And your app, as you're doing your breakfast, phone vibrates
and says, here's the time.
Here's my predicted time.
So you rush.
Maybe you'll skip something on breakfast or you'll--
I don't know.
So that is very poorly understood
from a research standpoint.
We don't really know how exactly that happens,
what percentage of people are actually changing when they
would arrive based on the app.
And we don't really know what the implications are.
Because you can't just say--
imagine if everybody had an app, and everybody used that app.
And you're running 20-minute headway service.
Now you say, well, everybody is going
to show up to time the arrival at the stop.
So let's not worry at all about reliability.
It doesn't matter when vehicles come because people know
and they time their arrivals.
So now we can speed up service.
But there is some sense of convenience of knowing
that it runs every 20 minutes.
The availability of service every 20 minutes
is a factor that wouldn't be considered if you did that.
So in some way, it is still important
even if people can time their arrival at stops,
to keep service as scheduled when it's long headway.
And we don't really--
how do you measure that?
How you quantify that convenience, that coverage?
All questions for researchers.
AUDIENCE: So is there--
for this time window, is there a defined threshold
to define something that is a very tight time frame?
Like median, long, and tight time frame for this?
And when does it matter?
Because obviously, tight is different in the mornings
when you have [INAUDIBLE].
GABRIEL SANCHEZ-MARTINEZ: This is-- that decisions are up
to the agency?
AUDIENCE: It's up to the agency.
GABRIEL SANCHEZ-MARTINEZ: Yeah.
And usually there's a trade-off where
you want to set a goal that is attainable.
You don't want to be reporting 30% reliability.
So it's a bar that moves according to the abilities
of the agency, usually.
That's what happens in practice.
If there are no more questions on low frequency service,
let's move to high frequency service.
A little more interesting.
Do you have a question?
AUDIENCE: Yeah.
What's the cut off there between high frequency
and low frequency?
GABRIEL SANCHEZ-MARTINEZ: Good question.
So what do you think?
[INTERPOSING VOICES]
That is a good point.
He said it depends which country you're in.
That's a very legitimate observation.
So it's not just US and non-US.
It's--
[INTERPOSING VOICES]
AUDIENCE: Urban, rural.
GABRIEL SANCHEZ-MARTINEZ: Here in the US,
here in Boston, what would you consider
to be high frequency service?
AUDIENCE: Up to 10-minute headways.
GABRIEL SANCHEZ-MARTINEZ: 10 minutes?
AUDIENCE: Up to 10 minutes.
AUDIENCE: Yeah, certainly not more than that.
GABRIEL SANCHEZ-MARTINEZ: If it's 12 minutes,
do you look at the schedule?
AUDIENCE: Yeah.
AUDIENCE: Yes.
GABRIEL SANCHEZ-MARTINEZ: OK.
All right.
AUDIENCE: [INAUDIBLE] divides it as 15 and [INAUDIBLE]
going up to 16 and 17.
GABRIEL SANCHEZ-MARTINEZ: So yeah, some agencies say 15.
In London, I think it's 12.
I think that's the cutoff.
Now, if you go to Chile and you say
that you're running 10 minute, they
think of that as long headway service-- very long.
Because they have buses that run every minute.
So that's high frequency, and seven minutes is low frequency.
So that's a distinction, at least
from an operational standpoint, that people make differently
in every country.
But in terms of waiting time strategy,
I think it still holds that it's somewhere between 10 and 15.
Maybe between 8 and 15.
We don't know.
Obviously, there's a continuum.
It's not like everybody switches at exactly some threshold.
It depends on the person, and what technology they have,
and what service they're taking.
Between those 8 and 15 minutes, or even 12 minutes,
there's going to be a transition from one strategy to the other.
And you know that when you're well in the high frequency
zone, your models of random, or at least independent,
arrivals of passengers at stops hold.
Whereas as you move towards 15 and longer, they stop holding
and you shouldn't be measuring waiting time like this.
AUDIENCE: I was asking that because, even
with 10 minutes, which is considered high frequency,
I still want to schedule myself for when I'm
going to get to the bus stop.
I'm not just like, oh, let me just walk to the bus stop
and I'll wait.
GABRIEL SANCHEZ-MARTINEZ: So for 10
minutes, do you actually consult the schedule?
AUDIENCE: Well, I consult the app for 10 minutes.
GABRIEL SANCHEZ-MARTINEZ: But do you
plan to take the 9:10 train?
Or-- you see, there's a distinction, like the day
before, you know I'm going to take the 9:10
AUDIENCE: If they were running clock-based, consistent
10-minute headways, then I would.
GABRIEL SANCHEZ-MARTINEZ: Then you would show up.
AUDIENCE: Yeah.
Yeah.
But they're not.
GABRIEL SANCHEZ-MARTINEZ: So for you,
10 is right there on the fence between the two, it seems.
More on the scheduled side, on the high frequency side,
perhaps.
AUDIENCE: Yeah.
GABRIEL SANCHEZ-MARTINEZ: OK.
But let's say that it's five minutes.
So now we're clear on that vague area.
So now you're in a zone where most people will
time their arrivals at stops-- sorry, will not
time their arrivals at stops.
They will show up when convenient.
And they expect to wait about half of the headway.
You know that if the headways are variable,
you're going to have that waiting time increasing.
So there's going to be a reliability buffer time
calculation that you can do.
And it's going to be the coefficient variation
of headway, will sort of affect.
That's the factor that sort of increases the expected waiting
time.
Punctuality is not as critical for the passengers.
They don't really care if every train
is five minutes late, as long as they
come in every five minutes.
It doesn't really matter that they're all five minutes late.
So really, what matters for a passenger
is bunching and long gaps.
We've talked about that before.
We know that in high frequency service,
there is a lot of vehicle interaction.
We can maybe review it quickly.
Think of this as a bus route.
And here's a vehicle.
Each of these are vehicles.
And there's a random arrival process.
Passengers are arriving randomly at the different stops.
So what happens when vehicles are not evenly spaced in time,
not in space.
