Applications of the theory of stochastic discrete event systems to array processors and scheduling in public transportation

Abstract
During the last couple of years the deterministic theory of discrete-event dynamic systems (DEDS) has received much attention. Recently, stochastic extensions have been obtained. The motivation is that, in practice, processing times or transportation times are quite often stochastic quantities. Variable processing times are found in wavefront array processors, in which the execution times of the nodes depend on the input data. An example of a matrix-matrix multiplication will be given where one of the matrices is sparse. It is assumed in this array processor that the time duration of the multiplication of two scalars depends on whether at least one of the operands is zero. Another application deals with a public transportation network; at each node the buses (or trains) must wait for each other such as to allow changeovers. The time duration from one node to the next is stochastic due to fluctuations in traffic. It turns out that within a given network, the routing of the different buslines in the system influences the maximum frequency with which each node is visited.

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