ON POISSON APPROXIMATIONS FOR SUPERPOSITION ARRIVAL PROCESSES IN QUEUES

Consideration is given to a queueing model with an arrival process that is the superposition (sum) of two or more independent processes. If the arrival process is the superposition of many independent, relatively sparse component processes, the authors invoke the theorem that a superposition process converges to a Poisson process as the number of component processes tend to infinity, and approximate the analytically intractable superposition process by the more tractable Poisson process. The Poisson process is often an appropriate model for arrival streams since arrival streams are often superpositions of many component processes.