On exponential ergodicity of multiclass queueing networks

摘要

One of the key performance measures in queueing systems is the decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have finite moments, then the queue lengths also have finite moments, so that the tail probability P(· > s) decays faster than s~(-n) for any n. It is natural to conjecture that the decay rate is in fact exponential.rnIn this paper an example is constructed to demonstrate that this conjecture is false. For a specific stationary policy applied to a network with exponentially distributed interarrival and service times, it is shown that the corresponding fluid limit model is stable, but the tail probability for the buffer length decays slower than s~(-log s).