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Convergence of the stationary distributions of M/M/s/K retrial queue as K tends to infinity

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  • Shin, Yang Woo

Abstract

We investigate the convergence of the stationary distributions x(K) of M/M/s/K retrial queue to the stationary distribution [pi] of M/M/s queue as K tends to infinity. It is showed that x(K) converges geometrically to [pi] in l1-sense and the convergence rate is characterized by the traffic intensity , where [lambda] and [mu] are the arrival rate and service rate, respectively.

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  • Shin, Yang Woo, 2008. "Convergence of the stationary distributions of M/M/s/K retrial queue as K tends to infinity," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1104-1117, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:1104-1117
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