Steady-state behavior of interacting queues-a numerical approach

The M queues that interact according to a model of multiple-access transmissions over a collision channel are considered. Each queue receives messages that it attempts to transmit in a classical slotted ALOHA fashion. The steady-state behavior of such systems is unknown except in certain simple cases. A numerical approach is proposed that permits the calculation, within any desired accuracy, of the joint queue size distribution as well as of the moments. The approach uses a technique that involves auxiliary systems of queues that dominate, in a well-defined sense, the given ones. Consideration of such dominating systems in some cases permits the study of the ergodic region of the original systems. The methodology developed here is applicable to contexts more general than that of multiple-access transmissions