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Study on the Queue-Length Distribution in Queue with Working Vacations

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  • Chuanyi Luo
  • Jiangyi Li
  • Yinghui Tang

Abstract

This paper analyzes a finite buffer size discrete-time queue with multiple working vacations and different input rate. Using supplementary variable technique and embedded Markov chain method, the queue-length distribution solution in the form of formula at arbitrary epoch is obtained. Some performance measures associated with operating cost are also discussed based on the obtained queue-length distribution. Then, several numerical experiments follow to demonstrate the effectiveness of the obtained formulae. Finally, a state-dependent operating cost function is constructed to model an express logistics service center. Regarding the service rate during working vacation as a control variable, the optimization analysis on the cost function is carried out by using parabolic method.

Suggested Citation

  • Chuanyi Luo & Jiangyi Li & Yinghui Tang, 2015. "Study on the Queue-Length Distribution in Queue with Working Vacations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-15, July.
    • Handle: RePEc:hin:jnddns:160697
    DOI: 10.1155/2015/160697
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