Queues with Partial Correlation

Aligning service mechanism and demand is achieved essentially in two ways: either service and/or arrival parameters are managed to vary with system state, or consecutive inter-arrival intervals and service times are not assumed to be independent. The former is by now well studied. In the latter, a bivariate distribution with negative exponential marginals, which can be constructed in many ways, constitutes a first attempt. With a particular construction involving a modified Bessel function of order zero, the waiting time density (as well as its stationary counterpart) of such a partially correlated generalization of $M/ M/1 $ is shown to have the hyperexponential distribution.

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