ROUTE CHOICE Dr. Randa Oqab Mujalli Route choice User Equilibrium - - PowerPoint PPT Presentation

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

• Dr. Randa Oqab Mujalli

Example 1:

• Dr. Randa Oqab Mujalli

• Dr. Randa Oqab Mujalli

Example 3

• 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]:

• Dr. Randa Oqab Mujalli





n x n

n

dw w t x S ) ( ) ( min

Where, n: a specific route, and tn(w): performance function corresponding to route n (w denotes flow, xn’s) This function is subject to the constraints that the flow on all routes is greater than or equal to zero (xn≥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, 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





n n

x q

• 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