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

In: The 19th International Conference on Industrial Engineering and Engineering Management

Author

Listed:
  • Xiao-ming Yu

    (University of Electronic Science and Technology of China)

  • De-an Wu

    (University of Electronic Science and Technology of China
    Kunming University of Science and Technology)

  • 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)

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.

Suggested Citation

  • Xiao-ming Yu & De-an Wu & Lei Wu & Yi-bing Lu & Jiang-yan Peng, 2013. "An M/M/1 Queue System with Single Working Vacation and Impatient Customers," Springer Books, in: Ershi Qi & Jiang Shen & Runliang Dou (ed.), The 19th International Conference on Industrial Engineering and Engineering Management, edition 127, chapter 0, pages 767-776, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-38391-5_81
    DOI: 10.1007/978-3-642-38391-5_81
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