I am looking for advice on how to deal with tolls in a regional model. I am concerned that our current long-standing approach does not reflect today’s reality of ETC. The current model calculates a toll impedance based on a value of time for the motorist (which is assumed to be one-half of median household income in the model area). About 95 percent of current toll facility motorists have transponders linked to an account that is automatically replenished when the account balance reaches a minimum threshold. Rather than physically handing over a $1 toll or even seeing a “$1 toll paid” flash before them as they enter the toll facility, the typical motorist only sees a credit card charge of say $30 once a month (or several months for an infrequent user). In my higher-than-average-income demographic, I personally do not think for a second whether I am saving 1 minute, or 2 minutes, or 3 minutes when I choose to take the toll facility. My daughter fits more with a typical household income and views her toll bill as just one of her many electronic conveniences (like a cell phone bill or Netflix or any of many other subscriptions with regular or monthly charges) and does not do a mental impedance calculation when choosing a travel path. I know my stories are just anecdotes, but I think a significant percentage of toll facility users have a similar perspective.

I have thought of a couple different approaches. Instead of applying a universal average for household income to determine a value of time, I could disaggregate the motorists into separate bins with high income (with no concern for what the toll is), mid-level income (maybe with still little regard for the toll), and low income (where the value of time is indeed an important consideration). Of course, how I rationalize these subsets is probably just arbitrary based on the model assignment results. I have also considered trying the old Bob Dial stochastic assignment. I have not used it in decades and am not aware of how well current models (TransCAD, in my case) do with stochastic assignments.

Your ideas and suggestions would be appreciated.

Kevin Hooper

Portland, Maine

207-415-9538

Hmmm, I imagine this will be a quite productive (as in voluminous)

discussion.

There's a whole literature on how the value of time is influenced by

income, trip purpose, and even production/attraction direction (P to A =

need to be at work on time; A to P = may be less critical when you return

home, further depending on family composition).

There's also established statistical procedures for treating time or cost

parameters as having a random distribution and estimating the variance of

that distribution. (I've done this in the "classic" Bison BIOGEME.)

Implementing a model with random parameters may be a bit more involved

because you're either writing custom code to make the random draw for each

individual, or relying on the options that platform vendors offer and their

associated limitations.

It might be worth noting that Dial's STOCH algorithm assumes stochastic

perturbations to fixed travel times or link impedances. It's not an

equilibrium method, but a one-shot one - a stochastic analog to the

deterministic All-or-Nothing assignment. You may be thinking of Caroline

Fisk's algorithm that essentially combines the Frank-Wolfe algorithm (to

reach user equilibrium from All-or-Nothing iterations) with Dial's STOCH.

STOCH and therefore Fisk's stochastic UE are both affected by the IIA

(independence from irrelevant alternatives) property of logit.

Now I'll start adding in some Colorado-specific information:

Most agencies that do travel modeling in Colorado (also) use

Caliper's TransCAD platform. It offers a Stochastic User Equilibrium

traffic assignment that isn't Fisk's algorithm, but rather one that makes

random draws of link free-flow times (perceived) each iteration. It uses

the Method of Successive Averages to achieve equilibrium. I don't know if

there's a version of Frank-Wolfe that can deal with random link quantities

- it's for the deterministic context.

TransCAD SUE offers options of three distributions to draw from: Normal

(Gaussian), Gumbel (Type 1 Extreme Value, the logit class), and Uniform. I

can be thick sometimes, so I wish the TransCAD documentation was more

explicit about "if you use the Normal option, the value you enter into the

Error box is used as the sigma/standard deviation parameter when drawing

from N( 0, Error ). If you use the Uniform option, draws are made from U[

-Error, +Error ] - or would it be U[ -Error/2, +Error/2 ] so Error is the

range. If you use the Gumbel option, the value in the Error box is related

to the scale parameter described in Ben Akiva and Lerman page whatever by

such-and-such equation."

CDOT and DRCOG (Denver Regional Council of Governments, from whose model

the CDOT model is derived) both use deterministic User Equilibrium.

