Maximizing reserve capacity for a signalized road network design problem

For an area traffic control road network with expansions of link capacity, the maximum possible increase in travel demands is considered while total delays for travelers are minimized with respect to the common cycle time, the starts and durations of green times and the offsets. Using the concept of reserve capacity of signal-controlled junctions, the problem of finding the maximum possible increase in traffic demands and determining optimal link capacity expansions can be formulated as a mathematical program with equilibrium constraints (MPEC). In this paper, we present a new solution approach for simultaneously solving the maximum increase in travel demands and minimizing link capacity expansion investment together with total delays of travelers on the basis of TRANSYT model. Subject to strict complementary slackness, we propose two MPEC problems where the equilibrium constraints are of KKT conditions. A projected quasi-Newton method is proposed to effectively solve this problem to the KKT points. Numerical computations are made on a real data signal-controlled network where good results are obtained