A tandem network of fluid queues with on-off arrivals
A tandem network of fluid queues with on-off arrivals
复制标题
具有开关到达的流畅队列的串联网络
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. M. Lonsdale
中科院分区：
文献类型：
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作者：
P. Harrison;P. M. Lonsdale
一段时间以来，流体模型被用来近似具有离散状态的随机网络。这些范围从传统的“繁忙的交通”近似的最新进展，在生化系统模型。在这里，我们得到了一个精确的解决方案，一对两个队列连接在一起，在第一个和第二个出发的开-关到达。所得到的矢量微分方程的求解方法是通过拉普拉斯变换，其直接产生联合矩（例如协方差）并且可以被反演以给出两个队列处的流体水平的稳态联合概率分布。该结果的准确性可用于验证模拟，而模拟又可用于验证更复杂的模型，并为更大网络的解析解提供了一条途径。
Fluid models have for some time been used to approximate stochastic networks with discrete state. These range from traditional ‘heavy traffic’ approximations to the recent advances in bio-chemical system models. Here we obtain an exact solution for a pair of two queues linked in tandem with on-off arrivals at the first and departures from the second. The solution method of the resulting vector differential equation is via Laplace transforms, which yields joint moments (e.g. covariance) directly and can be inverted to give the steady state joint probability distribution of the fluid levels at the two queues. The exactness of this result can be used to validate simulations, which in turn can be used to validate more complex models, and also suggests a route to analytical solution of larger networks.