So what happens when they're not evenly spaced?
AUDIENCE: The one that's close to the next one picks up less?
GABRIEL SANCHEZ-MARTINEZ: OK, so this vehicle
has a smaller gap ahead of it.
And therefore, because people are arriving
at some rate, in that time, for that rate,
fewer passengers will be taking this bus.
And that means that real times are shorter.
Vehicle catches up.
So now you have a bunch.
Eventually this vehicle will catch up to this one.
If this vehicle, the one ahead of it,
has a long headway ahead of it, the opposite happens.
More people than average arrive, and then that vehicle
has many more people in it.
The loads increase.
It slows down.
So those two effects work together to create bunching.
And we've talked about that.
And with bunching, the counterpart is long gaps.
You usually have a bunch and then a long gap.
Or a long gap preceding a bunch.
So you'll hear passengers complaining,
I've been waiting 15 minutes, and now three buses arrive,
as if that were ironic.
But that's actually exactly why it happens.
AUDIENCE: So what's the best strategy to deal with bunching?
GABRIEL SANCHEZ-MARTINEZ: We'll talk about many of them.
Yeah.
OK, so one observation is that some high frequency
routes have branches.
So they're only high frequency in the trunk,
and the individual branches are actually long headway.
And there, you have to run scheduled service
on the branches.
And then you have to, I guess, try
to run scheduled service on the trunk.
There might be some hybrid strategies,
but that's still the subject of research.
And of course, schedule control is much easier
than headway control.
You can do it without technology.
You can print a schedule, and the driver
can have the schedule in the vehicle.
And you can tell drivers, don't leave early.
And if they follow instructions, they won't leave early.
So if you want to control headways,
and you want to keep the vehicles evenly spaced,
now you need all this technology infrastructure
to detect where vehicles are, to predict the running
times between them, and to communicate instructions
to those vehicles so that the headways can be adjusted.
Here's a little reliability buffer time.
So let's talk about how to actually calculate it
in a high frequency, closed fare system.
So think of the London Tube.
You tap in the station, and then you tap out when you leave.
So you can measure the probability distribution
of travel time, or of journey time, from tap-in time
to tap-out time.
And we define the reliability buffer time
as the difference between the 95th percentile
and the 50th percentile of that journey time.
So again, if this distribution were much narrower,
then people would not have to budget that difference as they
plan to make a trip, to arrive at a certain time at work
or school.
Something interesting about this is
that London has somewhat recently started
refunding fares if people's journeys exceed
30 minutes of the expected.
So they're not doing it by percentile, but they--
so here's an application in fare policy,
which is not the most obvious one.
But you can certainly measure this reliability
of buffer time.
Yes, question.
AUDIENCE: Do you know how much it costs them?
GABRIEL SANCHEZ-MARTINEZ: No.
I don't think much.
Well, it is a lot in total.
AUDIENCE: [INAUDIBLE]
GABRIEL SANCHEZ-MARTINEZ: I don't remember
what percent of passengers.
I think the percent is quite low,
except if there's a big disruption it might be high.
But because of the sheer size of the network,
I'm sure that that adds up, too.
Yeah.
AUDIENCE: It's a good marketing strategy.
GABRIEL SANCHEZ-MARTINEZ: Yeah.
AUDIENCE: Builds confidence.
GABRIEL SANCHEZ-MARTINEZ: London, they
don't talk so much passengers.
They talk about their customers.
And they want to have customer service.
And so they like to have that internal mentality.
AUDIENCE: Well, how do they know someone wasn't dwelling
at a station as a passenger?
GABRIEL SANCHEZ-MARTINEZ: Because they
can look at other people doing that same trip.
So if somebody wants to hang out,
they're not going to get a free trip
just because they wanted to.
AUDIENCE: It's interesting.
In the daily metro, to prevent crowding,
if you spend too much time in the system,
they actually give you a penalty when you tap out.
And so some of the journeys are so long,
people actually have to rush to get out,
or else they suffer a [INAUDIBLE]..
GABRIEL SANCHEZ-MARTINEZ: Not very good reliability.
We can add that to the list.
Yeah.
AUDIENCE: How do they determine the expected journey time?
Is it median--
GABRIEL SANCHEZ-MARTINEZ: They look at this--
so they measure this.
And I'll show you the next slide.
Before we move on to the next slide,
any other questions on this one?
I saw several hands raised.
OK.
So they look at good days and bad days,
to answer your question.
So they pick some baseline of days
that have no major disruptions, service is running well.
It's the amount that they expect.
And then they'll measure reliability buffer time
on those days.
So that is an amount that they say
is sort of inherent to the operation
and not much under their control, unless they invest
in better signaling systems or things like this.
Anything in excess of that, if you look at,
now, all days together, will be something
that they could have avoided.
That's the idea.
This distinction between the baseline buffer time
and the access buffer time.
So if that x as buffer time exceeds some amount,
you can then say, well, we have a problem.
Passengers were taking much longer than we scheduled for,
or that we thought they could take, and therefore
let's refund the fare, because it was bad service.
AUDIENCE: This is for [INAUDIBLE] on the Victoria
Line?
GABRIEL SANCHEZ-MARTINEZ: Yes.
Northbound?
You mean this graph?
AUDIENCE: Mhm.
GABRIEL SANCHEZ-MARTINEZ: Yeah.
So northbound, southbound, yeah.
And the reference is right here.
David Uniman, 2009, so you can check it out in the library
if you're interested.
OK, so what happens when it's low frequency.
Now people are not arriving necessarily
to randomly or independent now.
They might actually be scheduling their arrival
to meet a particular train.
But of course, trains may not be running on schedule.
So you have this space-time diagram here.
We have time on the horizontal and space, or the stations,
on the vertical.
And you see that there is some degree
of variability in timing.
And if these vehicles were on time, maybe
they would be more evenly spaced.
So we have taps.
Here, there's a touch in at 8:00.
And so what we do is that we look at what's the next train?
When does that tap in aboard, and that's
how much they waited.
