MT/G/INFINITY QUEUES WITH SINUSOIDAL ARRIVAL RATES
MT/G/INFINITY QUEUES WITH SINUSOIDAL ARRIVAL RATES
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DOI：
10.1287/mnsc.39.2.241
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发表时间：
1993-02-01
影响因子：
5.4
通讯作者：
WHITT, W
中科院分区：
文献类型：
--
作者：
EICK, SG;MASSEY, WA;WHITT, W
本文描述了具有正弦到达率函数的M（t）/G/无穷大排队系统（具有非齐次Poisson到达过程）中平均忙碌服务台数随时间的变化.对于一个M（t）/G/infinity模型，在适当的初始条件下，已知在时间t的忙碌服务器数对每个t都服从泊松分布，因此全分布由其均值来表征。我们的公式显示了高峰拥塞如何滞后于高峰到达率，以及拥塞的范围比提供的负载范围小多少。简单的公式也可以被视为线性系统理论的结果，因为平均函数可以被视为应用于到达率函数的线性算子的图像。我们还调查了质量的各种近似的平均数的忙碌服务器，如逐点平稳近似和几个多项式近似。最后，我们将正弦到达率函数的结果应用于使用傅立叶级数处理一般周期到达率函数。这些结果的目的是提供一个更好的理解的行为的M（t）/G/无穷大模型和相关的M（t）/G/s/r模型，其中一些客户丢失或延迟。
In this paper we describe the mean number of busy servers as a function of time in an M(t)/G/infinity queue (having a nonhomogeneous Poisson arrival process) with a sinusoidal arrival rate function. For an M(t)/G/infinity model with appropriate initial conditions, it is known that the number of busy servers at time t has a Poisson distribution for each t, so that the full distribution is characterized by its mean. Our formulas show how the peak congestion lags behind the peak arrival rate and how much less is the range of congestion than the range of offered load. The simple formulas can also be regarded as consequences of linear system theory, because the mean function can be regarded as the image of a linear operator applied to the arrival rate function. We also investigate the quality of various approximations for the mean number of busy servers such as the pointwise stationary approximation and several polynomial approximations. Finally, we apply the results for sinusoidal arrival rate functions to treat general periodic arrival rate functions using Fourier series. These results are intended to provide a better understanding of the behavior of the M(t)/G/infinty model and related M(t)/G/s/r models where some customers are lost or delayed.