GI Many-Server Fluid Queue : Longer Online Version with Appendix
GI Many-Server Fluid Queue : Longer Online Version with Appendix
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GI 多服务器流体队列：带有附录的较长在线版本
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
W. Whitt
中科院分区：
文献类型：
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作者：
Yunan Liu;W. Whitt
本文介绍了一种确定性流体模型，该模型近似于多服务器 Gt/GI/st + GI 排队模型，并确定与时间相关的性能函数。流体模型具有随时间变化的到达率和服务能力、队列放弃以及非指数服务和耐心分布。两个关键假设是：(i) 系统在过载和欠载区间之间交替，以及 (ii) 指定流体模型的函数适当平滑。开发了一种算法来计算所有性能函数。它涉及在每个过载间隔期间对流体进入服务的时变速率的定点方程进行迭代求解，以及对时变的线头等待时间进行常微分方程的求解。进行仿真以证实该算法和近似是有效的。
This paper introduces a deterministic fluid model that approximates the many-server Gt/GI/st + GI queueing model, and determines the time-dependent performance functions. The fluid model has time-varying arrival rate and service capacity, abandonment from queue, and non-exponential service and patience distributions. Two key assumptions are that: (i) the system alternates between overloaded and underloaded intervals, and (ii) the functions specifying the fluid model are suitably smooth. An algorithm is developed to calculate all performance functions. It involves the iterative solution of a fixed-point equation for the time-varying rate that fluid enters service and the solution of an ordinary differential equation for the time-varying head-ofline waiting time, during each overloaded interval. Simulations are conducted to confirm that the algorithm and the approximation are effective.