You're comparing to scheduled departure,
which is in this case 8:06.
So because the train--
I don't know if I'm explaining this clearly.
So you can match the tap-in time to the closest
scheduled departure that follows that tap in.
And that's the train that the person intends to board.
And that's how much the person intends--
the difference between those two times is the amount of time
that the person intends to wait or expects to wait.
Any waiting time beyond that is excess waiting time.
And then you're going to do the same for the in-vehicle time.
That's where [INAUDIBLE] and that's
how you get reliability buffer time.
So you're now considering the waiting strategy is different.
And here's the reference.
2010, another thesis.
For bus, there's another challenge.
Well, there's two challenges.
The first one is we need to distinguish
between the performance of the contractor,
if it's a private operator and you're paying the bus
company to run service for you, and the performance
as the passenger sees it.
So as it says on the bottom, if service is unreliable,
the passenger doesn't care why it's unreliable.
But the operator needs to know if it's
the fault of the operator or if it
was an external reason that was not
under the control of the operator.
Why?
Why is that important?
Henry.
AUDIENCE: If there is traffic, then there could likely
be traffic downstream, as well.
And you would continue to be on the line
for the remainder of the trip.
GABRIEL SANCHEZ-MARTINEZ: OK.
But you're thinking of a specific trip.
Because I'm thinking more generally.
So why would the agency want to distinguish
between bad performance that can be assigned or blamed
on the operator versus bad performance that is exogenous.
AUDIENCE: Because if the bad service
is due to some act of God, then the agency maybe
can't hold the contractor accountable.
But if the contract and service provider did something wrong,
then there can be some kind of punishment.
GABRIEL SANCHEZ-MARTINEZ: OK, yes.
And in this case, a punishment under the contract
might be a penalty.
So they might withhold some-- if there's a performance bonus,
maybe the operator does not get that bonus
when there might be actually provisions for a penalty.
Or a discount on the payment.
And it doesn't have to be an act of God.
It can be normal traffic.
And the variability in travel times
that is expected because of traffic
that is not under the control of the operator.
But what if the operator is not maintaining his buses
and some vehicles have to be put out of service?
So the operator drops trips and now performance is not as good.
That is very clearly the fault of the operator,
and you want to penalize the operator.
So that's one challenge.
So you have to measure reliability,
but you might have to assign its sources.
You might have to calculate the sources of those
and sort of assign cost codes to whatever you measure.
And there might be a mix.
The other challenge is that typically, buses are only
tap on and not tap off.
So you have to--
journey time includes the in-vehicle portion.
So now you have to figure out where
this person alights to figure out the in-vehicle component.
And waiting time is another portion of this,
and the passenger doesn't tap in until they
have finished waiting.
So you have to go back and calculate, how long did they
wait?
So those are two minor challenges.
Here's a strategy.
For destinations, we have ODX.
So we can look at their next tap in.
We can do trip chaining, as we discussed previously,
and infer the destination for that person.
And for some people that will fail,
but we can scale up in probability.
We can say, well, if this person didn't have a next tap,
let's look at the distribution of passengers
who do have an next tap and let's
assume that these other people have destinations
that are in proportion--
distributed in the same way as people
who have destinations inferred.
And then from AVL, we can sort of do the same trick
that we did for rail.
We can assume that there is some process by which passengers
arrive at stops.
So if it's high-frequency bus service,
we say it's some arrival rate.
If it's low frequency service, we
say they arrive on time to match the schedule.
And then we can compare that with actual vehicle times.
So if we have an assumption about when
the passenger arrived, then we can calculate the difference
and measure the waiting time.
So it's more stochastic because we
don't know exactly when this person arrived.
But in probability, you know that in aggregate,
across all passengers, any one person arrived
between this bus and that bus.
So yeah.
Questions about this process for measuring journey time
reliability?
Comments?
AUDIENCE: One man complained about waiting time, it's
like with the bus.
Like, oh, with the scheduled bus,
if the person only waits one minute, that's great.
But if I'm waiting at my desk for eight minutes,
I actually was--
GABRIEL SANCHEZ-MARTINEZ: So that it
goes back to the discussion about apps
that we had just a few minutes ago,
that you can't just say that because there are apps,
then we can just run service unreliably
if it's long headway.
AUDIENCE: Yeah.
GABRIEL SANCHEZ-MARTINEZ: So if it's high frequency,
you probably won't care.
You'll just still go.
Or you'll be timing it, but you would have arrived randomly,
anyway, to some extent, i.e. your intention
to begin the trip is random, or at least independent
of the schedule.
But if it's long headway service, then yes,
you maybe stay at your desk or get a cup of coffee.
But you're still inconvenienced.
And so there's a penalty for it.
AUDIENCE: Right.
GABRIEL SANCHEZ-MARTINEZ: And we need to figure out
how to measure it.
And one way is to assume that people still arrive,
or want to arrive, on time.
And that's what we've been doing because that's what we
used to do, and kind of works.
But it's slightly different.
AUDIENCE: So how do you use the stochastic process
to estimate wait time?
GABRIEL SANCHEZ-MARTINEZ: Yeah.
So let's-- another timeline.
So in this case it's a timeline, not a space line.
So let's say that there's a tap at that time.
And the buses are arriving here, here, here.
Sorry.
Well, the tap has to be when the bus arrives,
or very close to it.
Because the person is tapping in at the bus.
So what you know for this person,
assuming that this bus isn't full,
is that that person arrived as late
as exactly when that vehicle arrived,
and as early as this vehicle.
So you know that the arrival time
of that person and the time at which they began waiting,
is a stochastic variable with a uniform distribution
on that range.
And you know the mean of that distribution
is half the headway.
So if the bus arrivals are high frequency
and the person is arriving randomly,
then this is certainly true.
If it's long headway service, then you
have to then consider what the scheduled times were.
So now you have to do a process similar to what
we did for rail, where--
let me just draw it here.
So if this bus was meant to arrive here,
then maybe you say, well, this person
must have been wanting to get on that bus.
And so you made them wait some extra time.
