An M/M/1 Queue System with Single Working Vacation and Impatient Customers

Xiao-ming Yu, Wu De-an (), Lei Wu, Yi-bing Lu and Jiang-yan Peng
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Xiao-ming Yu: University of Electronic Science and Technology of China
Wu De-an: University of Electronic Science and Technology of China
Lei Wu: University of Electronic Science and Technology of China
Yi-bing Lu: Kunming University of Science and Technology
Jiang-yan Peng: University of Electronic Science and Technology of China

Chapter Chapter 81 in The 19th International Conference on Industrial Engineering and Engineering Management, 2013, pp 767-776 from Springer

Abstract: Abstract In this paper, an M/M/1 queueing system with a single working vacation and impatient customers is considered. In this system, the server has a slow rate to serve during a working vacation and customers become impatient due to a slow service rate. The server waits dormant to the first arrival in case that the server comes back to an empty system from a vacation, thereafter, opens a busy period. Otherwise, the server starts a busy period directly if the queue system has customers. The customers’ impatient time follows independently exponential distribution. If the customer’s service has not been completed before the customer becomes impatient, the customer abandons the queue and doesn’t return. The model is analyzed and various performance measures are derived. Finally, several numerical examples are presented.

Keywords: Impatient customers; M/M/1 queue; Probability generating functions; Single working vacation (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-38391-5_81

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DOI: 10.1007/978-3-642-38391-5_81

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