Large-time asymptotics for the Gt/Mt/st+GIt many-server fluid queue with abandonment
Large-time asymptotics for the Gt/Mt/st+GIt many-server fluid queue with abandonment
复制标题
Gt/Mt/st GIt 多服务器流体队列的大时间渐近并放弃
DOI：
10.1007/s11134-010-9208-8
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发表时间：
2011
期刊：
影响因子：
1.2
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
我们之前介绍并分析了具有时变参数的Gt/Mt/st+GIt多服务器流体队列，旨在作为在有许多服务器和系统经历过载时期时相应的随机队列模型的近似值。在本文中，我们建立了该流体模型的渐近记忆丧失（ALOM）性质，即，我们证明了在正则条件下，随着时间t的演变，与初始条件渐近独立。我们表明，性能函数的差异随着时间的推移呈指数级快速消散，同样是在正则性条件下。应用ALOM方法证明了在所有有限初始条件下，平稳G/M/s+GI流体队列随着时间的推移收敛于稳态，周期Gt/Mt/st+GIt流体队列收敛于周期稳态。
We previously introduced and analyzed the Gt/Mt/st+GIt many-server fluid queue with time-varying parameters, intended as an approximation for the corresponding stochastic queueing model when there are many servers and the system experiences periods of overload. In this paper, we establish an asymptotic loss of memory (ALOM) property for that fluid model, i.e., we show that there is asymptotic independence from the initial conditions as time t evolves, under regularity conditions. We show that the difference in the performance functions dissipates over time exponentially fast, again under the regularity conditions. We apply ALOM to show that the stationary G/M/s+GI fluid queue converges to steady state and the periodic Gt/Mt/st+GIt fluid queue converges to a periodic steady state as time evolves, for all finite initial conditions.