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Technical Note: The MAP t / Ph t /∞ Queueing System and Multiclass [ MAP t / Ph t /∞] K Queueing Network

Author

Listed:
  • Ira Gerhardt

    (Department of Mathematics, Manhattan College, Riverdale, New York 10471)

  • Barry L. Nelson

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Michael R. Taaffe

    (Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia 24061)

Abstract

In this paper we demonstrate how a key adjustment to known numerically exact methods for evaluating time-dependent moments of the number of entities in the Ph t / Ph t /∞ queueing system and [ Ph t / Ph t /∞] K queueing network may be implemented to capture the effect of autocorrelation that may be present in arrivals to the more general MAP t / Ph t /∞ queueing system and multiclass [ MAP t / Ph t /∞] K queueing network. The MAP t is more general than the Ph t arrival process in that it allows for stationary nonrenewal point processes, as well as the time-dependent generalization of nonrenewal point processes. Modeling real-world systems with bursty arrival processes such as those in telecommunications and transportation, for example, necessitate the use of nonrenewal processes. Finally, we show that the covariance of the number of entities at different nodes and times may be described by a single closed differential equation.

Suggested Citation

  • Ira Gerhardt & Barry L. Nelson & Michael R. Taaffe, 2017. "Technical Note: The MAP t / Ph t /∞ Queueing System and Multiclass [ MAP t / Ph t /∞] K Queueing Network," INFORMS Journal on Computing, INFORMS, vol. 29(2), pages 367-376, May.
    • Handle: RePEc:inm:orijoc:v:29:y:2017:i:2:p:367-376
    DOI: 10.1287/ijoc.2016.0736
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    References listed on IDEAS

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    1. Gabriel R. Bitran & Sriram Dasu, 1993. "Approximating Nonrenewal Processes by Markov Chains: Use of Super-Erlang (SE) Chains," Operations Research, INFORMS, vol. 41(5), pages 903-923, October.
    2. Søren Asmussen, 2000. "Matrix‐analytic Models and their Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 193-226, June.
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