Queueing Syst (2007) 57: 129–145 DOI 10.1007/s11134-007-9046-5 Stability of join-the-shortest-queue networks

This paper investigates stability behavior in a variant of a generalized Jackson queueing network. In our network, some customers use a join-the-shortest-queue policy when entering the network or moving to the next station. Further-more, we allow interarrival and service times to have gen-eral distributions. For networks with two stations we derive necessary and sufficient conditions for positive Harris recur-rence of the network process. These conditions involve only the mean values of the network primitives. We also provide counterexamples showing that more information on distrib-utions and tie-breaking probabilities is needed for network