Traffic Assignment

1. Traffic Assignment

2. Traffic Assignment • Fourth Step in UTPS Modeling • Inputs: • Peak Hour, Passenger Vehicle Origin - Destination (O - D) Matrix • Network • Travel Time, Capacity, Direction • Outputs: • Peak Hour Volumes, Estimated Travel Times, and Volume to Capacity Ratios

3. Key Ingredients • Link performance functions (travel time vs traffic volume) • Turning delays (penalties) • Algorithm for assignment of traffic • Behavioral assumptions

4. Key Objectives • Obtain aggregate network measures • Estimate zone-to-zone travel times (costs) • Obtain link flows • Estimate routes for each O-D pair • Analyze O-D pairs • Obtain turning movements

5. Link Performance Functions • Mathematical Relationship Between Traffic Flow and Travel Time Linear Relationship Non-Linear Relationship Route Travel Time Capacity Free-Flow Travel Time Traffic Flow Traffic Flow

6. Example (BPR formula) V=volume, C=capacity, t0=free flow travel time

7. Example (BPR formula) V=volume, C=capacity, t0=free flow travel time

8. Key Ingredients • Link performance functions (travel time vs traffic volume) • Turning delays (penalties) • Algorithm for assignment of traffic • Behavioral assumptions

9. Types of Penalties • [TURNING] At intersections for turning left, right or through • [TRANSITION] Transition between two different types of highways (on-ramp, off-ramp movements) • [TRANSFER] Inter(multi)modal interchanges (waiting time at bus stop) BPR BPR BPR BPR

10. Key Ingredients • Link performance functions (travel time vs traffic volume) • Turning delays (penalties) • Algorithm for assignment of traffic • Behavioral assumptions

11. Algorithms • Uncongested vs Congested Networks (capacity) • Deterministic vs Stochastic (analyst’s ignorance and people’s heterogeneity) • With vs Without Traffic Control “feedback” (think of intersections’ control effects) • Treatment of time & equilibrium considerations • Combined with other steps

12. Comparison

13. Basic Assignment Methods (in TRANSCAD) • All or Nothing • STOCH • Incremental • Capacity Restraint • User Equilibrium • Stochastic User Equilibrium • System Optimum

14. All or Nothing Assignment • Assumption: • All drivers consider the same attributes for route choice: perceive and weigh them in the same way • All traffic is assigned to shortest path between each O-D pair • No congestion effect • Link costs are fixed • Simple, but not accurate

15. Path 1 Origin Destination Path 2 All or Nothing Assignment • All traffic from zone i to zone j uses the (initially) minimal travel time path • Roadway performance NOT enforced during assignment • May Become Inaccurate, but simple & fast method • NOT for congested networks

16. STOCH (Transcad) • Based on choice probability for each path from an origin to a destination • In a path TRANSCAD considers only reasonable links = links that take a traveler away from origin and closer to destination • Link travel time not dependent on link volume • Probability based on LOGIT (reviewed in modal choice) • Traveler chooses the most convenient path

17. Incremental Assignment • Many steps in the procedure • In each step one fraction of OD matrix assigned using all-or-nothing assignment • At each step link travel times are based on the volume assigned in previous step • May become very inaccurate

18. Capacity Restraint • Many steps in the procedure • All-or-Nothing and then compute travel times • All-or-Nothing using new travel times based on link performance (get new travel times) • All-or-Nothing using latest travel times • Algorithm may flip-flop

19. User Equilibrium • Assignment is performed such that travel time from zone i to zone j cannot be decreased by using an alternate route • Minimal time path used until congestion effects make an alternate path have the same travel time, both used until congestion effects make another alternate path have the same travel time and so on • Roadway performance enforced • Long, iterative process

20. Path 1 Origin Destination Path 2 UE – both paths same travel time Path 1 Cost Path 2 Cost Trips on Path 2 Trips on Path 1

21. Stochastic User Equilibrium • Similar to User Equilibrium, with error term introduced in determining shortest path • Paths with best travel time used by more vehicles • Less attractive paths used by less vehicles • More realistic behavior

22. System Optimum • Minimizes TOTAL travel time • Minimal travel time path for specific OD pairs not necessarily used • Think of an application for UPS • Roadway performance (travel time function of travel volume used)

23. Other Issues • Combining private car, transit, and trucks • Regional applications vs Statewide applications • Data quality and potential failures • Dynamic traffic assignment and related algorithms (see the site: http://www.mti.umd.edu/research/recentResearch.htm)

24. Why, when, and how of transportation planning Policy-planning-programming Geo-hierarchy and temporal hierarchy of plans Travel surveys and the total design method Types of surveys and ways to communicate with people Air quality/emissions Travel model and the four step procedures Trip generation models Trip distribution models Mode Choice Traffic assignment procedures Input to each and output from each step Regression models and why Mostly conceptual – but bring calculator just in case Exam Notes