Hi everyone,

I am working with a transit agency that operates a commuter rail line. They want to explore how to get the most riders per dollar spent, and the spending options in this case are either improving frequency or improving speed through track and vehicle improvements. The model I’m working with (a nested logit choice model in a traditional n-step gravity model), recognizes overall travel time (IVT + OVT) as a variable in the choice model utility equation, but there is no direct recognition of frequency other than its overall effect on travel time.

Seemingly that would be fine, as paths with low frequency might have rather onerous wait times (2x wait time factor), which then are accounted for in the utility equation. However, this particular model caps initial wait time at 5-minutes for rail and 7.5 minutes for buses (xfer time is half the headway of the next route in the path). Given the cap, it seems like a rail path with 10-minute frequency, where half the headway is 5-minutes, would be exactly the same travel time as a route with 90-minute frequency because initial wait is capped at 5-minutes. Thus, I think the model has no way of seeing that 10-minute service should attract more riders than 90-minute service, unless frequency is included as a utility equation variable, or unless this 5-min cap is loosened considerably.

I ran three sensitivity tests: 90 to 30-minute peak period frequency, then 30 to 10 and 90 to 10 to see if the model recognizes frequency. On the 90 to 30-minute test (three-fold increase), I got a 7% increase. I don’t have data for what I should have expected, but 7% for such a huge improvement seems quite low. Still, it was something, where I had predicted nothing. I believe the “something” probably comes from trips transferring from bus to rail. A transfer waits for half the headway of the next route, and it also weights transfer time with a 2.0 onerous factor. Thus, a transfer to a 90-minute rail is extremely unattractive relative to transferring to a 10-minute rail. But for trips directly accessing rail as the first mode, I don’t think it can see a difference.

For the 30 to 10 experiment (another three fold improvement), I got an additional 15%. For the 90 to 10, the overall increase was 23%. These are all in the right direction, but all seem really low relative to what I believe would likely happen in the real world. Unfortunately, I don’t presently have any real world data or researched elasticities by which to either adjust model outputs or to recommend model improvements.

Do any of you have insights on this topic or on the following questions?

1. Are you aware of research regarding how much of a change in ridership is typically associated with changes in frequency? Anyone have real-world data, perhaps where an agency took a 30-minute train or bus and started running at 15-minutes, and how that affected ridership?

2. Similar to the previous, I’m wondering about the elasticity of frequency and the elasticity of speed. Assuming frequency elasticity were .3, then I think a 100% increase in frequency (30 to 15 minutes), should produce a 30% increase in ridership (unless I’m misunderstanding how to apply such an elasticity. Would it be a 100% increase in frequency or a 50% decrease in wait time?).

3. Where it is easy to make transit “twice as frequent,” it is very hard to make any kind of transit go “twice as fast.” But let’s say you increase speed from 30 mph on average to 40 mph on average – a 33% increase in speed. If elasticity of speed is .2, then 33% increase in speed x .2 elasticity means roughly 7% ridership boost. Is my application of elasticities right (assuming I can find researched elasticities)? Any awareness of where to find such elasticities?

4. Any awareness of common practice or best practice for making models accurately sensitive to frequency changes and speed changes? How do other models handle market response to both frequency and speed?

5. Does a 5-minute cap on wait for rail seem reasonable, or are longer initial wait times more common in most models? What do you think of a 7.5-minute cap on bus wait? Is it good to show a longer initial wait time than occurs in reality, as a means of reflecting that infrequent service has a greater negative effect than merely the amount of time someone actually spends at the stop? (i.e., they elect not to ride because they need to be somewhere at 8:00 am, but their options are to get there 30 minutes early or 30 minutes late, so they don’t choose transit).

Any insights are greatly appreciated,

Mike Brown

Hello Mike,

1. Todd Litman's Victoria Transportation Policy Institute has a quite

comprehensive tabulation of transit elasticities at

https://www.vtpi.org/tranelas.pdf . Most of the elasticities discussed are

with respect to fare or other costs (such as cross-elasticities of auto

fuel price or parking cost). Service elasticities (frequency, vehicles per

day, revenue miles or kilometers) are shown in Tables 4, 12, and 13; and

the narrative of the Service Elasticities section that begins on page 12.

Recommended elasticities are given in Table 15. Note that service

elasticities may vary based on initial conditions, time of day, trip

purpose, traveler characteristics, and amount of time since the service

change (short-run versus long-run elasticities).

