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Calculation of delay characteristics for multiserver queues with constant service times

Author

Listed:
  • Gao, Peixia
  • Wittevrongel, Sabine
  • Walraevens, Joris
  • Moeneclaey, Marc
  • Bruneel, Herwig

Abstract

We consider a discrete-time infinite-capacity queueing system with a general uncorrelated arrival process, constant-length service times of multiple slots, multiple servers and a first-come-first-served queueing discipline. Under the assumption that the queueing system can reach a steady state, we first establish a relationship between the steady-state probability distributions of the system content and the customer delay. Next, by means of this relationship, an explicit expression for the probability generating function of the customer delay is obtained from the known generating function of the system content, derived in previous work. In addition, several characteristics of the customer delay, namely the mean value, the variance and the tail distribution of the delay, are derived through some mathematical manipulations. The analysis is illustrated by means of some numerical examples.

Suggested Citation

  • Gao, Peixia & Wittevrongel, Sabine & Walraevens, Joris & Moeneclaey, Marc & Bruneel, Herwig, 2009. "Calculation of delay characteristics for multiserver queues with constant service times," European Journal of Operational Research, Elsevier, vol. 199(1), pages 170-175, November.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:170-175
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    Citations

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    Cited by:

    1. Herwig Bruneel & Willem Mélange & Dieter Claeys & Joris Walraevens, 2017. "A two-class global FCFS discrete-time queueing model with arbitrary-length constant service times," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 164-178, April.
    2. Michiel De Muynck & Herwig Bruneel & Sabine Wittevrongel, 2023. "Analysis of a Queue with General Service Demands and Multiple Servers with Variable Service Capacities," Mathematics, MDPI, vol. 11(4), pages 1-21, February.

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