And then if this bus was scheduled to depart here,
then you know that bus was early.
So that means that some of the people that end up
tapping in here were probably trying to get on this bus
and they missed it.
Because they arrived between this and this time--
between the actual and the departed time.
So those are the people who suffer the most.
And that's more difficult to calculate.
You might have to assume some proportion of the people
you see here.
You could compare to a typical load
and see if there's an excess, and assume
that that excess would have been on the previous bus,
if that bus had departed on time.
So you have to use more assumptions.
OK.
So we understand how to measure reliability for rail tap ins
and tap outs, long headway, short headway, and for bus.
So strategies.
So the question Eli had earlier was, what do we do about it?
Now we can measure it.
So if you can measure something, you do something about it.
What can we do about it?
So two kinds of things.
We can use preventive strategies and corrective strategies.
Preventive strategies are aimed at maintaining normal service
and having some robust operations plans that
can handle unreliability without having a domino effect,
where everything cascades into unreliability.
And that it reduces the probability
that problems occur.
Corrective strategies are you know,
you're monitoring the system, you see unreliability,
and you do something to the system at that time to fix it,
to make it more reliable and to minimize
the impact on passengers.
So examples of preventive strategies
are having reserve fleet of drivers and vehicles.
If a driver is sick, you have another driver
and you send that driver.
Vehicle is not operating, you have another vehicle.
Having exclusive bus lanes.
So if you have great separation, you
get rid of some of the unreliability that
comes from traffic.
Traffic signal priority-- sorry, that
should be transit signal priority.
We talked about that in our previous lecture.
There are route design strategies.
So we know.
We've seen that longer routes are more reliable because they
have more time between recovery time, between layovers,
essentially.
They have fewer stops.
So there's less of a dwell time unreliability effect.
You can make schedules that have a good amount of recovery
at the end.
So you look at the percentiles and you
make sure that you're not picking the average
to calculate your cycle times.
And you set the timing points at good percentiles.
Maybe it's the median, maybe it's the 40th percentile.
And of course, hiring supervisors
to make sure that your people are showing up
and they're leaving on time rather than whenever they want,
et cetera.
So it's schedules.
So two critical decisions-- the cycle time, we know about that.
We know that it impacts cost and the reliability of departure
time of the terminal.
And you're very familiar with that,
I think, by now, so I don't have to spend as much time
discussing it.
Timing points is another.
So you can, in the middle of a bus route, have timing points.
So we know that there might be a terminal here
and a terminal here.
And whenever a bus arrives at the end to be,
they then have a layover to catch up.
We know that from assignment one, even.
But you can actually have points in the middle
where buses are also not allowed to leave early.
And so if you schedule the times of these in some way,
then buses might hold more or hold less,
and they will depart those points on time.
Where should you put those timing points, if at all?
AUDIENCE: Inter-transfers?
GABRIEL SANCHEZ-MARTINEZ: OK.
So one idea is that if there's a big train station here
or another bus line that also runs--
especially for low frequency service--
and people want to connect, they need to transfer,
and they want to connect.
You might actually have a timing point for both routes
there so the vehicles meet and people can switch vehicles.
So that's one idea.
What else?
AUDIENCE: Maybe after a high variability section, like after
[INAUDIBLE]?
GABRIEL SANCHEZ-MARTINEZ: OK.
So maybe this lane has a lot of traffic
and it's causing a lot of unreliability.
So you want to take care of it there instead
of letting it cascade into more variable headways, for example.
What else?
AUDIENCE: High demand, those stations.
GABRIEL SANCHEZ-MARTINEZ: High-demand stations.
OK.
So what about demand?
Demand is important, but what exactly?
AUDIENCE: I mean, if the bus is reliable at that stations, then
the passengers--
GABRIEL SANCHEZ-MARTINEZ: What do you mean?
For example, a lot of people getting off from this bus
to take that station, or to enter that train station, or--
AUDIENCE: People are getting onto the bus at that station.
GABRIEL SANCHEZ-MARTINEZ: OK.
So right upstream of sections where there are many boardings.
That's a very important thing because that's
where most people benefit.
And what else?
What else about passengers?
Where would you not want to do this?
Harry.
AUDIENCE: When the bus is full?
GABRIEL SANCHEZ-MARTINEZ: When the bus is full.
So if your load profile looks--
I don't know.
A lot of people get on here.
And they're mostly not getting off.
And they sort of come down like that.
Do you want timing points on that bus route?
You don't.
You don't want timing points because most people are
getting on here and they don't want to be held here and here.
And very few people might be boarding in this section.
So if you hold a timing point, you're
going to benefit few passengers and penalize,
by longer and more frustrating vehicle rides, many passengers.
So what if there's a big transfer station here,
and a lot of people transfer, and then
here there's another station and a lot of people get on.
So then this is a good place to have a timing point,
right before a lot of people board
and when you don't have many people on the bus.
The flow profile is low.
AUDIENCE: [INAUDIBLE] liability before that [INAUDIBLE]..
GABRIEL SANCHEZ-MARTINEZ: Exactly.
So you want to maximize the segment of the population that
will benefit from the strategy and minimize
the segment of the population that
will be hurt by the strategy, i.e. people in the bus.
OK.
So that's a word about number and location of timing points.
And then the schedule at each timing point.
What should you set the percentile at?
Should this be the median?
Should they be 80 percentile?
Should they be 30 percentile?
AUDIENCE: The median realm.
GABRIEL SANCHEZ-MARTINEZ: So what happens if you--
how many vehicles will have to be held?
What percent of vehicles will have
to be held if you set it to 80th percentile?
AUDIENCE: Oh, 80%.
GABRIEL SANCHEZ-MARTINEZ: 80%.
OK.
So 80% of vehicles would be sort of getting here and waiting.
That may be acceptable if, again, very few people are here
and a lot of people are boarding.
What if it's more of a mix?
Then you want to bring that down.
You dial it down.
So some people say set the half cycle
to somewhere between 90% and 95%--
we've done that-- and then set timing points at 65.
