Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity

Authors:
Bong Dae Choi;Bara Kim;Jeongsim Kim;In-Suk Wee
Affiliations:
Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Korea;Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Korea;Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Korea;Department of Mathematics, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul, 136-701, Korea
Venue:
Queueing Systems: Theory and Applications
Year:
2003

Citing 1
Cited 2

Asymptotic Behavior of Loss Probability in GI/M/1/K Queue as K Tends to Infinity

Queueing Systems: Theory and Applications

Asymptotic analysis and simple approximation of the loss probability of the GIX/M/c/K queue

Performance Evaluation
Estimating the loss probability under heavy traffic conditions

Computers & Mathematics with Applications

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Abstract

We obtain the exact convergence rate of the stationary distribution π(K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution π of the embedded Markov chain in GI/M/c queue as K→∞. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c=1 by nontrivial ways. Our results also strengthen the Simonot's results [5].