2. A typical industry assumption is that for services with frequencies of

once every 20 minutes or less, passengers will arrive randomly (that is,

according to a uniform random distribution, and without regard to any

published schedule), while passengers are motivated to check schedules of

less-frequent services in order to time their arrival to jointly minimize

waiting time and the chance of missing the transit vehicle departure.

According to these expectations, a cap on initial wait time should be set

at no less than 10 minutes, regardless of the mode. I believe this result

is based on the North American experience, so behavior may be different in

areas where transit is more frequent (such as Europe or Asia), and thus

passenger expectations and tolerances may be different.

3. The Colorado State Focus travel model uses a piecewise linear

transformation in converting headway to expected wait time:

For headways of 15 minutes or less, no adjustment is made before estimating

wait time as half the headway.

For headways of 16 to 60 minutes, the number of minutes in excess of 15 are

waited by 1/2.2 to create an "adjusted headway" that's then divided by 2.

For headways longer than 60 minutes, in addition to the 1/2.2 weight for

minutes 16 through 60, a weight of 1/3 is applied for every minute beyond

the first 60 minutes.

For your example of a 90-minute service we'd calculate an adjusted headway

of 15 + ( 60 - 15 ) / 2.2 + ( 90 - 60 ) / 3 = 45.5 minutes, and an expected

wait time of 22.7 minutes (rounded).

This doesn't necessarily mean that we expect passengers to show up at the

stop/station an average of 22.7 minutes before the departure of a 90-minute

service, but that such a service has a disutility related to its frequency

that's equivalent to waiting 22.7 minutes (weighted by a factor of 2.0 the

disutility of in-vehicle time, or similar). A passenger might show up 10

minutes before departure, so the remaining 12.7 minutes would actually be

"schedule delay" rather than wait time. ("Schedule delay" is the

inconvenience of a transit vehicle not departing when you'd want it to for

your schedule, so the trip may involve more time than desired spent at

home, in the office, or in some waiting room.)

4. Note that the formula to approximate wait time by 1/2 the headway

implicitly assumes a reliable (deterministic; perfect schedule adherence)

transit service and a uniform distribution of passenger arrival times at

the transit stop. For an unreliable service, researchers may assume an

independent & identically-distributed exponential distribution of transit

vehicle arrival/departure times - sometimes called "memoryless" - and in

this case, the expected wait time is identical to the headway (the mean of

the exponential distribution) rather than half of it. This case with an iid

exponential distribution is a particularly extreme unreliability, so

calculating wait time as a factor ("inter-arrival parameter" in TransCAD)

of say 70 or 80 percent of the headway may be more realistic in certain

situations.

*M. Scott Ramming, PhD, PE*

*My pronouns: he/him/his*

*Professional Engineer I, Mobility Analysis/Travel Modeling Unit*

* *

I usually work remotely Tues, Wed & Fri | Cell 303.870.6643

P 303.757.9754 | F 303.757.9727

2829 W. Howard Place, Denver CO 80204

scott.ramming@state.co.us | www.codot.gov | www.cotrip.org

On Tue, Nov 9, 2021 at 1:44 PM Mike Brown wrote:

> Hi everyone,

>

> I am working with a transit agency that operates a commuter rail line. They

> want to explore how to get the most riders per dollar spent, and the

> spending options in this case are either improving frequency or improving

> speed through track and vehicle improvements. The model I’m working with

> (a nested logit choice model in a traditional n-step gravity model),

> recognizes overall travel time (IVT + OVT) as a variable in the choice

> model utility equation, but there is no direct recognition of frequency

> other than its overall effect on travel time.

>

> Seemingly that would be fine, as paths with low frequency might have

> rather onerous wait times (2x wait time factor), which then are accounted

> for in the utility equation. However, this particular model caps initial

> wait time at 5-minutes for rail and 7.5 minutes for buses (xfer time is

> half the headway of the next route in the path). Given the cap, it seems

> like a rail path with 10-minute frequency, where half the headway is

> 5-minutes, would be exactly the same travel time as a route with 90-minute

> frequency because initial wait is capped at 5-minutes. Thus, I think the

> model has no way of seeing that 10-minute service should attract more

> riders than 90-minute service, unless frequency is included as a utility

> equation variable, or unless this 5-min cap is loosened considerably.

>

> I ran three sensitivity tests: 90 to 30-minute peak period frequency, then

> 30 to 10 and 90 to 10 to see if the model recognizes frequency. On the

> 90 to 30-minute test (three-fold increase), I got a 7% increase. I don’t

> have data for what I should have expected, but 7% for such a huge

> improvement seems quite low. Still, it was something, where I had

> predicted nothing. I believe the “something” probably comes from trips

> transferring from bus to rail. A transfer waits for half the headway of

> the next route, and it also weights transfer time with a 2.0 onerous factor.

