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Transient solution of an M/M/∞ queue with system's additional tasks and impatient customers

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  • R. Sudhesh
  • A. Azhagappan

Abstract

This paper studies the impatient behaviour in an infinite server queue with additional tasks assigned to the system. Whenever the system becomes empty, the system as a whole is assigned a secondary task of duration U whose distribution is exponential. Any arrival during the period U becomes impatient due to the unavailability of service facility. Each individual waiting customer activates an independent impatience timer of duration T which is exponentially distributed. When the system comes back after the completion of U, before T expires, the waiting customers are simultaneously taken for service and they leave the system after the completion of service. If T expires before the completion of task U, the customers abandon the system and never to return. The transient system size probabilities of this model are derived explicitly for both single and multiple task cases. The time-dependent mean and variance of system size are also derived. Further, numerical simulations are also presented to analyse the effect of system indices.

Suggested Citation

  • R. Sudhesh & A. Azhagappan, 2020. "Transient solution of an M/M/∞ queue with system's additional tasks and impatient customers," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 16(1), pages 82-97.
  • Handle: RePEc:ids:ijmore:v:16:y:2020:i:1:p:82-97
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    Cited by:

    1. Rakesh Kumar & Sapana Sharma, 2021. "Transient analysis of a Markovian queuing model with multiple-heterogeneous servers, and customers’ impatience," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 540-556, September.

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