Approximation of M/G/c Retrial Queue with M/PH/c Retrial Queue

  • Shin, Yang-Woo (Department of Statistics, Changwon National University) ;
  • Moon, Dug-Hee (Department of Industrial and Systems Engineering, Changwon National University)
  • Received : 20110900
  • Accepted : 20111000
  • Published : 2012.01.30


The sensitivity of the performance measures such as the mean and the standard deviation of the queue length and the blocking probability with respect to the moments of the service time are numerically investigated. The service time distribution is fitted with phase type(PH) distribution by matching the first three moments of service time and the M/G/c retrial queue is approximated by the M/PH/c retrial queue. Approximations are compared with the simulation results.


  1. Artalejo, J. R. and Gomez-Corral, A. (2008). Retrial Queueing Systems, A Computational Approach, Springer-Verlag, Berlin.
  2. Asmussen, S. (2003). Applied Probability and Queues, 2nd Ed., Springer-Verlag, New York.
  3. Bobbio, A., Horvath, A. and Telek, M. (2005). Matching three moments with minimal acyclic phase type distributions, Stochastic Models, 21, 303-326.
  4. Breuer, L., Dudin, A. N. and Klimenok, V. I. (2002). A retrial BMAP/PH/N system, Queueing Systems, 40, 433-457.
  5. Diamond, J. E. and Alfa, A. S. (1999). Matrix analytic methods for a multi-server retrial queue with buffer, Top, 7, 249-266.
  6. Falin, G. I. and Templeton, J. G. C. (1997). Retrial Queues, Chapman and Hall, London.
  7. Johnson, M. A. and Taaffe, M. R. (1989). Matching moments to phase distributions: mixture of Erlang distributions of common order, Stochastic Models, 5, 711-743.
  8. Latouche, G. and Ramaswami, V. (1999). Introduction to Matrix Analytic Methods in Stochastic Modelling, ASA-SIAM, Philadelphia.
  9. Tijms, H. C. (2003). A First Course in Stochastic Models, John Wiley & Sons.
  10. Whitt, W. (1982). Approximating a point process by a renewal process I: two basic methods, Operations Research, 30, 125-147.

Cited by

  1. ON APPROXIMATIONS FOR GI/G/c RETRIAL QUEUES vol.31, pp.1_2, 2013,