In preparation for opening HOT lanes - what we call Express Lanes - on US

36 between Denver and Boulder, a survey was conducted of corridor drivers

based on license plate video capture. People who also drove the I-25

Central Express Lanes (which were converted from HOV lanes in 2006) were of

particular interest. One result of that survey we use for modeling is that

roughly 75% of corridor drivers have ExpressToll transponders. We code our

networks with a composite toll based on 75% of users paying the

transponder/AVI rate and the other 25% paying the video license plate rate.

The report from that US 36 HOV/Express Lane user survey is no longer

publicly available on the web. Here's a slideshow that presents some

summary results, though not the ones relating to transponder ownership.

https://www.codot.gov/projects/archived-project-sites/i-25-hov-express-l...

I can connect you to colleagues at our Colorado Transportation Investment

Office (formerly High Performance Transportation Enterprise, and Colorado

Tolling Enterprise before that) if you're interested in the full report.

Other reports are here: https://www.codot.gov/programs/ctio/reports/reports

We also apply a 25% "perception discount" to the average/composite toll

rates we calculate from the AVI and license plate rates. This is to capture

the phenomenon you mention of "I didn't have to hand over actual cash at a

toll booth. I won't see my bill until the end of the month."

Presumably some drivers are sensitive to toll costs and travel time savings

trade-offs, or else HOT lanes would become as congested as the general

purpose lanes. (Though in Colorado, we have performance policies so that

tolls would be raised to keep traffic flowing at a set minimum acceptable

speed. I believe such policies are common.)

Don't forget to use CPI data to deflate your calculated perceived tolls

from current year dollars, to dollars from the year that the survey data

used to estimate your model coefficients were collected. Our model is based

on a 2010 household survey, and we're preparing to conduct its successor.

*M. Scott Ramming, PhD, PE*

*My pronouns: he/him/his*

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

DTD is dedicated to preparing Colorado's transportation system for the

future through planning, analysis, and innovation.

* *

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 Thu, Dec 1, 2022 at 1:40 PM CarsonKim wrote:

> I am looking for advice on how to deal with tolls in a regional model. I

> am concerned that our current long-standing approach does not reflect

> today’s reality of ETC. The current model calculates a toll impedance based

> on a value of time for the motorist (which is assumed to be one-half of

> median household income in the model area). About 95 percent of current

> toll facility motorists have transponders linked to an account that is

> automatically replenished when the account balance reaches a minimum

> threshold. Rather than physically handing over a $1 toll or even seeing a

> “$1 toll paid” flash before them as they enter the toll facility, the

> typical motorist only sees a credit card charge of say $30 once a month (or

> several months for an infrequent user). In my higher-than-average-income

> demographic, I personally do not think for a second whether I am saving 1

> minute, or 2 minutes, or 3 minutes when I choose to take the toll facility.

> My daughter fits more with a typical household income and views her toll

> bill as just one of her many electronic conveniences (like a cell phone

> bill or Netflix or any of many other subscriptions with regular or monthly

> charges) and does not do a mental impedance calculation when choosing a

> travel path. I know my stories are just anecdotes, but I think a

> significant percentage of toll facility users have a similar perspective.

>

> I have thought of a couple different approaches. Instead of applying a

> universal average for household income to determine a value of time, I

> could disaggregate the motorists into separate bins with high income (with

> no concern for what the toll is), mid-level income (maybe with still little

> regard for the toll), and low income (where the value of time is indeed an

> important consideration). Of course, how I rationalize these subsets is

> probably just arbitrary based on the model assignment results. I have also

> considered trying the old Bob Dial stochastic assignment. I have not used

> it in decades and am not aware of how well current models (TransCAD, in my

> case) do with stochastic assignments.

>

>

>

> Your ideas and suggestions would be appreciated.

> --

> Full post: https://tmip.org/content/accounting-tolls-traffic-assignment

>

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

>

> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/13883

>

>

Once upon a time, all the traffic assignment programs assigned one trip table minimizing one generalized-time, having a delay function. If it had tolls, you could add them to the generalized-time using some average value-of-time to convert. Most trips end up choosing one or the other in an all-or-nothing choice, with equilibrium leaving split options to few O-D movements.

