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How pre-emptive priority affects completion rate in an M/M/1 queue with Poisson reneging

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  • Nasrallah, Walid F.

Abstract

Queuing problems in which customers leave the queue without obtaining service (i.e. renege) have many applications. This paper looks at a queue where arrival, service and reneging events are all generated by independent Poisson processes, and customers are selected for service according to priority. A closed-form expression is derived for the probability of completing service for each priority class if high-priority customers always pre-empt low-priority ones. This result has applications in modeling the value of communications between members of an interacting population, such as a formal organization or an online community.

Suggested Citation

  • Nasrallah, Walid F., 2009. "How pre-emptive priority affects completion rate in an M/M/1 queue with Poisson reneging," European Journal of Operational Research, Elsevier, vol. 193(1), pages 317-320, February.
    • Handle: RePEc:eee:ejores:v:193:y:2009:i:1:p:317-320
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    References listed on IDEAS

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    1. Andreas Brandt & Manfred Brandt, 1999. "On a Two-Queue Priority System with Impatience and its Application to a Call Center," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 191-210, September.
    2. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Indifferent Clerks," Operations Research, INFORMS, vol. 5(5), pages 644-649, October.
    3. Walid F. Nasrallah, 2006. "When does management matter in a dog-eat-dog world: An “Interaction Value Analysis” model of organizational climate," Computational and Mathematical Organization Theory, Springer, vol. 12(4), pages 339-359, December.
    4. D. Y. Barrer, 1957. "Queuing with Impatient Customers and Ordered Service," Operations Research, INFORMS, vol. 5(5), pages 650-656, October.
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