Abstract
This paper focuses on converting the system optimum traffic assignment problem (SO-TAP) to system optimum fuzzy traffic assignment problem (SO-FTAP). The SO-TAP aims to minimize the total system travel time on road network between the specified origin and destination points. Link travel time is taken as a linear function of fuzzy link flow; thus each link travel time is constructed as a triangular fuzzy number. The objective function is expressed in terms of link flows and link travel times in a non-linear form while satisfying the flow conservation constraints. The parameters of the problem are path lengths, number of lanes, average speed of a vehicle, vehicle length, clearance, spacing, link capacity and free flow travel time. Considering a road network, the path lengths and number of lanes are taken as crisp numbers. The average speed of a vehicle and vehicle length are imprecise in nature, so these are taken as triangular fuzzy numbers. Since the remaining parameters, that are clearance, spacing, link capacity and free flow travel time are determined by the average speed of a vehicle and vehicle length, they will be triangular fuzzy numbers. Finally, the original SO-TAP is converted to a fuzzy quadratic programming (FQP) problem, and it is solved using an existing approach from literature. A numerical experiment is illustrated.
Highlights
The Traffic Assignment Problem (TAP) describes the distribution of vehicles in traffic through a network comprising a set of nodes and a set of directed links connecting these nodes
This paper considers the system optimum traffic assignment problem (SO-TAP) which has been extensively studied in the literature
The focus was on solving system optimum fuzzy traffic assignment problem (SO-FTAP) by minimizing the total system travel time
Summary
The Traffic Assignment Problem (TAP) describes the distribution of vehicles in traffic through a network comprising a set of nodes and a set of directed links connecting these nodes. The drivers do not want to deal with congestion while travelling from an origin point to a destination point. To overcome this congestion effect, many researchers have studied this problem. A specified flow x* creates a delay t* using performance function and in demand function t* corresponds to x*. This (x*,t*) point will be an equilibrium point and it is a solution of TAP, which is known as transportation network equilibrium problem. Since drivers do not want to waste their time in congested traffic, they could tend to change their routes to find any alternative path to reach their destination point, and a new equilibrium state will be observed
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