On Queue Length Moments in Fork and Join Queuing Networks with General Service Times
On Queue Length Moments in Fork and Join Queuing Networks with General Service Times
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具有一般服务时间的 Fork 和 Join 排队网络中的队列长度时刻
DOI：
10.1007/bfb0022209
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
I. Mura
中科院分区：
文献类型：
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作者：
S. Balsamo;I. Mura
Fork和join队列网络模型可用于表示和分析具有并发和同步约束以及共享资源的分布式和并行处理计算机系统的性能。并发性和同步性使得这种性能模型的求解比传统的排队网络分析更为复杂。我们考虑并行处理系统，其中一组独立任务同时执行，可以用fork和join队列网络表示。提出了一种近似分析开放分叉和加入排队网络的方法，该网络的一般服务时间分布由Coxian分布表示。具体地说，我们导出了联合队列长度分布的两个近似和该分布的所有矩的封闭形式表达式。我们证明了该方法给出了队列长度矩的下界和上界。
Fork and join queueing network models can be used to represent and analyse the performance of distributed and parallel processing computer systems with concurrence and synchronisation constraints and shared resources. Concurrence and synchronisation make the solution of such performance models more complex than classical queueing network analysis. We consider parallel processing systems where a set of independent tasks are executed simultaneously and can be represented by fork and join queueing networks. We present an approximate method to analyse open fork and join queueing networks with general service time distribution represented by Coxian distribution. Specifically, we derive two approximations of the joint queue length distribution and closed form expressions for all the moments of this distribution. We prove that the method provides lower and upper bounds on the queue length moments.