A NOTE ON INFINITE-SERVER MARKOV MODULATED AND SINGLE-SERVER RETRIAL QUEUES

Zhe Duan () and Melike Baykal-Gürsoy ()
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Zhe Duan: Management Science Department, School of Management, Xi'An Jiaotong University, No. 28 at Xianning West Road, Xi'An, Shaanxi Province, China, 710049, China
Melike Baykal-Gürsoy: Industrial and Systems Engineering Department, CAIT RUTCOR, Rutgers University, 96 Frelinghuysen Road, Piscataway, NJ 08854-801, USA

Asia-Pacific Journal of Operational Research (APJOR), 2014, vol. 31, issue 02, 1-17

Abstract: We reconsider the M/M/∞ queue with two-state Markov modulated arrival and service processes and the single-server retrial queue analyzed in Keilson and Servi [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471]. Fuhrmann and Cooper type stochastic decomposition holds for the stationary occupancy distributions in both queues [Keilson, J and L Servi (1993). The matrix M/M/∞ system: Retrial models and Markov modulated sources. Advances in Applied Probability, 25, 453–471; Baykal-Gürsoy, M and W Xiao (2004). Stochastic decomposition in M/M/∞ queues with Markov-modulated service rates. Queueing Systems, 48, 75–88]. The main contribution of the present paper is the derivation of the explicit form of the stationary system size distributions. Numerical examples are presented visually exhibiting the effect of various parameters on the stationary distributions.

Keywords: Markov modulated; stochastic decomposition; Kummer functions; retrial queue (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S021759591440003X

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