Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1228-1246.

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System Capacity Optimization Design and Optimal Control Policy (N*, D*) for M/G/1 Queue with p-Entering Discipline and Min(N, D, V)-Policy

Le Luo1,Yinghui Tang2,3,*()   

  1. 1 Nanchong Vocational & Technical College, Sichuan Nanchong 637000
    2 School of Fundamental Education, Sichuan Normal University, Chengdu 610068
    3 School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068
  • Received:2018-10-23 Online:2019-10-26 Published:2019-11-08
  • Contact: Yinghui Tang
  • Supported by:
    the NSFC(71571127)


This paper considers a M/G/1 queueing system with p-entering discipline and Min(N, D, V)-policy, in which the customers who arrive during multiple vacations enter the system with probability p(0 < p ≤ 1). By using the total probability decomposition technique and the Laplace transform, we discuss the transient distribution of queue length at any time t which started from an arbitrary initial state, and obtain the expressions of the Laplace transform of transient queue-length distribution. Moreover, we obtain the recursion expressions of the steady-state queue length distribution. Meanwhile, we discuss the optimal capacity design by combining the steady-state queue length distribution and numerical example. Finally, the explicit expression of the long-run expected cost rate is derived under a given cost structure. And by through numerical calculation, we determine the optimal control policy (N*, D*) for minimizing the long-run expected cost per unit time.

Key words: Multiple vacation, p-Entering discipline, Min(N, D, V)-policy, Queue length distribution, Optimal control policy

CLC Number: 

  • O121