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Re: [sumo-user] TR: Publics Roads (BPR) formula
  • From: François Vaudrin <francois.vaudrin.1@xxxxxxxxx>
  • Date: Mon, 22 Nov 2021 22:02:10 +0000
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  • Thread-topic: TR: [sumo-user] Publics Roads (BPR) formula

Hello Jakob,


Thanks for the reference, that sounds very interesting to me.


Since there is no closed loop on a highway, I'm thinking of artificially creating density with variable speed panels toward the end of the network.

Does it make sense?


Best
François

De : sumo-user <sumo-user-bounces@xxxxxxxxxxx> de la part de Jakob Erdmann <namdre.sumo@xxxxxxxxx>
Envoyé :ect User discussions <sumo-user@xxxxxxxxxxx>
Objet : Re: [sumo-user] Publics Roads (BPR) formula
 
Hello François,
Most likely, your scenario does not reach the required traffic density.
Feel free to post your files to enable more specific advice.

regards,
Jakob

Am Fr., 19. Nov. 2021 um 07:24 Uhr schrieb François Vaudrin <francois.vaudrin.1@xxxxxxxxx>:
This is  the BPR formula.

Best regards

François

De : François Vaudrin <francois.vaudrin.1@xxxxxxxxx>
Envoyé : vendredi 19 novembre 2021 01:07
À : mvaudrin <mvaudrin@xxxxxxxxxxx>
Objet : TR: [sumo-user] Publics Roads (BPR) formula
 
Info.

François
De : François Vaudrin <francois.vaudrin.1@xxxxxxxxx>
Envoyé : vendredi 19 novembre 2021 01:06
À : Sumo project User discussions <sumo-user@xxxxxxxxxxx>
Objet : RE: [sumo-user] Publics Roads (BPR) formula
 

Thank you for your answer Qichao,


You're right about the BPR formula, but that's not what we see with the SUMO simulations.


The function we get is a line of the following form:


y = mx + b


Whereas the function of BPR is exponential and tends towards an asymptote.


T = Tff (1 + α (Q*Qpc)**β



Perhaps this theory is debatable, because it dates from 1964 and the microsimulation tools were not available at the time.


But maybe I am wrong or there is something that I do not understand.


Best


François

De : sumo-user <sumo-user-bounces@xxxxxxxxxxx> de la part de Qichao Wang <qichao@xxxxxx>
Envoyé : jeudi 18 novembre 2021 22:35
À : Sumo project User discussions <sumo-user@xxxxxxxxxxx>
Objet : Re: [sumo-user] Publics Roads (BPR) formula
 
At much lower flow rates, you should see a flat line. As you increase the volume, you will see a point when the rate increases. When the capacity is lower than the demand, as time goes, the travel time should keep increasing. That basically means that there is no stable observed travel time (i.e., not a single point on your graph). 

You don’t need to create bottlenecks to fit a highway performance function. You can create a loop network to see the impact on having more cars on road. 

Thanks,
Qichao

On Thu, Nov 18, 2021 at 8:07 PM François Vaudrin <francois.vaudrin.1@xxxxxxxxx> wrote:

Hello everyone,


Has anyone ever tested the Bureau of Public Roads (BPR) formula with SUMO?


This formula was developed in the 1960s by the BPR to estimate travel time as a function of road capacity under free-flow conditions (such as on a highway). The transport time increases exponentially depending on the capacity of the road (see diagram in the attached file).


We would like to reproduce these phenomena with SUMO by gradually increasing the traffic flow and measuring the total time to empty the network. We then reproduced the results on a graph to check if it is similar to that of the BPR.


The problem is that we are not getting an exponential function, but a straight line (see results in the attached file) and that is not what the BPR predicted in the 1960s.


Does that make sense?


Do we have to introduce a bottleneck (or reduce the speed) at the end of the network to create a queue or traffic jam?


Thank you

François
CANADA
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