I actually prefer that the timing points are below 50.
Because then you can advertise to your passengers.
You're essentially lying to people and saying--
you're motivating people to arrive earlier than, most
often, the vehicle arrives.
So their probability of arriving and missing
a vehicle that departed early is lower
because you're telling them, expect an early departure,
essentially.
Except you don't call it early.
You say that's when it's scheduled to arrive.
So essentially you can control this
by scheduling a certain way, and then on the other side
by controlling it.
AUDIENCE: But the pushback when people are like,
oh, the bus is always running late.
GABRIEL SANCHEZ-MARTINEZ: Yeah.
Yeah, so it affects--
there's a balance.
I'm not saying, schedule it 10th percentile.
But I think a little below 50 is a good strategy.
Because then you would minimize holding.
You would only hold vehicles that
are really early, essentially.
And holding is frustrating.
You don't want to be doing it all the time.
So by scheduling at a lower percentile,
you don't hold as often.
And you don't hold for as long times.
All right.
You have to be careful when you do this,
when you have timing points.
Because then your AVL data will come in,
and you're going to say, what's the running time?
Well, if people are following your instructions,
the minimum running time will be whatever
your timing points are.
So maybe your distribution would look like this.
But because you have timing points,
you've chopped off the early portion.
And now it looks more like this.
And now your 95th percentile is more to the right
than it used to be, maybe.
Maybe not.
Maybe it stays where it is.
But you have to be careful with this.
Your average will certainly move to the right.
So just be careful about that.
One strategy is to distinguish holding from running,
but that's a little difficult with AVL sometimes.
Another strategy is to run a month without timing points,
essentially instruct your drivers not
to use timing points, and collect data for a month,
and then use that for planning.
So just the things we can do.
OK, now corrective strategies.
So obviously, supervision.
Having supervisors, having an operations control practice
is important.
There's different strategies.
This is one of my favorite topics in transit.
So holding-- you can do holding to schedule or to headway.
So what is holding to schedule?
That's a simple one.
We've mentioned it a dozen times,
and even in this lecture.
You don't allow a vehicle to depart early from a timing
point or from a terminal.
So if a vehicle arrives a minute early at a timing point,
you instruct that driver to hold one minute.
Even though that bus is able to move on,
that bus holds for one minute.
TSP we talked about.
What's deadheading?
AUDIENCE: Just moving a bus from one place
to another that's not a revenue [INAUDIBLE]..
GABRIEL SANCHEZ-MARTINEZ: OK.
So let's say that you have buses here,
and this is your terminal.
And there's a bus that you are about to depart.
And your headway, the scheduled headway is more like this.
So you were supposed to have a bus here, but you didn't.
Something happened and the bus wasn't there.
And now you have two buses there instead of one.
Maybe there was a bunching on the way back
and the bunch arrived late, as it usually happens.
So one strategy that you can use is to take the first one
and instruct a deadhead to somewhere around here.
So this bus would run without its head sign
on, not allowing anybody to board--
and that's why it's called a deadhead--
to this stop.
And then this bus departs immediately,
but it remains in service.
So if that deadhead can happen quickly, maybe not even
following the streets or the bus,
maybe there's a faster way.
And you inject it downstream.
You can speed things up, you can balance the headways.
What's expressing?
AUDIENCE: Skipping stops?
GABRIEL SANCHEZ-MARTINEZ: That's one way of doing expressions.
Expressing can be done from the terminal.
So the distinction between expressing and deadheading
is that expressing them with people inside.
So in this case, you could have allowed people
to board at the terminal and then said,
we're going to run express.
You tell people who are boarding,
we're going to run express.
So if you're getting off anywhere between here and here,
don't board.
And the vehicle then skips stops, but with people inside.
So I don't think I need to do a drawing for this one.
Expressing can also be done halfway through.
So if you have this situation, then you
could say these people might have boarded, not
knowing that this bus was going to be expressed,
but something happened.
Maybe the driver was slow.
Maybe there was some traffic accident and there were delays.
So you can then announce this bus is being expressed,
or this train is being expressed,
and we're going to skip the following three stops
and arrive somewhere.
So if you're getting off before the express,
you have to decide, are you going
to stay and then walk back?
Are you going to stay and then take transit the opposite way?
Or are you going to get off right now
and wait for the next vehicle?
So it's a higher penalty for passengers.
What about short term?
We've talked about all of these, but in the context of planning.
And now we're using them for real time control.
So this is deadheading.
[WRITING ON BOARD]
Right.
And then yeah, so short term.
[WRITING ON BOARD]
Here's the situation.
You have-- this doesn't happen often, but it does happen.
You have a bunch in one direction
and a very long gap in the other direction.
And what happens with bunching?
The bus behind is usually not very full.
So you stop these buses and say stop.
And you tell the people here to move to the bus ahead.
Get off the bus.
We're in short term.
We're going to terminate the trip here.
And those people will have to transfer to the next bus.
If you don't allow this to happen,
then it's really onerous for passengers
because they have to get off and wait for the next one.
So it's better if you coordinate it this way.
And then this bus gets sent here and begins operating
in the opposite direction.
AUDIENCE: How much of this is done automatically
versus a person looking at this--
GABRIEL SANCHEZ-MARTINEZ: I don't know of any case
where this is done automatically.
There has been researchers here at MIT and elsewhere, including
me, who have tried to write algorithms that
detect these opportunities.
But I don't know of any real implementation.
London buses does this, or at least they used to.
I think they still do.
But they really try to coordinate this.
They very rarely curtail trips without coordinating
in a bunch.
Because then people have to wait for the next one.
AUDIENCE: [INAUDIBLE] as well.
GABRIEL SANCHEZ-MARTINEZ: Pardon?
AUDIENCE: The train systems [INAUDIBLE]..
GABRIEL SANCHEZ-MARTINEZ: Yeah.
Yes.
So in trains, it's more common.
But it's usually a person in a control center determining
that they want to do this.
AUDIENCE: What's stopping them from [INAUDIBLE] algorithms?
