Parameter Mixing in Infinite-server Queues

In this chapter, the authors consider two infinite-server queueing models with a so-called mixed arrival process. First, they study the case of Coxian service times. Second, the authors consider a Markov-modulated infinite-server queue with general service times. In queueing theory, it is often assumed that the arrival process is a Poisson process with a constant rate. The authors consider an infinite-server queue where the arrival parameter repeatedly resamples after i.i.d. (independent, identically distributed) exponential amounts of time. They analyze the behavior of this queue and make comparisons to “standard” infinite-server queues with a fixed deterministic arrival parameter. The authors indicate how the differential equation can be used to obtain queue length moments.