BPR

A BPR link performance function implementation

Description

Travel time on a link segment for a particular mode is computed using a specific link performance function that relates flow uniquely to a travel time utilising a strictly increasing monotonic function know as the BPR¹ function. This function looks like the following

\(\Large \tau_{a,m} = \tau_{a,m}^{ \textrm {freeflow}}(1+ \alpha({v_a \over C_a})^{\beta}) \qquad \textrm{where } \tau_{a,m}^{ \textrm {freeflow}}= {L_a \over \vartheta_{a,m}}\)

with

\(\tau_{a,m}= \textrm{travel time on link segment } a \textrm{ for mode } m,\\ \vartheta_{a,m} = \textrm{free flow speed on link } a \textrm{ for mode } m,\\ \alpha = \textrm {calibration parameter},\\ \beta = \textrm {calibration parameter},\\ v_a = \textrm {measured flow on link segment} a,\\ L_a = \textrm {length of link segment} a,\\ C_a = \textrm {saturation flow on link segment} a,\)

The \(\alpha\) and \(\beta\) parameters can be configured hierarchically, where the most specific configuration takes precedence. The hierarchy is as follows:

default \(\alpha\) and \(\beta\)
default \(\alpha_m\) and \(\beta_m\) by mode \(m\)
default \(\alpha_{m,s}\) and \(\beta_{m,s}\) by mode \(m\) and link segment type \(s\)
default \(\alpha_{m,l}\) and \(\beta_{m,l}\) by mode \(m\) and link segment \(l\)

Whenever the more specific configuration is absentn the next most specific configuration is checked and applied, until we reach the simulation wide default which have been pre-set (or overridden by the user).

¹ United States, Bureau of Public Roads, Traffic assignment manual. (1964). Washington.

Defaults

Name	Default	Type	Unit
\(\alpha\)	0.5	`float`	`None`
\(\beta\)	4	`float`	`None`

Methods

Memory output formatter exposes the following methods

Name	Description
`.set_default_parameters(+)`	Override the default \(\alpha\) and \(\beta\) in various ways
`.set_parameters(+)`	Override the \(\alpha\) and \(\beta\) for specific link segments

Properties

This class has no properties (yet)

Example 1

from planit import *

# choose to run PLANit with a traditional static traffic assignment method
planit_instance = PLANit()
planit_instance.set(TrafficAssignment.TRADITIONAL_STATIC)

# set physical cost to BPR link performance function
planit_instance.assignment.set(PhysicalCost.BPR)

# override the default alpha and beta
alpha = 0.87
beta = 5
planit_instance.assignment.physical_cost.set_default_parameter(alpha, beta)

Source code

Class BPRCostWrapper in Wrappers.py

.set_default_parameters+

BPR link performance function method

.set_parameters+