Route Choice
Route Choice Fial step i sequetial approach Trip geeratio (umber of trips) Trip distributio (origis ad destiatios) Mode choice (bus, trai, etc.) Route choice (specific roadways used for each origi ad destiatio) Desired output from the traffic forecastig process: how may vehicles at ay time o a roadway
Complexity Route choice decisios are primarily a fuctio of travel times, which are determied by traffic flow Traffic flow Travel time Relatioship ca be captured i a variety of ways, icludig by highway performace fuctio
Outlie 1. Geeral 2. HPF Fuctioal Forms 3. Basic Assumptios 4. Route Choice Theories a. User Equilibrium b. System Optimizatio c. Compariso
Basic Assumptios 1. Travelers select routes o the basis of route travel times oly People select the path with the shortest TT Premise: TT is the major criterio, quality factors such as sceery do ot cout Geerally, this is reasoable 2. Travelers kow travel times o all available routes betwee their origi ad destiatio Strog assumptio: Travelers may ot use all available routes, ad may base TTs o perceptio 3. Travelers all make this choice at the same time
Travel Time HPF Fuctioal Forms Free Flow Liear No-Liear Commo No-liear HPF T T0 1 v c from the Bureau of Public Roads (BPR) Traffic Flow (veh/hr) Capacity
Speed (mph) Speed vs. Flow u f Free Flow Speed q k j u u u 2 f Ucogested Flow u m Cogested Flow Flow (veh/hr) Highest flow, capacity, q m q m is bottleeck discharge rate
Theory of User Equilibrium Travelers will select a route so as to miimize their persoal travel time betwee their origi ad destiatio. User equilibrium (UE) is said to exist whe travelers at the idividual level caot uilaterally improve their travel times by chagig routes. Frak Kight, 1924
Wardrop Wardrop s 1st priciple The jourey times i all routes actually used are equal ad less tha those which would be experieced by a sigle vehicle o ay uused route Wardrop s 2d priciple At equilibrium the average jourey time is miimum
Theory of System-Optimal Route Choice Preferred routes are those, which miimize total system travel time. With System-Optimal (SO) route choices, o traveler ca switch to a differet route without icreasig total system travel time. Realistically, travelers will likely switch to o-system-optimal routes to improve their ow TTs.
Formulatig the UE Problem Fidig the set of flows that equates TTs o all used routes ca be cumbersome. Alteratively, oe ca miimize the followig fuctio: mi x 0 t w dw = Route betwee give O-D pair t (w)dw = HPF for a specific route as a fuctio of flow w = Flow x 0 for all routes Miimize travel times
Formulatig the UE Problem mi x 0 t w dw mi x 0 t w dw x 0 mi t w dw = Route betwee give O-D pair t (w)dw = HPF for a specific route as a fuctio of flow w = Flow x 0 for all routes
Example (UE) Two routes coect a city ad a suburb. Durig the peak-hour morig commute, a total of 4,500 vehicles travel from the suburb to the city. Route 1 has a 60-mph speed limit ad is 6 miles log. Route 2 is half as log with a 45-mph speed limit. The HPFs for the route 1 & 2 are as follows: Route 1 HPF icreases at the rate of 4 miutes for every additioal 1,000 vehicles per hour. Route 2 HPF icreases as the square of volume of vehicles i thousads per hour.. Route 1 City Route 2 Suburb
Example: Compute UE travel times o the two routes
Example: Compute UE travel times o the two routes
Example: Compute UE travel times o the two routes
Example: Compute UE travel times o the two routes
Example: Compute UE travel times o the two routes
Theory of System-Optimal Route Choice Preferred routes are those, which miimize total system travel time. With System-Optimal (SO) route choices, o traveler ca switch to a differet route without icreasig total system travel time. Travelers ca switch to routes decreasig their TTs but oly if System-Optimal flows are maitaied. Realistically, travelers will likely switch to o-system-optimal routes to improve their ow TTs. Not stable because idividuals will be tempted to choose differet route.
Formulatig the SO Problem Fidig the set of flows that miimizes the followig fuctio: mi x t x mi x t x = Route betwee give O-D pair t (x ) = travel time for a specific route x = Flow o a specific route Miimize travel time times flow
Example (SO) Two routes coect a city ad a suburb. Durig the peak-hour morig commute, a total of 4,500 vehicles travel from the suburb to the city. Route 1 has a 60-mph speed limit ad is 6 miles log. Route 2 is half as log with a 45-mph speed limit. The HPFs for the route 1 & 2 are as follows: Route 1 HPF icreases at the rate of 4 miutes for every additioal 1,000 vehicles per hour. Route 2 HPF icreases as the square of volume of vehicles i thousads per hour. Compute UE travel times o the two routes. Route 1 City Route 2 Suburb
Example: Solutio
Example: Solutio
Compare UE ad SO Solutios User equilibrium System optimizatio Route 1 City Route 2 Suburb
Why are the solutios differet? Why is total travel time shorter? Notice i SO we expect some drivers to take a loger route. How ca we force the SO? Why would we wat to force the SO?
0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500 travel time (miutes) 30 25 UE 20 15 TT1 TT2 10 5 SO 0 flow (lik 1)
Total Travel time (mi) Total Travel time is Miimum at SO 120000 100000 80000 60000 40000 20000 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 Flow (lik 1)
By askig oe driver to take 3 miutes loger, I save more tha 3 miutes i the reduced travel time of all drivers (oliear) Total travel time if X 1 =1600 is 55829 Total travel time if X 1 =1601 is 55819