Exact Product Form Solution for Queueing Networks with Blocking

Abstract

This work investigates closed queueing networks with blocking composed of two stations with multiple servers. Blocking occurs when a job wanting to enter a full station is forced to remain in its source station, thus blocking the source station until room is available at the destination station. This type of blocking is known as classical blocking. We show that, for a two-station closed queueing network with blocking, there exists an equivalent nonblocking network with the same state space structure. Utilizing this concept, we demonstrate that two-station closed queueing networks with blocking have product form solutions.