> Thus, a transfer to a 90-minute rail is extremely unattractive relative to

> transferring to a 10-minute rail. But for trips directly accessing rail as

> the first mode, I don’t think it can see a difference.

>

> For the 30 to 10 experiment (another three fold improvement), I got an

> additional 15%. For the 90 to 10, the overall increase was 23%. These

> are all in the right direction, but all seem really low relative to what I

> believe would likely happen in the real world. Unfortunately, I don’t

> presently have any real world data or researched elasticities by which to

> either adjust model outputs or to recommend model improvements.

>

> Do any of you have insights on this topic or on the following questions?

>

> 1. Are you aware of research regarding how much of a change in

> ridership is typically associated with changes in frequency? Anyone have

> real-world data, perhaps where an agency took a 30-minute train or bus and

> started running at 15-minutes, and how that affected ridership?

>

> 2. Similar to the previous, I’m wondering about the elasticity of

> frequency and the elasticity of speed. Assuming frequency elasticity

> were .3, then I think a 100% increase in frequency (30 to 15 minutes),

> should produce a 30% increase in ridership (unless I’m misunderstanding how

> to apply such an elasticity. Would it be a 100% increase in frequency or

> a 50% decrease in wait time?).

>

> 3. Where it is easy to make transit “twice as frequent,” it is very

> hard to make any kind of transit go “twice as fast.” But let’s say you

> increase speed from 30 mph on average to 40 mph on average – a 33% increase

> in speed. If elasticity of speed is .2, then 33% increase in speed x .2

> elasticity means roughly 7% ridership boost. Is my application of

> elasticities right (assuming I can find researched elasticities)? Any

> awareness of where to find such elasticities?

>

> 4. Any awareness of common practice or best practice for making

> models accurately sensitive to frequency changes and speed changes? How

> do other models handle market response to both frequency and speed?

>

> 5. Does a 5-minute cap on wait for rail seem reasonable, or are

> longer initial wait times more common in most models? What do you think

> of a 7.5-minute cap on bus wait? Is it good to show a longer initial

> wait time than occurs in reality, as a means of reflecting that infrequent

> service has a greater negative effect than merely the amount of time

> someone actually spends at the stop? (i.e., they elect not to ride

> because they need to be somewhere at 8:00 am, but their options are to get

> there 30 minutes early or 30 minutes late, so they don’t choose transit).

>

>

> Any insights are greatly appreciated,

>

> Mike Brown

> --

> Full post:

> https://tmip.org/content/model-sensitivity-transit-frequency-and-speed

>

> Manage my subscriptions: https://tmip.org/mailinglist

>

> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/13690

>

>

Frank Spielberg – Thank you for pointing me to TCRP 95, Chapter 9. That had some great discussion about transit elasticities that was very helpful. I was able to construct a spreadsheet model from it to help compare what I am getting with what I should be getting. It implies elasticities of .3 to .5 where starting frequency is already pretty good (say 20 minutes or better), and .5 to .7 when starting frequency is more like 30 to 60, and .9 to 1.2 when starting frequency is above 60.

Scott Ramming – A lot of great stuff. This research from Todd Litman looks like it was published just a couple of weeks ago. It’s got great content on this very topic. He concludes that as a general rule, short-term ridership response to frequency improvements should see .5 to .7 elasticities, and long-term should see .7 to 1.1. This is far higher than the model I am working with is able to detect on its own, and points to the 5-minute wait time cap in this model as being problematic. You highlighted that the typical industry assumption is that if frequency is 20-minutes or better, expect primarily random arrivals (meaning that if a cap were used at all, 10 minutes is a much better choice than 5). But I also love the function you provided in lieu of a cap, which starts to incorporate inconvenience as well: “For a 90-minute service we'd calculate an adjusted headway of 15 + ( 60 - 15 ) / 2.2 + ( 90 - 60 ) / 3 = 45.5 minutes, and an expected wait time of 22.7 minutes (rounded).” That is a great function and I’ll work with this MPO to see if they can incorporate this.