Then we had to model HOV lanes. After a brief and forgettable era of practitioners having to cook up workarounds, vendors soon offered multi-class equilibrium assignments. At first these let you have only a small number of trip tables with different rules for which links could be used by particular trip tables.

Soon methods emerged to use these for tolled roads. You'd make a skim-time matrix for toll-refusers, and one allowing toll road use, then a discrete-choice model (or blast-to-the-past diversion curves) to split the trip table, then assign the two trip tables by their respective rules.

Most of today's assigners let you have numerous user-class trip tables, each associated with its own link-eligibility rule and link generalized-time. Many models now distribute the trip tables into 3 to 5 or so value-of-time bins (further distinguished into SOV-HOV eligibility classes). It is known that value-of-time is distributed for any income, so each bin should get trips from all income levels, the distribution still depending on income. Earlier stages of most modern demand models use household income distributions, so the means may be devised to track it to the vehicle-trip tables.

Both the discrete-choice and bin methods have their advantages and their criticisms. (Among these: Discrete choice lets you have a bias constant, but can become nonsensical when the network offers numerous use/refuse decisions, not just one. The bin method still has the all-or-nothing choice discontinuity problem, but only for each O-D's borderline bin rather than all the trips. More bins reduces this problem.)

Dial's "stoch" method from the 1960s-70s is not much of a solution. In the 1990s Dial worked on something like the value-of-time bin approach but with a continuous value-of-time distribution for each O-D. This would solve the discontinuity problem of the bin method. Little seems to have become of it in the end, judging from what the software vendors offer presently. (I think PTV offers something along those lines, but I haven't heard of any usages.)

This is an interesting topic, and Scott has already added most of my initial thoughts (and then some), but there is something I would add.

At a previous employer, we had bespoke assignment software that did explicit route choice at each step of the equilibration process (a Biconjugate Frank-Wolfe, in that case), which was a quite elegant solution.

As I was worried about path overlap, we set out to incorporate Scott's Path-Size Logit in the existing framework. In the process, we presented both the derivation of the problem (weirdly enough, the math had not been presented anywhere we could find in the literature) and explored the impact of path overlaps at equilibrium.

There are still some theoretical corner cases in this arena that bother me a bit, so it is good to see that there is still interest in the topic and somebody might come to solve those issues.

The paper is https://journals.sagepub.com/doi/10.1177/0361198119837496, but I am happy to send the PDF to any interested party.

Cheers,

Pedro

---- On Wed, 07 Dec 2022 21:33:53 +1000 John Gibb wrote ---

Once upon a time, all the traffic assignment programs assigned one trip table minimizing one generalized-time, having a delay function. If it had tolls, you could add them to the generalized-time using some average value-of-time to convert. Most trips end up choosing one or the other in an all-or-nothing choice, with equilibrium leaving split options to few O-D movements.

Then we had to model HOV lanes. After a brief and forgettable era of practitioners having to cook up workarounds, vendors soon offered multi-class equilibrium assignments. At first these let you have only a small number of trip tables with different rules for which links could be used by particular trip tables.

Soon methods emerged to use these for tolled roads. You'd make a skim-time matrix for toll-refusers, and one allowing toll road use, then a discrete-choice model (or blast-to-the-past diversion curves) to split the trip table, then assign the two trip tables by their respective rules.

Most of today's assigners let you have numerous user-class trip tables, each associated with its own link-eligibility rule and link generalized-time. Many models now distribute the trip tables into 3 to 5 or so value-of-time bins (further distinguished into SOV-HOV eligibility classes). It is known that value-of-time is distributed for any income, so each bin should get trips from all income levels, the distribution still depending on income. Earlier stages of most modern demand models use household income distributions, so the means may be devised to track it to the vehicle-trip tables.

Both the discrete-choice and bin methods have their advantages and their criticisms. (Among these: Discrete choice lets you have a bias constant, but can become nonsensical when the network offers numerous use/refuse decisions, not just one. The bin method still has the all-or-nothing choice discontinuity problem, but only for each O-D's borderline bin rather than all the trips. More bins reduces this problem.)

