行驶时间函数(路阻函数)：BPR(美国道路局Bureau of Public Road)函数

GEOG 111 & 211A
Transportation Planning
Example (BPR formula)
140 120 100 80 60 40 20 0 0
Travel time on link
V t t 0 1 C
Key Ingredients
• Link performance functions (travel time vs traffic volume) • Turning delays (penalties) • Algorithm for assignment of traffic • Behavioral assumptions
Path 1
Origin
Path 2
Destination
GEOG 111 & 211A
Transportation Planning
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
GEOG 111 & 211A
Transportation Planning
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
Transportation Planning
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
GEOG 111 & 211A
Transportation Planning
All or Nothing Assignment
• Assumption:
– All drivers consider the same attributes for route choice: perceive and weigh them in the same way
Yes
Wardrop’s equilibrium
Stochastic user equilibrium
GEOG 111 & 211A
Transportation Planning
Basic Assignment Methods
(in TRANSCAD)
• • • • • • •
All or Nothing STOCH Incremental Capacity Restraint User Equilibrium Stochastic User Equilibrium System Optimum
Free-Flow Travel Time Traffic Flow Traffic Flow
Capacity
GEOG 111 & 211A
Transportation Planning
Example (BPR formula)
1.2 1 0.8 0.6 0.4 0.2 0 0 500 1,000
GEOG 111 & 211A
Transportation Planning
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
GEOG 111 & 211A
Transportation Planning
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
GEOG 111 & 211A
Transportation Planning
Comparison
Stochastic effects included? No No Is capacity restraint included? All-or-Nothing Yes Pure stochastic Dial’s, Burrell’s
GEOG 111 & 211A
Transportation Planning
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
GEOG 111 & 211A
Transportation Planning
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)
GEOG 111 & 211A
Transportation Planning
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
GEOG 111 & 211A
Transportation Planning
Traffic Assignment
GEOG 111 & 211A
Transportation Planning
Traffic Assignment
• Fourth Step in UTPS Modeling • Inputs:
• All traffic is assigned to shortest path between each O-D pair • No congestion effect • Link costs are fixed • Simple, but not accurate
GEOG 111 & 211A
– Peak Hour, Passenger Vehicle Origin - Destination (O - D) Matrix – Network • Travel Time, Capacity, Direction
• Outputs:Biblioteka Baidu
– Peak Hour Volumes, Estimated Travel Times, and Volume to Capacity Ratios
BPR
BPR BPR
BPR
GEOG 111 & 211A
Transportation Planning
Key Ingredients
• Link performance functions (travel time vs traffic volume) • Turning delays (penalties) • Algorithm for assignment of traffic • Behavioral assumptions
Travel time on link
V t t 0 1 C
1,500 2,000 2,500

0 . 15 , 4 . 0 Volume in Vehicles/hour
V=volume, C=capacity, t0=free flow travel time
GEOG 111 & 211A
Transportation Planning
Link Performance Functions
• Mathematical Relationship Between Traffic Flow and Travel Time
Linear Relationship Route Travel Time Non-Linear Relationship
GEOG 111 & 211A
Transportation Planning
Key Ingredients
• Link performance functions (travel time vs traffic volume) • Turning delays (penalties) • Algorithm for assignment of traffic • Behavioral assumptions
500
1,000
1,500
2,000
2,500
0 . 15 , 20 . 0
Volume in Vehicles/hour
V=volume, C=capacity, t0=free flow travel time
GEOG 111 & 211A
Transportation Planning