Exterme values of BPR parameters

5 posts / 0 new
Last post
sramming_drcog
Exterme values of BPR parameters

Greetings to my colleague travel modelers, especially those of you working with static user equilibrium traffic assignment. I'd like to learn from any of your relevant experience.

We're considering a rather large value for beta = 39 in the BPR formula for our managed lanes facilities. By comparison, I think our next largest beta value would be around 7.5 for freeways. We're considering this experiment in order to reflect the operating policies of the toll concessionaire, who has committed to increasing tolls on SOVs and HOV2s in order to keep the managed lanes functioning at a reasonable level of service for the regional buses that also use the managed lanes. We expect that the increased toll levels would take effect when volumes exceed about 1,600 vehicles per hour in the single-lane (each direction) facility.

My questions for the group are:
1. If you use the BPR formula for traffic assignment, what is the largest value you use?
2. Have you noticed any considerations such as need for more iterations either in the traffic assignment routine or any over-arching speed feedback looping?

Thank you!

mikeflorian

Scott,

It is rare that one would use such a high value for the exponent in a
BPR volume/delay function.

The direct consequence is that there will be a need for a very large
number of iterations to achieve a reasonable relative gap. You should
try to reach at least a relative gap 0.0001. Even then, it is not
evident that you will prevent some use of the facilities that you seek
to free of certain flows. And you need a fast converging algorithm.

The largest exponent that we have used in an Emme application is 12.

Not sure what you mean by an /over-arching speed feedback looping/.

Mike

On 2017-08-08 4:20 PM, sramming_drcog wrote:
>
> Greetings to my colleague travel modelers, especially those of you
> working with static user equilibrium traffic assignment. I'd like to
> learn from any of your relevant experience.
>
> We're considering a rather large value for beta = 39 in the BPR
> formula for our managed lanes facilities. By comparison, I think our
> next largest beta value would be around 7.5 for freeways. We're
> considering this experiment in order to reflect the operating policies
> of the toll concessionaire, who has committed to increasing tolls on
> SOVs and HOV2s in order to keep the managed lanes functioning at a
> reasonable level of service for the regional buses that also use the
> managed lanes. We expect that the increased toll levels would take
> effect when volumes exceed about 1,600 vehicles per hour in the
> single-lane (each direction) facility.
>
> My questions for the group are:
> 1. If you use the BPR formula for traffic assignment, what is the
> largest value you use?
> 2. Have you noticed any considerations such as need for more
> iterations either in the traffic assignment routine or any
> over-arching speed feedback looping?
>
> Thank you!
>
> --
> Full post: https://tmip.org/content/exterme-values-bpr-parameters
> Manage my subscriptions: https://tmip.org/mailinglist
> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/3400

John Gibb

Hi Scott. Very much, yes, I've found experimentally the degree of the BPR function does a lot to assignment convergence and to feedback convergence, if there's significant congestion. As expected, higher degree leads to more iterations to reach a desired level of convergence (relative gap in assignment, displaced trips and skim change in feedback). I even experimented by changing a model's conical functions to the most similar BPR and got slower convergence in both assignment and feedback.
Now for opinion: I think a degree above 5 or 6 is usually too high anyway (for either BPR or conical). Such are often justified by steady-state traffic flow theory and observations, in which delay is infinite when demand exceeds capacity. (Somebody not long ago sent me a SF Bay-area loaded network with a 2-day delay on a Bay Bridge link.)

> On Aug 8, 2017, at 1:20 PM, sramming_drcog wrote:
>
> Greetings to my colleague travel modelers, especially those of you working with static user equilibrium traffic assignment. I'd like to learn from any of your relevant experience.
>
> We're considering a rather large value for beta = 39 in the BPR formula for our managed lanes facilities. By comparison, I think our next largest beta value would be around 7.5 for freeways. We're considering this experiment in order to reflect the operating policies of the toll concessionaire, who has committed to increasing tolls on SOVs and HOV2s in order to keep the managed lanes functioning at a reasonable level of service for the regional buses that also use the managed lanes. We expect that the increased toll levels would take effect when volumes exceed about 1,600 vehicles per hour in the single-lane (each direction) facility.
>
> My questions for the group are:
> 1. If you use the BPR formula for traffic assignment, what is the largest value you use?
> 2. Have you noticed any considerations such as need for more iterations either in the traffic assignment routine or any over-arching speed feedback looping?
>
> Thank you!
>
> --
> Full post: https://tmip.org/content/exterme-values-bpr-parameters
> Manage my subscriptions: https://tmip.org/mailinglist
> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/3400

