具有多重休假和Min(N,V)-策略控制的Geo/G/1离散时间排队

考虑服务员具有多重休假和系统采用min(N,V)-策略控制的离散时间Geo/G/1排队系统,使用全概率分解技术和更新过程理论,研究了系统在任意时刻n+的瞬态队长分布和稳态队长分布,得到了瞬态队长分布的z-变换表达式和稳态队长分布的递推表达式.进一步,得到了系统在时刻点n,n~-和外部观察时刻点的稳态队长分布.特别地,本文直接获得了一些特殊离散时间排队系统相应的结果.最后,通过数值实例阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中的重要价值.

Geo/G/1 discrete-time queue with multiple server vacations and Min(N,V)-policy

In this paper, we consider a discrete-time Geo/G/1 queueing system in which the server takes multiple vacations and the system adopts min(N,V)-policy. By using the total probability decomposition technique and renewal process theory, we study the transient and steady distributions of the queue length and obtain both the expression of the z-transformation of the transient distribution and the recursion expression of the steady distribution at arbitrary time epoch n⁺. Furthermore, we obtain the steady distribution of the queue length at time epoch n, n^-, and outside observer's time epoch, respectively. Especially, some corresponding results under special cases are directly given by our results obtained in this paper. Finally, by numerical examples we illustrate the important application value of the expression of the steady state queue-length distribution for calculating conveniently in the system capacity design.