corridor planning: a quick response strategy. background nchrp 187 - quick response urban travel...
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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?
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