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.
Original language | English (US) |
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Article number | 1440003 |
Journal | Asia-Pacific Journal of Operational Research |
Volume | 31 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2014 |
All Science Journal Classification (ASJC) codes
- Management Science and Operations Research
Keywords
- Kummer functions
- Markov modulated
- retrial queue
- stochastic decomposition