Abstract
Abstract The earliest arrival time and the minimal travelling time from source to destination are not, in general, the same. In fact they are different for a wide class of networks. The first is measured from the time one is ready to leave the source until his arrival at the destination. The second is measured only from the actual departure time from the source. Various forms of the earliest arrival problem, or equivalenlly the shortest route problem, have been studied: requirements for visiting specified nodes, penalties on turns, time-dependent lengths of arcs, and others. In this paper we discuss the case where some edges are closed for travelling during specified periods of time. Parking is permitted at 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. Given such restrictions on movement and parking in the network, travelling time may sometimes be shortened at the expense of later arrival time. The paper presents an algorithm for the solution of the minimal travelling problem. With a minor change this algorithm also solves the earliest arrival problem.
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