  Join the shortest queue (JSQ) refers to networks whose incoming jobs are
assigned to the shortest queue from among a randomly chosen subset of the
queues in the system. After completion of service at the queue, a job leaves
the network. We show that, for all non- idling service disciplines and for
general interarrival and service time distributions, such networks are stable
when they are subcritical. We then obtain uniform bounds on the tails of the
marginal distributions of the equilibria for families of such networks; these
bounds are employed to show relative compactness of the marginal distributions.
We also present a family of subcritical JSQ networks whose workloads in
equilibrium are much larger than for the corresponding networks where each
incoming job is assigned randomly to a queue. Part of this work generalizes
results in Foss and Chernova [12], which applied fluid limits to study networks
with the FIFO discipline. Here, we apply an appropriate Lyapunov function.
