Shortest path with time constraints on movement and parking

The shortest path problem is well known and a number of methods have been proposed for its solution. In its simplest form no restrictions or special costs are placed on movement in the network. Some variations of the problem have been presented and solved, such as requirements for visiting specified nodes, turn penalties and prohibitions and time-dependent length of arcs. In this paper we present and solve the case where we seek the shortest path when some arcs are closed for travelling during specified periods of time. We allow parking in the vertices of the network, when it is necessary to wait for an arc to be opened, but we also assume the possibility of “no-parking” or “occupied” periods in the nodes. This type of problem emerges, for example, in the management of railway system, or a network of narrow roads with convoys moving on it.