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This paper is concerned with modeling of networks with an extremely large number of components using partial differential equations (PDEs). This modeling method is based on the convergence of a sequence of underlying Markov chains of the network indexed by , the number of components in the network. As goes to infinity, the sequence converges to a continuum limit, which is the solution of a certain...
In this paper we investigate the continuum limits of a class of Markov chains. The investigation of such limits is motivated by the desire to model very large networks. We show that under some conditions, a sequence of Markov chains converges in some sense to the solution of a partial differential equation. Based on such convergence we approximate Markov chains modeling networks involving a large...
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