Thank you both for the help on this,

Mike Brown

From: Ramming - CDOT, Scott

Sent: Tuesday, November 16, 2021 9:22 PM

To: Mike Brown

Cc: TMIP

Subject: Re: [TMIP] Model sensitivity to transit frequency and speed

Hello Mike,

1. Todd Litman's Victoria Transportation Policy Institute has a quite comprehensive tabulation of transit elasticities at https://www.vtpi.org/tranelas.pdf . Most of the elasticities discussed are with respect to fare or other costs (such as cross-elasticities of auto fuel price or parking cost). Service elasticities (frequency, vehicles per day, revenue miles or kilometers) are shown in Tables 4, 12, and 13; and the narrative of the Service Elasticities section that begins on page 12. Recommended elasticities are given in Table 15. Note that service elasticities may vary based on initial conditions, time of day, trip purpose, traveler characteristics, and amount of time since the service change (short-run versus long-run elasticities).

2. A typical industry assumption is that for services with frequencies of once every 20 minutes or less, passengers will arrive randomly (that is, according to a uniform random distribution, and without regard to any published schedule), while passengers are motivated to check schedules of less-frequent services in order to time their arrival to jointly minimize waiting time and the chance of missing the transit vehicle departure. According to these expectations, a cap on initial wait time should be set at no less than 10 minutes, regardless of the mode. I believe this result is based on the North American experience, so behavior may be different in areas where transit is more frequent (such as Europe or Asia), and thus passenger expectations and tolerances may be different.

3. The Colorado State Focus travel model uses a piecewise linear transformation in converting headway to expected wait time:

For headways of 15 minutes or less, no adjustment is made before estimating wait time as half the headway.

For headways of 16 to 60 minutes, the number of minutes in excess of 15 are waited by 1/2.2 to create an "adjusted headway" that's then divided by 2.

For headways longer than 60 minutes, in addition to the 1/2.2 weight for minutes 16 through 60, a weight of 1/3 is applied for every minute beyond the first 60 minutes.

For your example of a 90-minute service we'd calculate an adjusted headway of 15 + ( 60 - 15 ) / 2.2 + ( 90 - 60 ) / 3 = 45.5 minutes, and an expected wait time of 22.7 minutes (rounded).

This doesn't necessarily mean that we expect passengers to show up at the stop/station an average of 22.7 minutes before the departure of a 90-minute service, but that such a service has a disutility related to its frequency that's equivalent to waiting 22.7 minutes (weighted by a factor of 2.0 the disutility of in-vehicle time, or similar). A passenger might show up 10 minutes before departure, so the remaining 12.7 minutes would actually be "schedule delay" rather than wait time. ("Schedule delay" is the inconvenience of a transit vehicle not departing when you'd want it to for your schedule, so the trip may involve more time than desired spent at home, in the office, or in some waiting room.)

4. Note that the formula to approximate wait time by 1/2 the headway implicitly assumes a reliable (deterministic; perfect schedule adherence) transit service and a uniform distribution of passenger arrival times at the transit stop. For an unreliable service, researchers may assume an independent & identically-distributed exponential distribution of transit vehicle arrival/departure times - sometimes called "memoryless" - and in this case, the expected wait time is identical to the headway (the mean of the exponential distribution) rather than half of it. This case with an iid exponential distribution is a particularly extreme unreliability, so calculating wait time as a factor ("inter-arrival parameter" in TransCAD) of say 70 or 80 percent of the headway may be more realistic in certain situations.

M. Scott Ramming, PhD, PE

My pronouns: he/him/his

Professional Engineer I, Mobility Analysis/Travel Modeling Unit

I usually work remotely Tues, Wed & Fri | Cell 303.870.6643

P 303.757.9754 | F 303.757.9727

2829 W. Howard Place, Denver CO 80204

scott.ramming@state.co.us | www.codot.gov | www.cotrip.org

On Tue, Nov 9, 2021 at 1:44 PM Mike Brown > wrote:

Hi everyone,

I am working with a transit agency that operates a commuter rail line. They want to explore how to get the most riders per dollar spent, and the spending options in this case are either improving frequency or improving speed through track and vehicle improvements. The model I’m working with (a nested logit choice model in a traditional n-step gravity model), recognizes overall travel time (IVT + OVT) as a variable in the choice model utility equation, but there is no direct recognition of frequency other than its overall effect on travel time.

Seemingly that would be fine, as paths with low frequency might have rather onerous wait times (2x wait time factor), which then are accounted for in the utility equation. However, this particular model caps initial wait time at 5-minutes for rail and 7.5 minutes for buses (xfer time is half the headway of the next route in the path). Given the cap, it seems like a rail path with 10-minute frequency, where half the headway is 5-minutes, would be exactly the same travel time as a route with 90-minute frequency because initial wait is capped at 5-minutes. Thus, I think the model has no way of seeing that 10-minute service should attract more riders than 90-minute service, unless frequency is included as a utility equation variable, or unless this 5-min cap is loosened considerably.

