Varwus stochastic models are proposed for transportation networks, by increasing order of complexity. The mathematical tools rely on queueing theory and asymptotic analysis. These models are mainly applied to service vehwle systems, like PRAXITELE, but the methods used are more far-reaching. In particular, the asymptotic independence of nodes is proved in the thermodynamical limit, i.e., when the volume of the system increases. IntroductionTransportation problems have for a long time been a source of interesting mathematical problems. New transportation problems now arise in the context of demand-driven systems (e.g., flexible route bus systems, flexible delivery. rental and self-service cars, etc.). In these systems, the demand cannot be modeled by simple deterministic methods. and stochastic models seem suitable for carrying out an analysis of performance. This paper is a continuation of the preliminary study [8] and provides some understanding in the behavior of so-called service vehicle networks(SVN). It can be viewed as a creation of models. Some of them are classical and rely on so-called product form networks; others can hardly be solved analytically, but asymptotics when the size of the system increases can be obtained.Basically, a customer arrives at a station (node, station, parking lot), where he takes a car, if any is available, to reach some other station (destination), where he leaves the car. Section 2 is devoted to the simplest case, in which the number of available cars is unbounded. Here time-dependent parameters are allowed. The model of w assumes a finite number V of cars, no capacity constraints, and no waiting room for customers, who are lost if there is no car when they arrive. Section 4 deals with a more difficult case: at each station, the capacity for parking places is limited and there is also a finite waiting room for clients at each station. An asymptotic analysis is presented for a symmetrical network, in which the number of cars and the number of nodes simultaneously increase. In w generalizations are proposed, some of them being the object of ongoing works. Non-Time-Homogeneous Input Process and Infinite-Server QueuesConsider an open queueing network with N stations. At time t, customers arrive at node i, i = 1 ..... N. according to a non-time-homogeneous Poisson process, with deterministic parameter (Ai(t), t > 0). These N processes are assumed to be independent. A customer arriving at node i is provided with a car and goes to node j with some probability Pij, so that the matrix P = (Pij) is stochastic. In this model, the number of available cars is assumed to be unlimited. After having reached his destination, a customer leaves the network.Let us introduce the following random variables, for all i,j --l,..., N: * rii, the time to go from node i to node j, the corresponding distribution function being Bii(x); 9 xii(t), the number of cars which, at time t, are on their way from i to j. Now to each link (origin-destination pair) (i, j) with Pij > 0, we associate a fictitious node ha...
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