Is it that the algorithms are not good enough or--
GABRIEL SANCHEZ-MARTINEZ: That's part of it.
And then yeah.
I think I would say that's part of it.
The other is maybe a lack of interest
or a lack of faith in the computer.
There's a system in place.
It's just, you know, it's hard.
AUDIENCE: But there are two elements to this problem.
One is that you have to detect a problem in one direction.
And the other thing is that you have
to detect an opportunity in the other direction.
GABRIEL SANCHEZ-MARTINEZ: So this doesn't happen very often.
AUDIENCE: There are two parts here
that are completely independent from each other.
GABRIEL SANCHEZ-MARTINEZ: They're not independent,
though.
If the route is long you actually have--
even though in a short route, in any given segment,
the probability of this happening
is low, if you have a long route it's much higher.
It's like the point you brought up with Professor Fritz'
lecture, you said, oh, the chances of a bus benefiting
from this are very small.
And then you said, well, what if it's a long route
and there are 20 signals?
Same thing applies here.
You might have a long route with many windows,
and the chances that there is one window at any given
time in the rush hour is actually pretty high.
AUDIENCE: And then the other thing is, as the controller--
suppose I'm the controller, I have the algorithm.
And my computer starts beeping and gets all excited.
I have to respond quickly to this,
because that opportunity will pass.
GABRIEL SANCHEZ-MARTINEZ: And getting back
to algorithms and anticipation, what's
sort of neat about algorithms is that you
can try to predict that this will happen rather than waiting
until it happens to react.
And if you can do that early enough,
you might actually instruct a bus
that is departing the terminal to short term later on.
And if you do that, then you can set the head sign
on the bus to the short version.
And people who are boarding it are
going to know that it's going to be
short term so you won't have to coordinate
with the bus next to it.
You don't have to have a bunch, in other words.
So you can then minimize the problem
to finding a long gap here and predicting
when that gap will meet the next bus that's being dispatched.
You need algorithms for that.
It's very difficult to do it.
AUDIENCE: What do you tell the passengers?
Do you tell the passengers, listen, guys, this bus
might get short termed, just so you know.
GABRIEL SANCHEZ-MARTINEZ: No.
You change the head sign.
And you say this bus is running to Central Square instead
of Harvard.
AUDIENCE: Yeah.
AUDIENCE: Wouldn't you know this is going
to happen during commute hours?
Like the red line--
I mean, I suppose for trains, the red line is so long.
But if you know your [?OE?] are mainly in the downtown area,
wouldn't you know beforehand that you want to just have
higher frequency on this one branch?
GABRIEL SANCHEZ-MARTINEZ: That would
be a service planning, short terming strategy, not
a real-time control strategy.
So we make the distinction.
Both are short terming, but this is something
that you decide in real time to bring the service that you
are delivering more close to what you plan to deliver.
Which is different from strategy in service planning, where
you identify when we talked about rider or quarter
strategies.
There might be a core of your route that has higher demand
and you have short terms to have frequency higher at that point.
Very different reasons and horizons
for planning and all sorts of things.
OK, use of reserve vehicles, this happens more with rail
than bus.
You could have it with bus, too, though.
I know that in South America they do it with bus.
So you have some buses stationed somewhere
in the city near key routes.
And they're just waiting there for an opportunity.
[LAUGHTER]
[CHATTER]
Right.
So then someone in a control center sees a long gap
and they call that bus and say, there's a big, long gap there.
Rush.
Go into that corridor and start operating Route X. So
they can inject a vehicle.
And you can do that with rail, too, if you have pocket tracks.
So you might have pocket tracks somewhere and sort of insert
a train.
Ari knows something about that.
OK, so mostly, if you do holding,
holding's the best strategy for keeping service on track.
You don't usually want to do the more aggressive strategies
because they hurt passengers and they require
much more coordination effort.
But if you have a major disruption,
sometimes you need them.
Holding by itself won't cut it.
Holding can be done in a bunch of different ways.
You can hold to schedule adherence.
We've spoken about that.
For headway, we've kind of brushed it off
and said headway adherence.
Well, there's actually a lot of ways you can do that.
So one of them is to look at the schedule
and realize that the time between scheduled trips
is five minutes.
So now instead of actually trying
to stick to the actual times, you
want to stick to a separation of five minutes between vehicles,
because that's the time that was scheduled.
So that would be scheduled headway adherence.
The next-- and these are in order of sophistication.
So the next one is threshold headway adherence.
So if you think about it, there's
no reason why the scheduled difference between departure
times is the best threshold that you should use for holding.
There might be one that is a minute less or a minute higher
that results in better performance.
Why not?
What physical reason is there for the scheduled
time being the best one.
There isn't any.
So if you optimize the threshold,
you can get better performance.
And usually the optimal threshold is below,
it's shorter than the schedule.
So you hold less often.
The problem with headway adherence
is that you hold too much, essentially.
So then there's headway regularity.
Don't worry about the schedule at all,
or about any predetermined headway.
You have a separation between vehicles.
And I know that if I have vehicles,
I want my vehicles spaced this way.
But instead, I have this situation.
So I want this vehicle to hold until it is here.
Or rather, what will really happen
is this vehicle will stay there.
You will ask it to stay there.
And you want this vehicle to move on
and this vehicle to move on to these positions.
And now they're even, and then you
let that vehicle go at that point.
So that's even headway holding.
AUDIENCE: That seems pretty easy to implement.
How often is it--
GABRIEL SANCHEZ-MARTINEZ: Now it is.
It used to be very hard.
So how would you implement targeted headway holding
without technology?
AUDIENCE: [INAUDIBLE]
GABRIEL SANCHEZ-MARTINEZ: No, but how would you?
You can't do it.
AUDIENCE: You need a supervisor [INAUDIBLE]..
GABRIEL SANCHEZ-MARTINEZ: You need a supervisor.
So in London there was actually a time
when you didn't need a supervisor
because you had the driver getting off the bus,
and hitting a button on a post, and it starts a timer,
and then the driver leaves.
