1. Corridor planning: a quick response strategy

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

3. 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

4. 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

5. 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

6. Solution for sample problem Travel Time Receptivity ( t -0.5 ) ( t -0.5 ) Portion of total Trips 90.3330.37918,900 120.2890.32816,400 150.2580.29314,700 Sum0.8801.00050,000

7. 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.

8. Dial’s Quick response model (cont) Dial’s concept is a probabilistic model, with different mathematic form and only two route choices (initially) where: V mtr = volume on min. time route t m = time on improved minimum time route t i = current time on route i V t = total trips within the corridor Θ = diversion parameter Q: what is the effect of a large Θ? hint: be careful … what is the sign of the exponent?

9. Dial Quick response model – cont’d Volume on non-minimum route shown as:

10. 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 V i and V mtr are based on the existing split of traffic in the corridor and the current travel times.

11. Example 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)

12. 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:

13. 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

14. Graphical method

15. 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 before 2)recompute Θ using routes 2 and 3 volumes and times, to distribute new trips on 2, with route 3 as competing route 3)Go through iterative process with calculated volumes two or more times to fine tune adjustments. 4)See if it converges – it may not 5)Then what?

16. 3 corridor example

17. 7869 from previous 871 from previous

19. 7869 from prev 871 from prev 1016 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.

20. 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? (5 th iteration) Show all of your work and assumptions

21. 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

22. Kannel adjustment for Quick response model: Table results (Θ = 0.351) time Calculated receptivity Relative probability or share Assigned Volume 60.1220.8468070 120.1150.103980 140.0070.051490 Sum Sum0.1441.0009540

23. Kannel’s adjustment for Quick response model Dial’s Kannel’s iteration #2 proposed 6 min route 80008070 12 min route 885 980 14 min route 655 490 No way to know which is correct, but does either answer change the number of lanes?