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Journals ACM SIGMETRICS Performance Evaluation Review Volume 30 Issue 3

Our model is a constrained homogeneous random walk in Z + d . 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 in 11. In this paper we show that computing exactly the stationary probability for this type of random walks is an undecidable problem: 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.

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Computing stationary probability distributions and large deviation rates for constrained random walks.: the undecidability results.

Gamarnik, David
ACM SIGMETRICS Performance Evaluation Review , Volume 30 (3)
Association for Computing Machinery – Dec 1, 2002

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