异步多重休假G^(X)/GI^(Y)/k排队系统排队长度的比较

A Comparison for Queue Lengths of G^(X)/GI^(Y)/k Queue Systems with Asynchronous Multiple Vacation

本文讨论了异步多重休假G^(X)/GI^(Y)/k排队系统的排队长度,运用随机序的理论和方法,通过顾客来到人数、服务次数及服务容量等诸多随机变量在不同窗口下的增凸序,得到了异步多重休假排队系统在这些窗口排队长度的增凸序,通过顾客来到数向量在不同窗口下的超摸序,给出了这些窗口排队长度的增凸序。

This paper investigates the queue length of an G^（X）/GI^（Y）/k queuing system with asynchronous multiple vacation. By using the theory and methods of stochastic orders, the increasing convex ordering of queue lengths in different windows is derived by the increasing convex orderings of random variables such as arriving customer size, service frequency and service capacity in these windows, and the increasing convex ordering of queue lengths in different windows is also given through the supermodular ordering of vectors of arriving customer size in these windows.