Minimizing response times and queue lengths in systems of parallel queues
Minimizing response times and queue lengths in systems of parallel queues
复制标题
最小化并行队列系统中的响应时间和队列长度
DOI：
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发表时间：
1999
影响因子：
1
通讯作者：
D. Towsley
中科院分区：
文献类型：
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作者：
G. Koole;P. Sparaggis;D. Towsley
我们考虑的问题路由客户的两个并行队列之一。到达与系统的状态无关，但在其他方面是任意的。假设队列容量无限，服务时间为独立同分布序列。随机变量递增似然比（ILR）分布，我们证明了最短队列（SQ）的政策，最大限度地减少各种成本泛函相关的队列长度和响应时间。我们给出了一个反例，表明当服务时间具有增加的危险率但在似然率意义下不增加时，这个结果一般不成立。最后，我们证明了当容量有限时，SQ策略随机最大化离开过程，最小化损失计数过程。
We consider the problem of routeing customers to one of two parallel queues. Arrivals are independent of the state of the system but otherwise arbitrary. Assuming that queues have infinite capacities and the service times form a sequence of i.i.d. random variables with increasing likelihood ratio (ILR) distribution, we prove that the shortest queue (SQ) policy minimizes various cost functionals related to queue lengths and response times. We give a counterexample which shows that this result is not generally true when the service times have increasing hazard rate but are not increasing in the likelihood rate sense. Finally, we show that when capacities are finite the SQ policy stochastically maximizes the departure process and minimizes the loss counting process.