‘Stop-recirculate’ for exponential product form queueing networks with departure blocking

The steady-state queue-size distribution of Jacksonian queueing networks with departure blocking is shown to have exactly the same product form under both a ‘stop’ and a ‘recirculate’ protocol. Under the stop protocol services are interrupted while under the circulate protocol jobs leaving the network are recycled into the network, when blocking occurs. Extensions to networks with multiple jobclasses and interconnected network clusters are also given. The equivalence result is of both practical and theoretical interest and seems to reveal a new phenomenon of product forms.