Nearly periodic behavior in the overloaded $G/D/s+GI$ queue
Nearly periodic behavior in the overloaded $G/D/s+GI$ queue
复制标题
过载的 $G/D/s GI$ 队列中的近周期性行为
DOI：
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发表时间：
2011
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
在一般条件下，GI/D/s + GI多服务台排队系统中的顾客数在t时刻收敛于一个唯一的平稳分布.然而，模拟表明，样本路径通常表现出近周期性的行为在很长的时间间隔，当系统过载和s是大的，只要系统不开始在稳定状态。此外，观察到的精确的周期性行为严重依赖于初始条件。我们通过研究确定性流体模型来深入了解瞬时行为，该模型是由于多服务器重流量限制而产生的。极限流体模型也有一个唯一的稳定点，但当t → ∞时，该稳定点不会从任何其他初始状态接近。相反，流体模型的性能接近其不可数的许多周期性稳定状态之一，这取决于初始条件。仿真实验表明，该模型的时变性能与流场的时变性能具有很好的近似性。
Under general conditions, the number of customers in a GI/D/s + GI many-server queue at time t converges to a unique stationary distribution as t → ∞. However, simulations show that the sample paths routinely exhibit nearly periodic behavior over long time intervals when the system is overloaded and s is large, provided that the system does not start in steady state. Moreover, the precise periodic behavior observed depends critically on the initial conditions. We provide insight into the transient behavior by studying the deterministic fluid model, which arises as the many-server heavy-traffic limit. The limiting fluid model also has a unique stationary point, but that stationary point is not approached from any other initial state as t → ∞. Instead, the fluid model performance approaches one of its uncountably many periodic steady states, depending on the initial conditions. Simulation experiments confirm that the time-dependent performance of the stochastic queueing model is well approximated by the flu...