Concavity of the throughput of tandem queueing systems with finite buffer storage space
Concavity of the throughput of tandem queueing systems with finite buffer storage space
复制标题
有限缓冲存储空间串联排队系统吞吐量的凹性
DOI：
10.2307/1427472
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发表时间：
1990
影响因子：
1.2
通讯作者：
J. Shanthikumar
中科院分区：
文献类型：
--
作者：
L. Meester;J. Shanthikumar
本文考虑了具有m个级和有限个中间缓冲存储空间的串级排队系统。每个阶段有一个单一的服务器和服务时间是独立的和指数分布。在第一阶段前面有无限的客户供应。对于这个系统，我们证明了在时间间隔[0，t]（对于任何t ≥ 0）内，离开m个阶段中每个阶段的客户数量是强烈随机增加的，并且缓冲存储容量是凹的。因此，该串联存储系统的吞吐量是缓冲存储容量的递增和凹函数。我们建立了这个结果，使用一个样本路径递归的离开过程的m个阶段的串联系统，这可能是独立的利益。通过沿着队列的可逆性，获得最佳的缓冲区空间分配的吞吐量最大化的三级串联队列的吞吐量。
We consider a tandem queueing system with m stages and finite intermediate buffer storage spaces. Each stage has a single server and the service times are independent and exponentially distributed. There is an unlimited supply of customers in front of the first stage. For this system we show that the number of customers departing from each of the m stages during the time interval [0, t] for any t ≧ 0 is strongly stochastically increasing and concave in the buffer storage capacities. Consequently the throughput of this tandem queueing system is an increasing and concave function of the buffer storage capacities. We establish this result using a sample path recursion for the departure processes from the m stages of the tandem queueing system, that may be of independent interest. The concavity of the throughput is used along with the reversibility property of tandem queues to obtain the optimal buffer space allocation that maximizes the throughput for a three-stage tandem queue.