Title: First two moment entropy maximisation approach for M/G/1 queues with second optional service and server breakdowns

Authors: Dong-Yuh Yang; Kuo-Hsiung Wang; W. L. Pearn

Addresses: Institute of Information and Decision Sciences, National Taipei College of Business, Taipei 100, Taiwan. ' Department of Business Administration, Asia University, Taichung 41354, Taiwan. ' Department of Industrial Engineering and Management, National Chiao Tung University, Hsinchu 30050, Taiwan

Abstract: We consider the M/G/1 queue with second optional service and server breakdowns. A customer leaves the system either after the first required service with probability (1 – θ) or immediately goes for a second optional service with probability θ after the completion of the first required service. For this queueing model, it is rather difficult to obtain the steady-sate probability explicitly. We apply the maximum entropy approach to approximate the system size distributions by using the first and second moments of the system size. Accuracy comparisons between the two approximate solutions are conducted. Numerical results indicate that using the first moment approach is more accurate than using the second moment approach.

Keywords: accuracy comparison; second optional services; maximum entropy principle; server breakdowns; queuing models.

DOI: 10.1504/IJSOI.2011.045561

International Journal of Services Operations and Informatics, 2011 Vol.6 No.4, pp.310 - 331

Received: 15 Aug 2011
Accepted: 25 Oct 2011
Published online: 13 Mar 2015 *

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