ROUTE CHOICE Dr. Randa Oqab Mujalli
Route choice User Equilibrium • The rule of choice underlying user equilibrium is that travelers will select a route so as to minimize their personal travel time between the origin and destination. User equilibrium is defined as: The travel time between a specified origin and destination on all used routes is the same and is less than or equal to the travel time that would be experienced by a traveler on any unused route [Wardrop, 1952]. Dr. Randa Oqab Mujalli
Example 1: Dr. Randa Oqab Mujalli
Dr. Randa Oqab Mujalli
Example 3 Dr. Randa Oqab Mujalli
Dr. Randa Oqab Mujalli
Mathematical Programming Approach to User Equilibrium • Equating travel time on all used routes is straight forward approach to user equilibrium, but can become cumbersome when many alternative routes are involved. • The approach used to solve this computational obstacle is to formulate the user equilibrium as a mathematical program. • Specifically, user-equilibrium route flows can be obtained by minimizing the following function [Sheffi, 1985]: x n min S ( x ) t ( w ) dw n n 0 Dr. Randa Oqab Mujalli
Where, n: a specific route, and t n (w): performance function corresponding to route n (w denotes flow, x n ’s ) This function is subject to the constraints that the flow on all routes is greater than or equal to zero (x n ≥ 0) and the flow conservation holds (the flow on all routes between an origin and destination sums to the total number of vehicles, q, travelling between the origin and destination, q x n n Formulating the user equilibrium problem as a mathematical program allows an equilibrium solution to very complex highway networks (many O- Ds) Dr. Randa Oqab Mujalli
Dr. Randa Oqab Mujalli
Dr. Randa Oqab Mujalli
Dr. Randa Oqab Mujalli
1 1 Dr. Randa Oqab Mujalli
Dr. Randa Oqab Mujalli
Dr. Randa Oqab Mujalli
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