xtending the FW Method to Solve Transit Assignment Problem with Fleet Capacity Constraint
Planning for public transportation systems requires solving the transit assignment models in order to determine the distribution pattern of travelers between the transit lines. Transit assignment problem is defined on a transit network which a travel time and a frequency function will be defined for each link. In uncongested transit networks that the capacity of the transit vehicles are infinite, the problem is formulated as a linear programming (LP) model by considering fixed travel time and frequency for links and it is solved by LP algorithms. In congested transit networks that the capacity of the transit vehicles are finite, the problem is written as a non-linear programming model by considering flow dependent travel time and fixed frequency for links which the link flows are its variables. The method of successive average (MSA) as an inexact method is applied to solve this problem. The purpose of this paper is to extend the Frank and Wolfe (FW) method for solving the transit assignment problem with fleet capacity constraint. The problem is formulated with the flow dependent travel times and it is solved by both the MSA and extended FW for a sample test network. The proposed algorithm shows a fast rate of convergence based on the numerical results.
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