Our model is a constrained homogeneous random walk in .The convergence to stationarity for such a random walk can often be checked by constructing a Lyapunov function.The same Lyapunov function can also be used for computing approximately the stationary distribution of this random walk,using methods developed by Meyn and Tweedie in [34 ].In this paper we show that,for stationary homogeneous random walks,computing the stationary probability exactly is an undecidable problem,even if a Lyapunov function is available.That is no algorithm can exist to achieve this task.We then prove that computing large deviation rates for this model is also an undecidable problem.We extend these results to a certain type of queueing systems.The implication of these results is that no useful formulas for computing stationary probabilities and large deviations rates can exist in these systems.
By: David P. Gamarnik
Published in: RC22607 in 2002
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