I ran three sensitivity tests: 90 to 30-minute peak period frequency, then 30 to 10 and 90 to 10 to see if the model recognizes frequency. On the 90 to 30-minute test (three-fold increase), I got a 7% increase. I don’t have data for what I should have expected, but 7% for such a huge improvement seems quite low. Still, it was something, where I had predicted nothing. I believe the “something” probably comes from trips transferring from bus to rail. A transfer waits for half the headway of the next route, and it also weights transfer time with a 2.0 onerous factor. Thus, a transfer to a 90-minute rail is extremely unattractive relative to transferring to a 10-minute rail. But for trips directly accessing rail as the first mode, I don’t think it can see a difference.

For the 30 to 10 experiment (another three fold improvement), I got an additional 15%. For the 90 to 10, the overall increase was 23%. These are all in the right direction, but all seem really low relative to what I believe would likely happen in the real world. Unfortunately, I don’t presently have any real world data or researched elasticities by which to either adjust model outputs or to recommend model improvements.

Do any of you have insights on this topic or on the following questions?

1. Are you aware of research regarding how much of a change in ridership is typically associated with changes in frequency? Anyone have real-world data, perhaps where an agency took a 30-minute train or bus and started running at 15-minutes, and how that affected ridership?

2. Similar to the previous, I’m wondering about the elasticity of frequency and the elasticity of speed. Assuming frequency elasticity were .3, then I think a 100% increase in frequency (30 to 15 minutes), should produce a 30% increase in ridership (unless I’m misunderstanding how to apply such an elasticity. Would it be a 100% increase in frequency or a 50% decrease in wait time?).

3. Where it is easy to make transit “twice as frequent,” it is very hard to make any kind of transit go “twice as fast.” But let’s say you increase speed from 30 mph on average to 40 mph on average – a 33% increase in speed. If elasticity of speed is .2, then 33% increase in speed x .2 elasticity means roughly 7% ridership boost. Is my application of elasticities right (assuming I can find researched elasticities)? Any awareness of where to find such elasticities?

4. Any awareness of common practice or best practice for making models accurately sensitive to frequency changes and speed changes? How do other models handle market response to both frequency and speed?

5. Does a 5-minute cap on wait for rail seem reasonable, or are longer initial wait times more common in most models? What do you think of a 7.5-minute cap on bus wait? Is it good to show a longer initial wait time than occurs in reality, as a means of reflecting that infrequent service has a greater negative effect than merely the amount of time someone actually spends at the stop? (i.e., they elect not to ride because they need to be somewhere at 8:00 am, but their options are to get there 30 minutes early or 30 minutes late, so they don’t choose transit).

Any insights are greatly appreciated,

Mike Brown

--

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That the long-term service elasticity is close to 1 is strong evidence of one of the worst and most prevalent errors in the application of logit-style formulations to mode split, that is, giving transit as choice to people who have no reasonable ability to use transit.

Alan

Hi Alan, Todd Litman said that for many things related to transit, but

namely fare and frequency sensitivity, long-term elasticity is 2 to 3 times

as much as short term. So I think what you're saying is that the logit

models, or at least many MPO models, may be biased to produce results based

on a short-term sensitivity (what people would do NOW if given new choices),

but in reality the models should be reflecting a situation where the full

array of choices being modeled in a scenario will have had a chance to

"settle in" over say a 10-year period.

If looking at a transit system change in year 2 vs 10, there are many who

will ignore the option in year 2, perhaps being unaware of the choice, or

unmotivated to try it yet. But by year 10 they have finally had a chance

to discover it, try it, and decided to keep doing it, and you're hypothesis

is that the industry may be biased toward year 2 when it should be telling

the story of year 10? This likely would apply to other options such as

biking.

Mike Brown

From: HOROWITZ=uwm.edu@mg.tmip.org On Behalf

Of ajhorowitz

Sent: Friday, November 19, 2021 10:38 AM

To: TMIP

Subject: Re: [TMIP] Model sensitivity to transit frequency and speed

That the long-term service elasticity is close to 1 is strong evidence of

one of the worst and most prevalent errors in the application of logit-style

formulations to mode split, that is, giving transit as choice to people who

have no reasonable ability to use transit.

Alan

--

Full post:

https://tmip.org/content/model-sensitivity-transit-frequency-and-speed

Manage my subscriptions: https://tmip.org/mailinglist

Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/13690

As a slight clarification, in response to a note from Mike Brown, the emphasis of my comment needs to be placed on the "1" rather than on the "long-term".