The map/ph/1 retrial queue

We consider the MAP/PH/1 retrial queue. We obtain a sufficient condition for ergodicity and derive a numerical method for obtaining the stationary distribution of states and the distribution and moments of the waiting time. We derive a method for obtaining a bound on probability lost due to truncation when the service time distribution is a member of a certain class by considering approximations which stochastically dominate the exact queue

[1]  P. Jacobs,et al.  Finite birth-and-death models in randomly changing environments , 1984, Advances in Applied Probability.

[2]  Vaidyanathan Ramaswami,et al.  A logarithmic reduction algorithm for quasi-birth-death processes , 1993, Journal of Applied Probability.

[3]  René Boel,et al.  Performance analysis and optimal threshold policies for queueing systems with several heterogeneous servers and Markov modulated arrivals , 1997 .

[4]  San-qi Li,et al.  Analysis of multi-media traffic queues with finite buffer and overload control. I. Algorithm , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

[5]  Attahiru Sule Alfa,et al.  Matrix analytical methods for M/PH/1 retrial queues , 1995 .

[6]  Andreas Brandt,et al.  On the Pathwise Comparison of Jump Processes Driven by Stochastic Intensities , 1994 .

[7]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[8]  Peter G. Taylor,et al.  Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes , 1995 .

[9]  Bruce Hajek,et al.  Birth-and-death processes on the integers with phases and general boundaries , 1982, Journal of Applied Probability.

[10]  W. Whitt On approximations for queues, III: Mixtures of exponential distributions , 1984, AT&T Bell Laboratories Technical Journal.

[11]  T. Altiok On the Phase-Type Approximations of General Distributions , 1985 .

[12]  Sergey N. Stepanov OPTIMAL CALCULATION OF CHARACTERISTICS OF MODELS WITH REPEATED CALLS , 1988 .

[13]  William A. Massey,et al.  New stochastic orderings for Markov processes on partially ordered spaces , 1984, The 23rd IEEE Conference on Decision and Control.

[14]  Behnam Pourbabai,et al.  Single server stochastic recirculation systems , 1987, Comput. Oper. Res..

[15]  Marcel F. Neuts,et al.  Numerical investigation of a multiserver retrial model , 1990, Queueing Syst. Theory Appl..