Corridor planning: a quick response strategy

Background

NCHRP 187 - Quick Response Urban Travel Estimation Techniques (1978)

• Objective: provide tools and transferable model parameters for communities to forecast activity, using limited data

NCHRP 365 - Travel Estimation Techniques for Urban Planning (1998)

• Objective: update procedures from NCHRP 187• Needs to be updated again (see:

http://www.edthefed.com/xferability/ )

Corridor Diversion Model

• NCHRP 187 and 365 present an “alternative” traffic assignment model similar to stochastic assignment– Based on multi-path probability model concepts of Dial

• First: Consider a basic application

Corridor Diversion Model Starting point

Prob (route r) = Receptivity* on route r

Total receptivity on all competing routes

Where:• Prob (route r) = probability of choosing route r

• Receptivity could be 1/(travel time)x

*receptivity is the opposite of resistance

Sample problem

Given: three competing routes, j, with travel times of 9, 12, and 15 minutes. Total of 50,000 vehicles moving through the corridor.

Model : P(r) = t -0.5 Σ t -0.5

j

Procedure:Calculate the relative probability of each route, and

multiply by total trips

Solution for sample problem

Travel TimeTravel Time ReceptivityReceptivity ( t ( t -0.5 -0.5 ))

Portion of Portion of totaltotal

TripsTrips

99 0.3330.333 0.3790.379 18,90018,900

1212 0.2890.289 0.3280.328 16,40016,400

1515 0.2580.258 0.2930.293 14,70014,700

SumSum 0.8800.880 1.0001.000 50,00050,000

Dial’s Quick response model

Diversion model to estimate a re-assignment of trips among competing routes in a corridor, given that travel time reductions are achieved on an improved route in the corridor.

Dial’s Quick response model (cont)

Dial’s concept is a probabilistic model, with different mathematic form and only two route choices (initially)

where:

Vmtr = volume on min. time routetm = time on improved minimum time routeti = current time on route i Vt = total trips within the corridorΘ = diversion parameter

tttmtr Ve

Vim

)(1

1

Q: what is the effect of a large Θ?hint: be careful … what is the sign of the exponent?

Dial Quick response model – cont’d

Volume on non-minimum route shown as:

ttt

tt

i Ve

eV

im

im

)(

)(

1

Dial’s Quick response model – cont’d

Issue: If the exponential format is the correct model, what is the appropriate coefficient for Θ?

For the two route choice (solve for Θ in the first equation):

The Vi and Vmtr are based on the existing split of traffic in the corridor and the current travel times.

im

mtr

i

tt

VV

)ln(

ExampleExample

Improve route (A) from 4 lanes to five, each direction … what happens?

Assume free flow speeds are 60mph for the freeway (route A) and 30mph for the arterial (route B)

v/c ratio for a 5 lane facility:

Using highway capacity curves, lookup speed (=50mph):

Compute theta (and assume it stays fixed):

Find new travel time on mtr:

Re-compute v/c ratio and do another iteration if speed is too far off. In this case, computed speed is 48 mph (from charts) and is close to the original 50mph

Compute new traffic split

vphe

Vmtr 7869)12407500(1

1)0.120.6(367.0

vphe

eVi 871)12407500(

1 )0.120.6(367.0

)0.120.6(367.0

Graphical method

What if we have three routes?

Three corridor routes: Sample problem indicates that each non-minimum route be

computed by:1) compute the diversion between two fastest routes as before2) recompute Θ using routes 2 and 3 volumes and times, to

distribute new trips on 2, with route 3 as competing route3) Go through iterative process with calculated volumes two or

more times to fine tune adjustments.4) See if it converges – it may not5) Then what?

3 corridor example

7869 from previous

871 from previous

219.00.2

438.0

1412

)1240800

ln(

CB

vphe

Vmtr 1144)800871(1

1)145.10(219.0

vphe

eVi 528)800871(

1 )145.10(219.0

)145.10(219.0

7869 from prev

871 from prev1016 now

655 now

May want to iterate once more … if you do, the split between A and B will become 7855 and 1157, then redo B-C, and so on. Assume thetas are constant.

Homework• Continue to iterate the example on the previous page 5 times • Use the BPR equation to relate travel time to v/c ratio• assume alpha = 0.55, beta = 3.9 for 4 lane freeway (route A before)• assume alpha = 0.645, beta = 3.9 for 5 lane freeway (route A after)• assume alpha = 1.0, beta = 4.0 for other (routes B and C)• assume capacity of route A before adding a lane is 8000, after adding lane

= 10,000 per direction, free speed = 60mph (both)• assume capacity of route B = 1850 per direction, free speed = 30mph • assume capacity of route C = 1250 per direction, free speed = 25mph • Did it converge? • How many vehicles will use each of the three routes? (5th iteration)• Show all of your work and assumptions

Kannel’s adjustment for Quick response model

Consider using single equation for all routes Model : P(r) = 1/ e (Θti )

Σ 1/ e (Θti ) where Θ can be calculated as per Dial for each of the

slower routes relative to the faster route and a weighted average, based on volumes of the slower routes is used.

i

Kannel adjustment for Quick response model: Table results (Θ = 0.351)

timetime Calculated Calculated receptivityreceptivity

Relative Relative probability probability

or shareor share

Assigned Assigned VolumeVolume

66 0.1220.122 0.8460.846 80708070

1212 0.1150.115 0.1030.103 980980

1414 0.0070.007 0.0510.051 490490

SumSum 0.1440.144 1.0001.000 95409540

Kannel’s adjustment for Quick response model

Dial’s Kannel’s iteration #2 proposed

6 min route 8000 807012 min route 885 98014 min route 655 490

No way to know which is correct, but does either answer change the number of lanes?