• Shin, Yang-Woo (Department of Statistics, Changwon National University)
  • Received : 2010.12.03
  • Accepted : 2011.02.10
  • Published : 2011.05.30


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


  1. 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.
  2. J. R. Artalejo and A. Gomez-Corral, Modelling communication systems with phase type service and retrial times, IEEE Communications Letters 11 (2007), 955-957.
  3. J. R. Artalejo and A. Gomez-Corral, Retrial Queueing Systems, A Computational Approach, Springer-Verlag, Hidelberg, 2008.
  4. L. Bright and P. G. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Stochastic Models 11 (1995), 497-525.
  5. 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.
  6. G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman and Hall, London, 1997.
  7. 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.
  8. 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.
  9. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 1985.
  10. H. M. Liang and V. G. Kulkarni, Monotonicity properties of single server retrial queues, Stochastic Models 9 (1993), 373-400.
  11. 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.
  12. W. Whitt, Approximating a point process by a renewal process, I: two basic methods, Operations Research 30 (1982), 125 - 147.
  13. 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.