Minimum Time and Minimum Cost-Path Problems in Street Networks with Periodic Traffic Lights

This paper investigates minimum time and minimum cost path problems in street networks regulated by periodic traffic lights. We show that the minimum time path problem is polynomially solvable. On the other hand, minimum cost path problems are generally NP-hard. Special, realistic, cases which are polynomially solvable are discussed. Dynamic shortest path problems often arise in transportation applications. Several models have been defined and analyzed depending on the properties of the travel time and of the cost functions (e.g., continuous or discrete), on the possibility of waiting at the nodes (e.g., no waiting, waiting at each node, waiting only at the origin nodes), on the presence of time windows associated with the nodes, etc. For more details about shortest path problems in dynamic transportation networks, see KIRBY and Despite the extensive literature on dynamic shortest path problems, no paper has yet focused on the case in which multiple time windows are associated with each node. This is the situation addressed in this paper. More precisely, we study the case of street networks regulated by periodic traffic lights at some (or possibly at all) intersections, where green phases are interpreted as multiple