A Simultaneous Solution for Reserve Capacity Maximization and Delay Minimization Problems in Signalized Road Networks

Ozgur Baskan,Huseyin Ceylan,Cenk Ozan

doi:10.1155/2019/6203137

Abstract

In this study, we present a bilevel programming model in which upper level is defined as a biobjective problem and the lower level is considered as a stochastic user equilibrium assignment problem. It is clear that the biobjective problem has two objectives: the first maximizes the reserve capacity whereas the second minimizes performance index of a road network. We use a weighted-sum method to determine the Pareto optimal solutions of the biobjective problem by applying normalization approach for making the objective functions dimensionless. Following, a differential evolution based heuristic solution algorithm is introduced to overcome the problem presented by use of biobjective bilevel programming model. The first numerical test is conducted on two-junction network in order to represent the effect of the weighting on the solution of combined reserve capacity maximization and delay minimization problem. Allsop & Charlesworth’s network, which is a widely preferred road network in the literature, is selected for the second numerical application in order to present the applicability of the proposed model on a medium-sized signalized road network. Results support authorities who should usually make a choice between two conflicting issues, namely, reserve capacity maximization and delay minimization.

Highlights

As it is well known, road users may be delayed at signalized intersections on urban roads because of implementing inappropriate signal timings even if traffic flow is less than capacity
For α = 0.8, μ and performance index (PI) are found as 1.08 and 495.40, respectively. It means that when α equals 0.8, the road network can accommodate about 8% more travel demand with ensuring links do not exceed their capacities while PI increases about 45%
This study deals with the simultaneous solution of reserve capacity maximization and delay minimization problems by optimizing traffic signal timings

Summary

Introduction

As it is well known, road users may be delayed at signalized intersections on urban roads because of implementing inappropriate signal timings even if traffic flow is less than capacity. Ceylan and Bell [10] solved the RCMP by optimizing traffic signal timings including offset term in different stages They developed a two-stage algorithm in the stochastic user equilibrium (SUE) manner. To evaluate the users’ reaction to this arrangement performed at the upper level, the lower level is presented as a SUE assignment problem In this context, it is assumed that the local authority tries to simultaneously optimize traffic signal timings by maximizing the reserve capacity and minimizing PI by taking into account the users’ reactions in SUE manner. It is assumed that the local authority tries to simultaneously optimize traffic signal timings by maximizing the reserve capacity and minimizing PI by taking into account the users’ reactions in SUE manner This mutual interaction between users and local authority is presented by using biobjective BLPM. The conclusions and future directions are given in the last section

Problem Formulation

Model Development

Numerical Applications

E Number

Findings

Conclusions and Future Studies