Traffic Assignment Definition of Traffic Assignment Traffic Assignment

Traffic Assignment • Definition of Traffic Assignment • Traffic Assignment Methods • • • All-or-nothing User Equilibrium (UE) System Optimum (SO) CE 45000 Urban Transportation Planning 1

Roadway Network CE 45000 Urban Transportation Planning 2

Traffic Assignment Ø Determine routes used for O-D pairs with number of automobiles & transit vehicles on highway segments Ø Determining expected traffic volumes on links Ø Data required: Ø Number of trips between zone pairs (from trip distribution) Ø Available highway/transit routes between zones Ø Travel times on each route Ø Decision rule (algorithm) to determine route selection Ø External trips not considered in trip distribution CE 45000 Urban Transportation Planning 3

Traffic Assignment Models • Primary models: • • • All-or-nothing assignment User Equilibrium (UE) assignment System Optimum (SO) assignment Capacity restraint assignment Dynamic assignment CE 45000 Urban Transportation Planning 4

All-or-nothing Traffic Assignment • One path between every O-D pair • Travel time is constant, does not depend on congestion or traffic flow. • No congestion / capacity restraint T 1= 10 mins 1 Total Traffic =12 2 T 2= 15 mins CE 45000 Urban Transportation Planning 5

All-or-nothing, example CE 45000 Urban Transportation Planning 6

All-or-nothing, Steps Step 1: Find Shortest route between the TAZs Step 2: Assign all trips to links compromising shortest route Step 3: Continue until trips between all TAZ pairs have been assigned Advantages Disadvantages Simple Assume all traffic will travel on shortest path Inexpensive Results easy to understand CE 45000 Urban Transportation Planning Create unrealistic flow patterns 7

Principles for UE and SO “John Glen Wardrop (1922– 1989), born in Warwick, England, was an English mathematician and transport analyst who developed what became known as Wardrop's. ” Wikipedia first and second principles of equilibrium in the field of traffic assignment. 1 st Principle: No driver can unilaterally reduce his/her travel costs by shifting to another route. 2 nd Principle: Drivers cooperate with one another in order to minimize total system travel time. CE 45000 Urban Transportation Planning 8

Travel Time Link Cost Function Traffic Volume CE 45000 Urban Transportation Planning 9

Bureau of Public Roads (BPR) Function Freeways α β 70 mph 0. 88 9. 8 60 mph 0. 83 5. 5 50 mph 0. 56 3. 6 Multilane Highways α β 70 mph 1. 00 5. 4 60 mph 0. 83 2. 7 50 mph 0. 71 2. 1 CE 45000 Urban Transportation Planning Typically used if no actual data: α = 0. 15 β = 4. 0 10

In-class Problem Traffic = V Travel time = T V 1 T 1= 10+3*V 1 1 2 V 2 T 2= 15+2*V 2 CE 45000 Urban Transportation Planning 11

Comparison of Results Model t 1 t 2 x 1 x 2 z TSTT AON UE SO V 1 T 1= 10+3*V 1 1 2 V 2 T 2= 15+2*V 2 CE 45000 Urban Transportation Planning 12

User Equilibrium (UE), and System Optimum (SO) Ø User equilibrium: travel times on all used paths between O & D are same; no traveler can improve travel time by unilaterally changing routes Ø System optimum: minimal total system travel time (cost) CE 45000 Urban Transportation Planning 13

UE vs. SO Ø UE: Ø No travelers can improve their travel times by shifting routes Ø Iterative process Ø Achieves convergent solution Ø SO: Ø Travelers will behave such that total system travel time will be minimized Ø System optimal flows are not stable, since there is always temptation that travelers switch to non-system-optimal routes to improve their own travel times CE 45000 Urban Transportation Planning 14

In-class Problem Write objective function of UE and SO? x 1 T 1 1 2 x 2 T 2 CE 45000 Urban Transportation Planning 15

In-class Problem Consider 400 travelers desire to travel from zone 2 to zone 3; and 300 are from zone 1 to 3. Calculate flow on each link from UE and SO. CE 45000 Urban Transportation Planning 16

Dynamic Traffic Assignment (DTA) Ø Dynamic Traffic Assignment (DTA): modeling approach that captures relationship between dynamic route choice behaviors (path and start time) & transportation network characteristics Ø Behavioral assumption of DTA: people are “greedy”; travelers choose least travel time (or least cost) route between their origin & destination Ø Travel involves time, cost or disutility travelers try to minimize Ø Route travel time depends on choices made by all travelers (congestion effects) CE 45000 Urban Transportation Planning 17