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2 results

Empirical convergence rates for continuous-time Markov chains
Part of
Geoffrey Pritchard, David J. Scott
Journal:

Journal of Applied Probability / Volume 38 / Issue 1 / March 2001

Published online by Cambridge University Press:

14 July 2016, pp. 262-269

Print publication:

March 2001
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We consider the problem of estimating the rate of convergence to stationarity of a continuous-time, finite-state Markov chain. This is done via an estimator of the second-largest eigenvalue of the transition matrix, which in turn is based on conventional inference in a parametric model. We obtain a limiting distribution for the eigenvalue estimator. As an example we treat an M/M/c/c queue, and show that the method allows us to estimate the time to stationarity τ within a time comparable to τ.

Throughput maximization in a loss queueing system with heterogeneous servers
Matthew J. Sobel
Journal:

Journal of Applied Probability / Volume 27 / Issue 3 / September 1990

Published online by Cambridge University Press:

14 July 2016, pp. 693-700

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September 1990
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Assigning each arriving customer to the fastest idle server is shown to maximize throughput (equivalently, minimize blocking probability) in a queueing model with Poisson arrivals, heterogeneous exponential servers, and no waiting room. If a cost structure is imposed on this model, under specified conditions the same policy minimizes the expected discounted cost and the long-run average cost per unit time.

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2 results

Empirical convergence rates for continuous-time Markov chains

Throughput maximization in a loss queueing system with heterogeneous servers