The next bus comes along and it sees the time.
So it knows, like, ah, OK, this is when I have to leave.
So you can do that, even without wireless communication.
Even in headway you can't do that.
You need communication.
Somebody needs to know the vehicle before,
the vehicle after, that means they communicated.
So it's much more of a recent strategy in terms of--
AUDIENCE: Oh, so in this strategy
you're not necessarily trying to maintain a certain headway.
GABRIEL SANCHEZ-MARTINEZ: No certain headway.
It's often when it emerges from the system.
AUDIENCE: OK.
GABRIEL SANCHEZ-MARTINEZ: Yep.
And that's actually-- if we want to split hairs,
there's different kinds of ways of doing unit headway.
And let's not get into it.
Then the most sophisticated class is optimization.
And there's something called rolling horizon optimization.
So what happens there is that you use a simulation
model, essentially, to predict how the system would
evolve if you're holding time for a certain configuration.
And you can test a bunch of different headway holding
configurations and pick the one that's
best at a given time based on those forecasts.
In other words, pick the holding time that maximizes performance
across forecasts.
And so what's neat about this is that they can trade off waiting
time and in-vehicle time.
When you hold, the people inside the vehicle are waiting more.
The winners of this strategy are people who would miss that bus
and have to wait for the following bus that
has a long headway ahead of it.
So by evening out the headways, you
make everybody wait about the same.
And that minimizes average waiting time and average
crowding, et cetera.
So optimization strategy can predict or keep
track of how many people are inside vehicles.
And it can know, well, I know this is the penalty.
I know this is the benefit.
Let's trade these off and let's hold the optimal amount of time
such that the total time is minimized.
And you can multiply by factors that
take into account this utility of waiting being higher
than the disutility of being inside the vehicle.
So what that does is it reduces excessive holding.
So if you know that you have a full vehicle,
you don't hold it, even if it's very close to the next one.
Why would you hold a vehicle that
is full, even if it's this one right here bunched
to the next one.
You don't.
You don't want to hold it.
What if the vehicle isn't full, but it will be full
five stops ahead, because demand is very high for some reason.
And you know that.
Then optimization algorithm will see that because it's
predicting for next hour.
So it'll be able to pick a strategy that
improves performance.
One challenge is drivers.
If you hold too much, then drivers
might be 20 minutes late for their shift,
for their meal break.
What do you do about that?
That's still a challenge.
And that's a challenge throughout.
But there is opportunity with optimization algorithms
to insert constraints that take those into account so
that your holding policy is something
that you can implement.
AUDIENCE: It seems like [INAUDIBLE] would be
to [INAUDIBLE] the algorithm.
If it's taking 45 minutes to come up
with this great solution, then [INAUDIBLE]..
GABRIEL SANCHEZ-MARTINEZ: So this problem is [INAUDIBLE]..
And if you crunched all the possibilities,
you would never finish.
So you need a very good algorithm
to find something fast.
Yeah.
So there's two different ways of doing rolling horizon
optimization.
One way is to have constant running times in demands
within the prediction horizon.
So imagine this blue window being your--
this is the time right now, and you're predicting
over the next, say, hour.
And that's the blue window.
What is actually happening is that your running times are
going up slowly and gradually.
Your demand is going up slowly, gradually
because you're in the PND.
If you are using static input, you
have to say what the running time is for the whole horizon.
So what you might do is break up the day into periods.
And if you start at this time, anytime before this,
you set some average.
And then once you cross that threshold,
you set a different average.
But then you miss out on some information.
So I worked on a model that actually
takes some dynamic inputs, too, to consider
these transitions, essentially.
And the way it works is you have these dynamic functions
of running times and demand.
You can see the current system state.
You send that to a model.
The model passes on those inputs and some holding time
configuration to a performance model, which essentially
forecasts what the system would do,
how the vehicle would move, where passengers would board,
all those things.
And then that gets sent to a cost model, which says,
how much are people waiting?
How much are people in vehicles?
Let's add those up and figure out what the average is.
And then that gets sent back to the optimization model,
and the optimization model says, what
if we, instead of doing that, let's turn this knob
and increase that holding time and decrease this one,
go again.
So it can do that on a loop, essentially,
until it finds optimal times.
The objective function is the average time in the system.
So Wv is like extra time in the vehicle.
So it's the time that a person spends
at a stop in the vehicle, not moving because the vehicle is
being held.
So you're adding time to that person.
And then Ws is waiting time at the stop.
And we can multiply by some factor
because we know that waiting time is more onerous.
There's a bunch of constraints.
I'll skip the differences between static and dynamic.
Essentially it's that running time
so demand can be functions of time now.
Here's what happens.
So here we test four different strategies.
The first one here, TH, is threshold holding.
EH is even headway holding.
OS is optimization of static inputs,
and OD is optimization with dynamic inputs.
And then we tested--
if we look at the bottom two sets of four,
these are cases where both of the men and the running times
are dynamic.
So they're both transient.
And we tested a case of low crowding
and a case of high crowding.
So what we see is that in all cases of low crowding--
by the way, the bottom 2/3 sets of runs are cases where maybe
running times are dynamic but demand isn't, or demand is
dynamic and running times aren't.
So if you look at all the cases of low crowding,
the white ones here, there's very little difference
in performance.
So it means that you don't really
need the most sophisticated strategy.
And the benefit of a very sophisticated optimization
strategy with dynamic inputs is not really
going to bring you a lot of benefit.
If you look at the high crowding case, what you see
is that there is a pretty significant benefit
of even headway holding over even optimized threshold
holding.
But moving to the model with optimization
doesn't do much for you if there's
a lot of sort of dynamics and system potentially.
So part of that is because the static inputs high information
about when those vehicles will fill up.
And when you insert that information into the system,
then the optimizer can see more of what happens
and can improve performance.
Here to the left is lower cost and therefore better.
Yeah, there's more to parse here,
but we're running out of time, so I'm
going to skip a few slides.
So you have control problems, routine disturbances
where you lose speed adjustments and holding lightly.
