Demand-Driven Traffic Assignment Problem Based on Travel Time Reliability

This paper deals with a road-pricing scheme that aims at alleviating congestion phenomena or air and noise pollution in some areas of a transportation network in such a way that the volumes of traffic flow on entry links to these areas do not exceed their respective predetermined thresholds by levying appropriate tolls at these links. This paper begins to show that the road-pricing scheme is equivalent to a problem that determines optimal Lagrangian multipliers for a user equilibrium traffic assignment problem with link capacity constraints. It then proceeds to devise a novel trial-and-error procedure requiring observed traffic flows at the entry links only, to identify a solution for the road-pricing scheme when link travel time functions, origin–destination demand functions, and users’ value of travel time are unknown. The procedure is as follows. A trial on a set of given tolls is conducted, and then the resultant link flows are observed. According to these observed traffic flows, a new set of tolls for the next trial is adjusted by executing a simple projection operation. The trial-and-error procedure is, in fact, a variation of a gradient projection method for dual formulation of the traffic assignment problem, and its convergence can be guaranteed under mild conditions. Accordingly, a conjecture for the convergence of trial-and-error implementation of the congestion pricing proposed by economists is rigorously proved. Furthermore, the iterative procedure presented in this paper in practice can facilitate the estimation of such tolls by land transport authorities.

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System Optimum Fuzzy Traffic Assignment Problem

PROMET - Traffic&Transportation ◽

10.7307/ptt.v31i6.3210 ◽

2019 ◽

Vol 31 (6) ◽

pp. 611-620

Author(s):

Gizem Temelcan ◽

Hale Gonce Kocken ◽

Inci Albayrak

Keyword(s):

Travel Time ◽

Assignment Problem ◽

Road Network ◽

Traffic Assignment ◽

Triangular Fuzzy Numbers ◽

System Optimum ◽

Average Speed ◽

Traffic Assignment Problem ◽

Path Lengths ◽

Link Travel Time

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.

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