Advances and Applications in Statistics
Volume 41, Issue 2, Pages 109 - 128
(August 2014)
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MARKOVIAN QUEUEING SYSTEM WITH SELF REGULATORY SERVERS
K. V. Abdul Rasheed and M. Manoharan
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Abstract: In this paper, we consider Markovian queueing systems whose service speed is regulated according to the number of customers in the system. First, we consider a model in which a single server has two service rates and say slow and fast rates, respectively. If the number of customers in the system exceeds a particular point, then the server switches to the fast rate. The steady state probabilities are derived based on which some performance measures such as the expected number in the system/queue and the expected waiting time are obtained. Further, we expand this model to one having single server and two service switches, followed by one with C servers and one service switch and finally to a model with C servers and two service switches. Performance measures of these models are derived. A Matlab program for numerical implementation of the steady state solutions of the models is developed and numerical illustrations are provided. |
Keywords and phrases: Markovian queueing system, self regulatory system, servers with switches, steady state probabilities, state-dependent service. |
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