On multiplexing flows: Does it hurt or not?

This paper analyzes queueing behavior subject to multiplexing a stochastic process M(n) of flows, and not a constant as conventionally assumed. By first considering the case when M(n) is iid, it is shown that flows´ multiplexing `hurts´ the queue size (i.e., the queue size increases in distribution). The simplicity of the iid case enables the quantification of the `best´ and `worst´ distributions of M(n), i.e., minimizing/maximizing the queue size. The more general, and also realistic, case when M(n) is Markov-modulated reveals an interesting behavior: flows´ multiplexing `hurts´ but only when the multiplexed flows are sufficiently long. An important caveat raised by such observations is that the conventional approximation of M(n) by a constant can be very misleading for queueing analysis.