Title: A single and batch service queue with random breakdowns

Authors: Lotfi Tadj; Jau-Chuan Ke

Addresses: Silberman College of Business, Fairleigh Dickinson University, Vancouver, BC, Canada ' Department of Applied Statistics, National Taichung University of Science and Technology, No. 129, Sec. 3, Sanmin Rd., Taichung 404, Taiwan

Abstract: We consider a single and batch service queue with Poisson arrivals and general service time distributions. In this model the server serves the customers either one at a time (manual service) or in batches (service by a machine). If the number of units in the queue is less than the control level c, then the server adopts the manual service (serves the units one by one). However, if the queue size is c or more, then the server adopts the batch service and serves the units in a batch of size c. Furthermore, the server may break down while providing either the single service or the batch service. Finally, a cost model is developed to determine the optimal value of c.

Keywords: single service queues; batch service queues; control limit; random breakdowns; steady-state distribution; Poisson arrivals; general service time distributions; cost models; modelling.

DOI: 10.1504/IJSSCI.2014.066517

International Journal of Services Sciences, 2014 Vol.5 No.2, pp.116 - 132

Received: 30 Mar 2013
Accepted: 13 May 2014
Published online: 14 Jan 2015 *

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