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A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns

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  • Monita Baruah
  • Kailash C. Madan
  • Tillal Eldabi

Abstract

We study the behavior of a batch arrival queuing system equipped with a single server providing general arbitrary service to customers with different service rates in two fluctuating modes of service. In addition, the server is subject to random breakdown. As soon as the server faces breakdown, the customer whose service is interrupted comes back to the head of the queue. As soon as repair process of the server is complete, the server immediately starts providing service in mode 1. Also customers waiting for service may renege (leave the queue) when there is breakdown or when server takes vacation. The system provides service with complete or reduced efficiency due to the fluctuating rates of service. We derive the steady state queue size distribution. Some special cases are discussed and numerical illustration is provided to see the effect and validity of the results.

Suggested Citation

  • Monita Baruah & Kailash C. Madan & Tillal Eldabi, 2014. "A Batch Arrival Single Server Queue with Server Providing General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns," Journal of Probability and Statistics, Hindawi, vol. 2014, pages 1-12, January.
    • Handle: RePEc:hin:jnljps:319318
    DOI: 10.1155/2014/319318
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    Cited by:

    1. Khamis A. K. ALMaqbali & Varghese C. Joshua & Achyutha Krishnamoorthy, 2023. "Multi-Class, Multi-Server Queueing Inventory System with Batch Service," Mathematics, MDPI, vol. 11(4), pages 1-29, February.

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