THE PHYSICS OF THE M(T)/G/IOTA QUEUE
THE PHYSICS OF THE M(T)/G/IOTA QUEUE
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DOI：
10.1287/opre.41.4.731
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发表时间：
1993-07-01
影响因子：
2.7
通讯作者：
WHITT, W
中科院分区：
文献类型：
--
作者：
EICK, SG;MASSEY, WA;WHITT, W
建立了M（t）/G/无穷大排队系统的一般结构性结果，并导出了描述该排队系统的时变性能的简单公式。我们知道，对于适当的初始条件，在时间t的忙碌服务器的数量对于每个t都有泊松分布。我们的研究结果表明，如何依赖于时间的平均函数m依赖于时间依赖的到达率函数λ和服务时间分布。例如，当lambda是二次函数时，平均值m（t）与逐点平稳近似lambda（t）E[S]一致，其中S是服务时间，除了时滞和空间偏移。值得注意的是，平稳M/G/infinity模型众所周知的不敏感特性不适用于非平稳M（t）/G/infinity模型;时间相关均值函数m依赖于超出其均值的服务时间分布。服务时间平稳超额分布起着重要的作用。当λ在时间t之前减小时，m（t）在服务时间变化性中增大，但是当λ在时间t之前增大时，m（t）在服务时间变化性中减小。我们建议使用这些无限服务器的结果来近似描述的多服务器系统中，一些到达丢失或延迟的时间依赖的行为。
We establish some general structural results and derive some simple formulas describing the time-dependent performance of the M(t)/G/infinity queue (with a nonhomogeneous Poisson arrival process). We know that, for appropriate initial conditions, the number of busy servers at time t has a Poisson distribution for each t. Our results show how the time-dependent mean function m depends on the time-dependent arrival-rate function lambda and the service-time distribution. For example, when lambda is quadratic, the mean m(t) coincides with the pointwise stationary approximation lambda(t)E[S], where S is a service time, except for a time lag and a space shift. It is significant that the well known insensitivity property of the stationary M/G/infinity model does not hold for the nonstationary M(t)/G/infinity model; the time-dependent mean function m depends on the service-time distribution beyond its mean. The service-time stationary-excess distribution plays an important role. When lambda is decreasing before time t, m(t) is increasing in the service-time variability, but when lambda is increasing before time t, m(t) is decreasing in service-time variability. We suggest using these infinite-server results to approximately describe the time-dependent behavior of multiserver systems in which some arrivals are lost or delayed.