Solving a signalized traffic intersection problem with NLP solvers

Abstract

Mathematical Programs with Complementarity Constraints (MPCC) finds many applications in areas such engineering design, economic equilibrium and mathematical theory itself. In this work we consider a queuing system model resulting from a single signalized traffic intersection regulated by pre-timed control in an urban traffic network. The model is formulated as an MPCC problem and may be used to ascertain the optimal cycle and the green split allocation. This MPCC problem is also formulated as its NLP equivalent reformulation. The goal of this work is to solve the problem, using both MPCC and NLP formulations, minimizing two objective functions: the average queue length over all queues and the average waiting time over the worst queue. The problem was codified in AMPL and solved using some optimization software packages.