Dial's "stoch" method from the 1960s-70s is not much of a solution. In the 1990s Dial worked on something like the value-of-time bin approach but with a continuous value-of-time distribution for each O-D. This would solve the discontinuity problem of the bin method. Little seems to have become of it in the end, judging from what the software vendors offer presently. (I think PTV offers something along those lines, but I haven't heard of any usages.)

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Bi-criteria assignment methods with variable VOT such as the one by Leurent seem to be applicable to your problem description.

You can read about this approach here: bi-criteria assignments

{Fabien Leurent. The Theory and Practice of a Dual Criteria Assignment Model with a continuously

distributed Value-of-Time. ISTTT, Jul 1996, Lyon, France. pp. 455-477. hal-00348537}

PTV-Visum has an assignment variant with an implementation of this approach. Data to estimate, calibrate and validate the required parameters is tricky to obtain.

Chetan Joshi, P.E.

PTV Group

Pedro:

CUBE voyager provides the same embedded route choice within the equilibrium assignment which provides good results and provides for dynamic pricing within the assignment. Given enough assignment iterations the process converges well. With the added flexibility that Voyagers provides it is possible to have variations in key parameters by purpose and vehicle type.

If you send me the PDF of your paper, that would be appreciated......

Thanks

David

David Schellinger, P.E.

Senior Principal - Modeling & Toll Feasibility Analysis

Stantec Consulting Services, Inc.

Direct (610)-862-7704

Mobile (215) 933-9755

david.schellinger@stantec.com

From: c=margo.co@mg.tmip.org On Behalf Of Pedro Camargo

Sent: Wednesday, December 7, 2022 8:20 AM

To: TMIP

Subject: Re: [TMIP] Accounting for Tolls in Traffic Assignment

This is an interesting topic, and Scott has already added most of my initial thoughts (and then some), but there is something I would add.

At a previous employer, we had bespoke assignment software that did explicit route choice at each step of the equilibration process (a Biconjugate Frank-Wolfe, in that case), which was a quite elegant solution.

As I was worried about path overlap, we set out to incorporate Scott's Path-Size Logit in the existing framework. In the process, we presented both the derivation of the problem (weirdly enough, the math had not been presented anywhere we could find in the literature) and explored the impact of path overlaps at equilibrium.

There are still some theoretical corner cases in this arena that bother me a bit, so it is good to see that there is still interest in the topic and somebody might come to solve those issues.

The paper is https://journals.sagepub.com/doi/10.1177/0361198119837496, but I am happy to send the PDF to any interested party.

Cheers,

Pedro

---- On Wed, 07 Dec 2022 21:33:53 +1000 John Gibb wrote ---

Once upon a time, all the traffic assignment programs assigned one trip table minimizing one generalized-time, having a delay function. If it had tolls, you could add them to the generalized-time using some average value-of-time to convert. Most trips end up choosing one or the other in an all-or-nothing choice, with equilibrium leaving split options to few O-D movements.

Then we had to model HOV lanes. After a brief and forgettable era of practitioners having to cook up workarounds, vendors soon offered multi-class equilibrium assignments. At first these let you have only a small number of trip tables with different rules for which links could be used by particular trip tables.

Soon methods emerged to use these for tolled roads. You'd make a skim-time matrix for toll-refusers, and one allowing toll road use, then a discrete-choice model (or blast-to-the-past diversion curves) to split the trip table, then assign the two trip tables by their respective rules.

Most of today's assigners let you have numerous user-class trip tables, each associated with its own link-eligibility rule and link generalized-time. Many models now distribute the trip tables into 3 to 5 or so value-of-time bins (further distinguished into SOV-HOV eligibility classes). It is known that value-of-time is distributed for any income, so each bin should get trips from all income levels, the distribution still depending on income. Earlier stages of most modern demand models use household income distributions, so the means may be devised to track it to the vehicle-trip tables.

Both the discrete-choice and bin methods have their advantages and their criticisms. (Among these: Discrete choice lets you have a bias constant, but can become nonsensical when the network offers numerous use/refuse decisions, not just one. The bin method still has the all-or-nothing choice discontinuity problem, but only for each O-D's borderline bin rather than all the trips. More bins reduces this problem.)

