A batch arrival queue with a vacation time under single vacation policy |
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| Authors: | Gautam |
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| Affiliation: | 1. Department of Mathematics, Indian Institute of Technology, Kharagpur- 721302, India;2. Department of Mathematics, National Institute of Technology, Raipur- 492010, India;1. College of Computer Science and Electronic Engineering, and Key Laboratory for Embedded and Network Computing of Hunan Province, Hunan University, Changsha, Hunan, 410082, China;2. School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, China;3. Department of Computer Science, State University of New York, New Paltz, NY 12561, USA;1. Department of Computer Science and Information Management, Providence University, Taichung 43301, Taiwan;2. Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan;3. Institute of Information and Decision Sciences, National Taipei University of Business, Taipei 100, Taiwan |
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| Abstract: | We consider an Mx/G/1 queueing system with a vacation time under single vacation policy, where the server takes exactly one vacation between two successive busy periods. We derive the steady state queue size distribution at different points in times, as well as the steady state distributions of busy period and unfinished work (backlog) of this model.Scope and purposeThis paper addresses issues of model building of manufacturing systems of job-shop type, where the server takes exactly one vacation after the end of each busy period. This vacation can be utilized as a post processing time after clearing the jobs in the system. To be more realistic, we further assume that the arrivals occur in batches of random size instead of single units and it covers many practical situations. For example in manufacturing systems of job-shop type, each job requires to manufacture more than one unit; in digital communication systems, messages which are transmitted could consist of a random number of packets. These manufacturing systems can be modeled by Mx/G/1 queue with a single vacation policy and this extends the results of Levy and Yechiali, Manage Sci 22 (1975) 202, and Doshi, Queueing Syst 1 (1986) 29. |
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| Keywords: | Mx/G/1 queue Vacation time Single vacation policy Queue size and unfinished work |
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