Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (2): 380-392.

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Analysis of the Departure Process for Geo/G/1 Discrete-Time Queue with Single Server Vacation and Min-Policy

Lan Shaojun1, Tang Yinghui1,2   

  1. 1 School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066;
    2 School of Fundamental Education, Sichuan Normal University, Chengdu 610066
  • Received:2015-10-21 Revised:2016-01-13 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    Supported by the NSFC (71171138, 71571127)

Abstract:

In this paper we investigate the departure process for a Geo/G/1 discrete-time queueing system in which the server takes single server vacation and the system adopts Min(N, V)-policy. In this study, by employing the total probability decomposition law, renewal theory and probability generating function technique, the transient and the steady probability that the server is busy at any epoch n+ are derived. Furthermore, we also obtain the expression of the probability generating function for the expected number of departures occurring in the time interval (0+, n+] from any initial state. Meanwhile, the relationship among departure process, server busy-state process and the service renewal process in server busy period is found, which shows the especial structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by the results obtained in this paper. Finally, the asymptotic expansion for calculating expected number of departures conveniently is presented.

Key words: Discrete-time queue, Min(N, V)-policy, Single server vacation, Departure process, Expected number of departures

CLC Number: 

  • O226
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