Dial's "stoch" method from the 1960s-70s is not much of a solution. In the 1990s Dial worked on something like the value-of-time bin approach but with a continuous value-of-time distribution for each O-D. This would solve the discontinuity problem of the bin method. Little seems to have become of it in the end, judging from what the software vendors offer presently. (I think PTV offers something along those lines, but I haven't heard of any usages.)

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Hi David,

I remember seeing a presentation by somebody from Citilabs (2018 ITM, maybe?), but I remember that equilibration was pretty poor (MSA, if I recall correctly) and nowhere near the current required standards.

I also do not recall if the issue of path overlap was being taken into consideration. Do you know what is the case?

Cheers,

Pedro

---- On Wed, 07 Dec 2022 23:54:18 +1000 Schellinger, David wrote ---

Pedro:

CUBE voyager provides the same embedded route choice within the equilibrium assignment which provides good results and provides for dynamic pricing within the assignment.

Given enough assignment iterations the process converges well. With the added flexibility that Voyagers provides it is possible to have variations in key parameters by purpose and vehicle type.

If you send me the PDF of your paper, that would be appreciated……

Thanks

David

David Schellinger, P.E.

Senior Principal – Modeling & Toll Feasibility Analysis

Stantec Consulting Services, Inc.

Direct (610)-862-7704

Mobile (215) 933-9755

mailto:david.schellinger@stantec.com

From: c=mailto:margo.co@mg.tmip.org On Behalf Of Pedro Camargo

Sent: Wednesday, December 7, 2022 8:20 AM

To: TMIP

Subject: Re: [TMIP] Accounting for Tolls in Traffic Assignment

This is an interesting topic, and Scott has already added most of my initial thoughts (and then some), but there is something I would add.

At a previous employer, we had bespoke assignment software that did explicit route choice at each step of the equilibration process (a Biconjugate Frank-Wolfe, in that case), which was a quite elegant solution.

As I was worried about path overlap, we set out to incorporate Scott's Path-Size Logit in the existing framework. In the process, we presented both the derivation of the problem (weirdly enough, the math had not been presented anywhere we could find in the

literature) and explored the impact of path overlaps at equilibrium.

There are still some theoretical corner cases in this arena that bother me a bit, so it is good to see that there is still interest in the topic and somebody might come to solve those issues.

The paper is https://can01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fjourna..., but I am happy to send the PDF to any interested party.

Cheers,

Pedro

---- On Wed, 07 Dec 2022 21:33:53 +1000 John Gibb wrote ---

end up choosing one or the other in an all-or-nothing choice, with equilibrium leaving split options to few O-D movements.

for which links could be used by particular trip tables.

by their respective rules.

into SOV-HOV eligibility classes). It is known that value-of-time is distributed for any income, so each bin should get trips from all income levels, the distribution still depending on income. Earlier stages of most modern demand models use household income

distributions, so the means may be devised to track it to the vehicle-trip tables.

still has the all-or-nothing choice discontinuity problem, but only for each O-D's borderline bin rather than all the trips. More bins reduces this problem.)

bin method. Little seems to have become of it in the end, judging from what the software vendors offer presently. (I think PTV offers something along those lines, but I haven't heard of any usages.)

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On behalf of Howard Slavin:

Some of you might find this old working paper helpful in augmenting the discussion of toll road assignment models particularly with respect to issues with “toll diversion” methods. The paper can be found at

https://www.caliper.com/pdfs/caliper-a-note-on-toll-road-assignment-meth...

Howard Slavin, PhD

President | Caliper Corporation

|||||||||||||||||||||||||||||||||||||||||||||||||||||

1172 Beacon St, Ste 300 • Newton MA 02461 USA

Direct: 617-340-2001 • Main: 617-527-4700

howard@caliper.com • www.caliper.com

I know that some current regional models recognize transponder ownership as an intermediate choice (e.g. TourCast in the Twin Cities)... way back in the day, I fitted a diffusion-of-innovations curve to help predict how growth of the EZ-Tag system would affect toll traffic and revenue forecasts in the Houston region, the reason being that ETC users were actually charged a different toll (in addition to saving time spent in line at toll booths) and this needed to be reflected in multi-class toll traffic assignment.

