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Sharp results on convergence rates for the distribution of GI/M/1/K queues as K tends to infinity
Part of
- Special processes
- Operations research and management science
Bong Dae Choi, Bara Kim
Journal:

Journal of Applied Probability / Volume 37 / Issue 4 / December 2000

Published online by Cambridge University Press:

14 July 2016, pp. 1010-1019

Print publication:

December 2000
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In this paper, we investigate how fast the stationary distribution π(K) of an embedded Markov chain (time-stationary distribution q(K) of the GI/M/1/K queue converges to the stationary distribution π of the embedded Markov chain (time-stationary distribution q) of the GI/M/1 queue as K tends to infinity. Simonot (1997) proved certain equalities. We obtain sharper results than these by finding limit values limK→∞σ-K||π(K) - π|| and limK→∞σ-K||q(K) - q|| explicitly.

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Sharp results on convergence rates for the distribution of GI/M/1/K queues as K tends to infinity