nmarshallvt

This issue highlights the inherent limitations in trying to constrain
traffic volumes either to capacity or to a level set by policy with a
static traffic assignment (STA) algorithm. I have been substituting dynamic
traffic assignment (DTA) in entire regional travel demand models with
feedback of the DTA travel times to the other model steps. I presented this
work at the recent Planning Applications conference - presentation slides
can be found here:

http://www.trbappcon.org/2017conf/PresentationDetails.aspx?abstractid=38

I have submitted a paper for the 2018 TRB Annual Meeting that includes
benchmarks with travel demand models from regions of different sizes. In
general, I have found DTA replacement to be practical for regions up to
about 2 million population using a single $5,000 computer with 8 fast
cores. Larger regions likely would need to invest in more computer
capacity, and might also need to make model changes for this to be
practical.

In moving from STA to DTA, I have been struck by how the peak period trip
tables that we routinely assign to networks are incompatible with roadway
capacity. The Bay Bridge example cited by John Gibb is extreme in degree,
but over-capacity assignments are commonplace and really are nonsense. With
unrealistic trip tables in the STA models, trying to link conventional
models with subarea DTA is problematic. Applying DTA at the regional level
including feedback to get more realistic trip tables eliminates these
problems.

Norm Marshall

On Wed, Aug 9, 2017 at 8:44 AM, John Gibb wrote:

> Hi Scott. Very much, yes, I've found experimentally the degree of the BPR
> function does a lot to assignment convergence and to feedback convergence,
> if there's significant congestion. As expected, higher degree leads to more
> iterations to reach a desired level of convergence (relative gap in
> assignment, displaced trips and skim change in feedback). I even
> experimented by changing a model's conical functions to the most similar
> BPR and got slower convergence in both assignment and feedback.
> Now for opinion: I think a degree above 5 or 6 is usually too high anyway
> (for either BPR or conical). Such are often justified by steady-state
> traffic flow theory and observations, in which delay is infinite when
> demand exceeds capacity. (Somebody not long ago sent me a SF Bay-area
> loaded network with a 2-day delay on a Bay Bridge link.)
>
> > On Aug 8, 2017, at 1:20 PM, sramming_drcog wrote:
> >
> > Greetings to my colleague travel modelers, especially those of you
> working with static user equilibrium traffic assignment. I'd like to learn
> from any of your relevant experience.
> >
> > We're considering a rather large value for beta = 39 in the BPR formula
> for our managed lanes facilities. By comparison, I think our next largest
> beta value would be around 7.5 for freeways. We're considering this
> experiment in order to reflect the operating policies of the toll
> concessionaire, who has committed to increasing tolls on SOVs and HOV2s in
> order to keep the managed lanes functioning at a reasonable level of
> service for the regional buses that also use the managed lanes. We expect
> that the increased toll levels would take effect when volumes exceed about
> 1,600 vehicles per hour in the single-lane (each direction) facility.
> >
> > My questions for the group are:
> > 1. If you use the BPR formula for traffic assignment, what is the
> largest value you use?
> > 2. Have you noticed any considerations such as need for more iterations
> either in the traffic assignment routine or any over-arching speed feedback
> looping?
> >
> > Thank you!
> >
> > --
> > Full post: https://tmip.org/content/exterme-values-bpr-parameters
> > Manage my subscriptions: https://tmip.org/mailinglist
> > Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/3400
> --
> Full post: https://tmip.org/content/exterme-values-bpr-parameters
> Manage my subscriptions: https://tmip.org/mailinglist
> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/3400
>

--
Norm Marshall, President
Smart Mobility Inc.
205 Billings Farm Road #2E-1
White River Jct., VT 05001

802-649-5422
802-356-2969 cell

ajit.makhija@gm...

