Stability of join-the-shortest-queue networks: Analysis by fluid limits

The standard fluid model tool is employed to investigate stability behavior in a variant of a generalized Jackson queueing network. In the network, some customers use a join-the-shortest-queue policy when entering the network or moving to the next station. Furthermore, we allow interarrival and service times to have general distributions. For networks with two stations, necessary and sufficient conditions are given for positive Harris recurrence of the network process. These conditions involve only the mean values of the network primitives. Two counterexamplesare provided to show that more information on distributions and tie-breaking probabilities is needed for networks with more than two stations, in order to characterize the stability of such systems. However, if the routing probabilities in the network satisfy a certain homogeneity condition, then it is proved that the stability behavior can be explicitly determined, again using the mean value parameters of the network.