However, ETC is no longer an innovation, and in markets where transponder adoption has reached saturation it may have effects that aren't captured by cost and time savings alone. The ubiquity of the technology and frictionless nature of the transaction may indeed create irrational behavior similar to that of the free bus fares discussed in another thread a few weeks ago, where perceived costs appear less than the actual direct impact on a driver's bank account and time budget.

Thanks,

--Colby Brown

https://manhan.co

https://transportation.social

________________________________

From: khooper1=maine.rr.com@mg.tmip.org on behalf of CarsonKim

Sent: Thursday, December 1, 2022 3:39 PM

To: TMIP

Subject: [TMIP] Accounting for Tolls in Traffic Assignment

I am looking for advice on how to deal with tolls in a regional model. I am concerned that our current long-standing approach does not reflect today’s reality of ETC. The current model calculates a toll impedance based on a value of time for the motorist (which is assumed to be one-half of median household income in the model area). About 95 percent of current toll facility motorists have transponders linked to an account that is automatically replenished when the account balance reaches a minimum threshold. Rather than physically handing over a $1 toll or even seeing a “$1 toll paid” flash before them as they enter the toll facility, the typical motorist only sees a credit card charge of say $30 once a month (or several months for an infrequent user). In my higher-than-average-income demographic, I personally do not think for a second whether I am saving 1 minute, or 2 minutes, or 3 minutes when I choose to take the toll facility. My daughter fits more with a typical household income and views her toll bill as just one of her many electronic conveniences (like a cell phone bill or Netflix or any of many other subscriptions with regular or monthly charges) and does not do a mental impedance calculation when choosing a travel path. I know my stories are just anecdotes, but I think a significant percentage of toll facility users have a similar perspective.

I have thought of a couple different approaches. Instead of applying a universal average for household income to determine a value of time, I could disaggregate the motorists into separate bins with high income (with no concern for what the toll is), mid-level income (maybe with still little regard for the toll), and low income (where the value of time is indeed an important consideration). Of course, how I rationalize these subsets is probably just arbitrary based on the model assignment results. I have also considered trying the old Bob Dial stochastic assignment. I have not used it in decades and am not aware of how well current models (TransCAD, in my case) do with stochastic assignments.

Your ideas and suggestions would be appreciated.

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Hi Colby and all

I agree that toll transponder models are less useful than they were a decade ago when cashless tolling was less common. In fact, we have removed the component from some TourCast models during recent updates (note, though, that having this component is not a characteristic of the TourCast framework, but rather something that has been included in some TourCast models, none recently).

Perceived toll costs are unknown when cashless tolling is used, and we can't observe perceived costs. We are essentially using actual toll costs as a proxy for perceived costs. This implies that perceived costs are proportional to actual costs, but we don't know if that's the case, and I am unaware of any studies where different assumptions about perceived costs have been used.

Tom Rossi

Cambridge Systematics, Inc.

Something else to consider is whether the 'full' driver population is sensitive to tolling features. Research by Mark Burris (Texas A&M) and John Brady (Cintra US) revealed the following (presented at TRB in 2020).

* Most travelers were not really choosing between lanes--they always used the same lane regardless of travel time and toll.

* Willingness to pay for travel time savings (expressed as toll paid divided by time saved on the managed lanes (MLs) was consistent across traveler groups when broken down by how frequently they traveled on the MLs.

* Travelers that did use both sets of lanes (termed "choosers") often made choices that appeared counter intuitive based on travel time savings and toll rate.

Basically, a significant number of travelers chose to avoid the MLs regardless of time savings.

Regards,

RTM

From: c=margo.co@mg.tmip.org On Behalf Of Pedro Camargo

Sent: Wednesday, December 7, 2022 5:20 AM

To: TMIP

Subject: Re: [TMIP] Accounting for Tolls in Traffic Assignment

[EXTERNAL EMAIL]

The paper is https://journals.sagepub.com/doi/10.1177/0361198119837496, but I am happy to send the PDF to any interested party.

Cheers,

Pedro

---- On Wed, 07 Dec 2022 21:33:53 +1000 John Gibb wrote ---

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