Approximations for Superposition Arrival Processes in Queues

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Abstract
S. L. Albin has described extensive simulations of queue behavior for a system with a single server and an arrival process that is a superposition of n renewal processes. The simulations show, among other things, that as n increases for a fixed traffic intensity ρ, the queue behavior approaches that of the M/M/1 system. The rate of convergence, however, becomes much slower as the traffic intensity ρ comes closer to 1. Several qualitative effects shown in the simulations are explained here. In particular it is shown that the approach to the M/M/1 system requires that n(1 − ρ)2 ≫ 1.

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