- Volume 29 Issue 3_4
We present an algorithmic solution for the stationary distribution of the M/M/c retrial queue in which the retrial times of each customer in orbit are of phase type distribution of order 2. The system is modeled by the level dependent quasi-birth-and-death (LDQBD) process.
Supported by : Changwon National University
- A. S. Alfa and W. Li, PCS networks with correlated arrival process and retrial phenome- non, IEEE Transactions on Wireless Communications 1 (2002), 630-637. https://doi.org/10.1109/TWC.2002.804077
- J. R. Artalejo and A. Gomez-Corral, Modelling communication systems with phase type service and retrial times, IEEE Communications Letters 11 (2007), 955-957.
- J. R. Artalejo and A. Gomez-Corral, Retrial Queueing Systems, A Computational Approach, Springer-Verlag, Hidelberg, 2008.
- L. Bright and P. G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Stochastic Models 11 (1995), 497-525. https://doi.org/10.1080/15326349508807357
- J. E. Diamond and A. S. Alfa, Approximation method for M=PH=1 retrial queues with phase type inter-retrial times, European Journal of Operational Research 113 (1999), 620-631. https://doi.org/10.1016/S0377-2217(98)00004-6
- G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman and Hall, London, 1997.
- A. Gomez-Corral, A bibliographical guide to the analysis of retrial queues through the matrix analytic techniques, Annals of Operations Research 141 (2006), 163-191. https://doi.org/10.1007/s10479-006-5298-4
- Q. M. He and Y. Q. Zhao, Ergodicity of the BM AP/PH/s/s + K retrial queue with PH-retrial times, Queueing Systems 35 (2000), 323-347. https://doi.org/10.1023/A:1019110631467
- R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
- H. M. Liang and V. G. Kulkarni, Monotonicity properties of single server retrial queues, Stochastic Models 9 (1993), 373-400. https://doi.org/10.1080/15326349308807271
- Y. W. Shin, Fundamental matrix of transient QBD generator with finite states and level dependent transitions, Asia-Pacific Journal of Operational Research 26 (2009), 697-714. https://doi.org/10.1142/S0217595909002407
- W. Whitt, Approximating a point process by a renewal process, I: two basic methods, Operations Research 30 (1982), 125 - 147. https://doi.org/10.1287/opre.30.1.125
- T. Yang, M. J. M. Posner, J. G. C. Templeton and H. Li, An approximation method for the M/G/1 retrial queues with general retrial times, European Journal of Operational Research 76 (1994), 552-562. https://doi.org/10.1016/0377-2217(94)90286-0