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.