Queueing-network Stability: Simulation-based Checking

Queueing networks are either stable or unstable, with stable networks having finite performance measures and unstable networks having asymptotically many customers as time goes to infinity. Stochastic simulation methods for estimating steady-state performance measures often assume that the network is stable. Here, we discuss the problem of checking whether a given network is stable when the stability-checking algorithm is allowed only to view arrivals and departures from the network. 1 THE STABILITY-CHECKING PROBLEM Given only simulation code of a queueing-network model, we consider the problem of developing a statistical algorithm to check whether the network is stable. Informally, stable means that the network behavior does not explode in the limit as time goes to infinity. Note that this problem is about long-run network equilibrium, not initial-transient bias of point estimators.