Acceptance instant distributions in product-form closed queueing networks with blocking

Abstract

Arrival Instant Theorem is one of the most important theoretical results established in the studies of classical product-form queueing networks. Closed queueing networks with blocking have been shown to have product-form equilibrium distributions in certain cases, e.g. with repetitive service blocking mechanism. In this paper, theoretical results on acceptance instant distribution which is defined as queue length distribution of such networks seen by a customer at the instant of its acceptance to a service node are established and their extensions discussed.