Urban Traffic Flow Management Problem through a Bilevel Optimisation approach

Abstract

There are various strategies used to alleviate the problem of traffic congestion. These include increasing the capacity, using coordinated traffic signal systems, and building new infrastructure. Traffic flow models have many applications and can assist the traffic authority in planning purposes. In this study we present a deterministic model formulation of a hierarchical traffic flow management problem. The study considers the traffic authority minimising the total travel time taken by the traffic that flows over the whole network system to clear while the driver who intend to minimise their own flow, is part of the constraints. There are two decision makers in this practical problem. On the upper level we have the traffic authority who decides the free flow speed and cycle length to set on each traffic light. On the other hand the drivers are free to choose the route from their origin to the destination of their choice. We deal with a two level optimisation problem, with a single leader and multiple followers which is later converted to a single leader and single follower problem. In this problem we consider a signal controlled network only and the travel time function used is a volume delay function called the Bureau of Public Roads (BPR) formula, we combine it with the modified Webster equation which computes the waiting time on a traffic signal. Bilevel problems are classified as NP-hard problems and are difficult to solve. In this problem we work with a non-linear travel cost function. The lower level problem is a binary-type problem, and it is not possible to find its derivative, therefore we cannot use the derivative optimisation methods to solve the lower level problem. In addition, some variables of both the lower and upper level objectives are implicit, making it difficult to find its derivative. In this regard we choose to employ a meta heuristic algorithm that can solve deterministic bilevel problems effectively. In particular we use Binary Particle Swarm Optimisation (BPSO) technique to solve the lower level problem after choosing the leader’s actions using the systematic sampling technique. The results indicate that this model can be useful to the traffic authority as it can be applied in urban areas that have signal controlled intersections in their roadways. The model has been implemented and a particular example is used to simulate the results.