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Journal of Probability and Statistics
Volume 2014, Article ID 319318, 12 pages
Research Article

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

1Brunel University, UK
2College of Information Technology, Ahlia University, Bahrain
3Brunel Business School, Brunel University, UK

Received 29 July 2013; Revised 4 November 2013; Accepted 13 November 2013; Published 8 January 2014

Academic Editor: Shein-chung Chow

Copyright © 2014 Monita Baruah et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.