TRN-35

BPR volume–delay

t = t0 (1 + α (V/C)^β). Bureau of Public Roads; α = 0.15, β = 4 classic.

Reading speed

TrafficBPR

Governing equation

t=t_0\bigl(1+\alpha(V/C)^\beta\bigr)

where

t_0: Free-flow time (min)
V: Volume (veh/h)
C: Capacity (veh/h)
\alpha: α (—)
\beta: β (—)
t: Travel time (min)

Lecture brief

Historical brief

Highway and traffic theory crystallized with Greenshields’ 1935 speed–density line, then AASHTO stopping sight and equivalent axles. The lab is that operational arithmetic of flow, braking and pavement load. This sheet (TRN-35 — BPR volume–delay) is the form associated with BPR. Working symbols: $t_0$ , $V$ , $C$ , $\alpha$ , $\beta$ $\rightarrow$ $t$ . A smooth travel-time function for assignment. Steeper β makes congestion bite later and harder.

Purpose

Purpose: compute

t

from

t_0

V

C

\alpha

\beta

in Transport via

t=t_0\bigl(1+\alpha(V/C)^\beta\bigr)

t = t0 (1 + α (V/C)^β). Bureau of Public Roads; α = 0.15, β = 4 classic. Use it when a real transport question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

t_0 = 8.000\,\mathrm{min}

V = 1400.000\,\mathrm{veh/h}

C = 1800.000\,\mathrm{veh/h}

\alpha = 0.150\,\mathrm{—}

\beta = 4.000\,\mathrm{—}

, the governing relation

t=t_0\bigl(1+\alpha(V/C)^\beta\bigr)

yields

t = 8.44\,\mathrm{min}

. A free time, a V/C, a rising travel time. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Free-flow time t_08 minVolume V1400 veh/hCapacity C1800 veh/hα \alpha0.15 —β \beta4 —

Outputs

Travel time t8.44 min

Reading speed

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Narration of this film

A free time, a V/C, a rising travel time.

A smooth travel-time function for assignment. Steeper β makes congestion bite later and harder.

Reading speed

Watch on YouTube