Ideally volume delay functions parameters shouldn't vary a lot between
general purpose freeway lanes and managed lanes. The solution to your
problem could be by considering income based impedance by varying value of
times into your highway skims/assignment model, basically moving from
single income class assignment to multi income class assignment. We at
AECOM have implemented this procedure for managed lanes in Washington D.C.
metro area as a part of ridership forecasting effort for proposed extension
of VRE commuter rail service which runs along I-66 corridor in Northern
Virginia. This procedure significantly improved the mode shares on managed
lanes and ridership elasticity to proposed service headways. Planning
Applications conference - presentation slides can be found here:

http://www.trbappcon.org/2017conf/PresentationDetails.aspx?abstractid=134

Kind regards,
Ajit Makhija

On Wed, Aug 9, 2017 at 9:48 AM, nmarshallvt
wrote:

> This issue highlights the inherent limitations in trying to constrain
> traffic volumes either to capacity or to a level set by policy with a
> static traffic assignment (STA) algorithm. I have been substituting dynamic
> traffic assignment (DTA) in entire regional travel demand models with
> feedback of the DTA travel times to the other model steps. I presented this
> work at the recent Planning Applications conference - presentation slides
> can be found here:
>
> http://www.trbappcon.org/2017conf/PresentationDetails.aspx?abstractid=38
>
> I have submitted a paper for the 2018 TRB Annual Meeting that includes
> benchmarks with travel demand models from regions of different sizes. In
> general, I have found DTA replacement to be practical for regions up to
> about 2 million population using a single $5,000 computer with 8 fast
> cores. Larger regions likely would need to invest in more computer
> capacity, and might also need to make model changes for this to be
> practical.
>
> In moving from STA to DTA, I have been struck by how the peak period trip
> tables that we routinely assign to networks are incompatible with roadway
> capacity. The Bay Bridge example cited by John Gibb is extreme in degree,
> but over-capacity assignments are commonplace and really are nonsense. With
> unrealistic trip tables in the STA models, trying to link conventional
> models with subarea DTA is problematic. Applying DTA at the regional level
> including feedback to get more realistic trip tables eliminates these
> problems.
>
> Norm Marshall
>
> On Wed, Aug 9, 2017 at 8:44 AM, John Gibb wrote:
>
> > Hi Scott. Very much, yes, I've found experimentally the degree of the BPR
> > function does a lot to assignment convergence and to feedback
> convergence,
> > if there's significant congestion. As expected, higher degree leads to
> more
> > iterations to reach a desired level of convergence (relative gap in
> > assignment, displaced trips and skim change in feedback). I even
> > experimented by changing a model's conical functions to the most similar
> > BPR and got slower convergence in both assignment and feedback.
> > Now for opinion: I think a degree above 5 or 6 is usually too high anyway
> > (for either BPR or conical). Such are often justified by steady-state
> > traffic flow theory and observations, in which delay is infinite when
> > demand exceeds capacity. (Somebody not long ago sent me a SF Bay-area
> > loaded network with a 2-day delay on a Bay Bridge link.)
> >
> > > On Aug 8, 2017, at 1:20 PM, sramming_drcog wrote:
> > >
> > > Greetings to my colleague travel modelers, especially those of you
> > working with static user equilibrium traffic assignment. I'd like to
> learn
> > from any of your relevant experience.
> > >
> > > We're considering a rather large value for beta = 39 in the BPR formula
> > for our managed lanes facilities. By comparison, I think our next largest
> > beta value would be around 7.5 for freeways. We're considering this
> > experiment in order to reflect the operating policies of the toll
> > concessionaire, who has committed to increasing tolls on SOVs and HOV2s
> in
> > order to keep the managed lanes functioning at a reasonable level of
> > service for the regional buses that also use the managed lanes. We expect
> > that the increased toll levels would take effect when volumes exceed
> about
> > 1,600 vehicles per hour in the single-lane (each direction) facility.
> > >
> > > My questions for the group are:
> > > 1. If you use the BPR formula for traffic assignment, what is the
> > largest value you use?
> > > 2. Have you noticed any considerations such as need for more iterations
> > either in the traffic assignment routine or any over-arching speed
> feedback
> > looping?
> > >
> > > Thank you!
> > >
> > > --
> > > Full post: https://tmip.org/content/exterme-values-bpr-parameters
> > > Manage my subscriptions: https://tmip.org/mailinglist
> > > Stop emails for this post: https://tmip.org/mailinglist/
> unsubscribe/3400
> > --
> > Full post: https://tmip.org/content/exterme-values-bpr-parameters
> > Manage my subscriptions: https://tmip.org/mailinglist
> > Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/3400
> >
>
> --
> Norm Marshall, President
> Smart Mobility Inc.
> 205 Billings Farm Road #2E-1
> White River Jct., VT 05001
>
> 802-649-5422
> 802-356-2969 cell
> --
> Full post: https://tmip.org/content/exterme-values-bpr-parameters
> Manage my subscriptions: https://tmip.org/mailinglist
> Stop emails for this post: https://tmip.org/mailinglist/unsubscribe/3400
>