Then there's short-term disruptions
that might last between five and 30 minutes.
And there you can apply the strategies
that we've discussed.
And then there's very long, much longer interruptions
in service for which you need to do something major,
like bringing out bus service to replace train service.
And so only holding, short terming,
expressing, deadheading, they're not going to cut it.
You have a much bigger problem to deal with.
Here's a situation in a rail operation
where there's a signal failure, or perhaps there's
a suicide attempt, and there's a person on the tracks.
And you have this train that's standing there and can't move.
So the first thing you should do is
hold the trains downstream, immediately
downstream of the blockage.
If you don't do that, they will run around and queue up
on the other end.
And the people entering these stations
are going to wait a long time.
and those stations are going to fill up.
The other thing you should do is these trains that are lined up
here should be expressed as soon as the blockage is
cleared up so that you can move those vehicles forward.
And the vehicles at the end of the queue
can begin normal operation.
Does that make sense?
A lot of the very sophisticated models
are not used in practice for a number of reasons.
Sometimes it's that the models are simplistic.
Sometimes it's sort of a lack of faith in models.
Often it has to do with the data in real time
about where vehicles are not being that good.
So actually detecting where vehicles are
could be a major challenge.
And you need that information to make the determination of what
the optimal strategy is.
Recently our lab did a pilot of a real experiment
with the Green Line holding two headways instead
of the schedule.
So right now they use paper sheets
and they have a schedule.
And Jeff Fabian, who's a student in the lab,
designed an app that has all the train and driver information.
And it also calculates the even headway departing time.
So that departure time which would cause an even headway.
And for two weeks we had the inspectors of the terminal
use that instead of the paper schedule.
And what happened-- here's a picture of the app.
So you have all the trains for the day.
There's color coding.
So green is coming up and you can see
all these times are different.
So 9:36, there's some extra holding there for the train
that had been scheduled at 9:34 so that the headways are even
coming out.
And here's what happened.
The variability decreased by about 40% in some cases,
if you look at the coefficient of variation.
And you only look at trains that were compliant.
What really happened overall was a mix of things.
There was some noncompliance with headway times,
some insistence in departing on time to the schedule,
and then sometimes a compliance to the [INAUDIBLE] headway
policy.
So here's the coefficient of variation.
You know what that is.
You know that lower is better and the Green Line is lower,
so it's better.
You can calculate the equivalent benefit
that you would get by adding trains
to service in terms of decreasing waiting time.
You can increase frequency by adding new trains.
So decrease in variability of headways
was equivalent to adding 1.7 trains.
Which is money.
AUDIENCE: Yeah, but if I'm not mistaken-- you can correct me
if I'm wrong.
There is a mechanism in this algorithm
that tries to go back gradually to the schedule.
GABRIEL SANCHEZ-MARTINEZ: No, I wouldn't
characterize it that way.
There are constraints to prevent situations where there aren't
enough trains to be departed.
And there are some constraints on how much holding
there can be, et cetera.
So yeah, there's an intention not
to have too much of a cascading holding throughout the day.
But it's not so much as a programmed linear trend
towards schedule or anything like that.
AUDIENCE: Because you're going off schedule, does--
GABRIEL SANCHEZ-MARTINEZ: Slightly.
AUDIENCE: Slightly.
So would you ever run into issues
with communicating with the public?
GABRIEL SANCHEZ-MARTINEZ: Green Line, especially in peaks,
high frequency, not running very reliably, anyway.
So I don't know anyone that looks at the schedule.
Maybe very early in the morning, but I don't know.
Maybe late at night, but I don't know.
AUDIENCE: I've totally used Green Line's schedule
late at night.
GABRIEL SANCHEZ-MARTINEZ: Late at night.
Yeah, late at night, I think it would happen.
But I don't think that during the day it would happen.
And what happened with this late at night
is that the schedule is reliable enough
that the even headway times are the scheduled times, anyway.
So there's no issue with that.
AUDIENCE: So would there be an issue in terms of applying this
to a more robust system?
GABRIEL SANCHEZ-MARTINEZ: We learned a lot from this pilot.
And I think whoever implements the next rail system will
have to rejudge his thesis.
Because there's so much that we learned, about compliance,
about issues with data.
I recommend reading it.
Eli.
AUDIENCE: Can you explain how it's determining
the headway that it should be?
GABRIEL SANCHEZ-MARTINEZ: It's even headway.
AUDIENCE: It's just maintaining event.
It's not like optimizing.
GABRIEL SANCHEZ-MARTINEZ: No optimization.
It's a very simple even headway strategy.
Prediction of the time it takes this train
to reach the next one, prediction
of the time it takes the trailing train
to arrive at the terminal, and then
using those to calculate the headways, essentially.
And then determining the holding time
to keep that train the middle and then
adding some constraints to prevent excessive holding.
Also to prevent-- if there was a long gap,
you might want to not hold the second one too much.
Send those together.
Here's something interesting.
Here's a space-time graph.
Time horizontal.
Green here shows compliance and red shows non-compliance.
So the first thing we see is that when
there's a lot of green, those lines are nicely evenly spaced.
So that's good.
That's the lower coefficient to variation.
When you see red, you see some bunching later on.
That doesn't happen immediately.
And it's slight.
Notice how slight the deviations can be.
But you see the effects of the dwell time effect
and the crunching happening.
The other thing that happens is that they have someone
controlling at reservoir.
So they have someone stationed there holding trains,
keeping them evenly spaced, more or less.
And which trains are being held?
The ones that are not as green, right?
So you've sent a train that might be full of people.
And you've decided that you somehow
need it to depart a little bit earlier
than the algorithm said.
And then you wait till you fold to them and hold two minutes.
You could have avoided that by having left a little later
from the terminal.
AUDIENCE: They're never hold at Fenway?
Fenway seems to--
GABRIEL SANCHEZ-MARTINEZ: No.
No, just long hold times.
So that's the end.
Sorry for being a few minutes late.
If you have questions on holding or real-time control,
let me know.
Next lecture is on fare policy.