A Geometric Product-Form Distribution for a Queueing Network by Non-Standard Batch Arrivals and Batch Transfers
A Geometric Product-Form Distribution for a Queueing Network by Non-Standard Batch Arrivals and Batch Transfers
复制标题
非标准批量到达和批量传输排队网络的几何乘积分布
DOI：
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发表时间：
1997
影响因子：
1.2
通讯作者：
P. Taylor
中科院分区：
文献类型：
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作者：
M. Miyazawa;P. Taylor
针对具有成批移动的连续时间开放排队网络，我们引入了一种批服务规则，称为装配-转移批服务。在该服务规则下，在一个节点上同时服务请求数量的客户，并且如果那里有足够的客户，则可能将其作为一批不同大小的客户转移到另一个节点；否则，该节点被清空。我们假设到达过程、服务时间和路线是马尔可夫设置的，其中批次大小通常是分布的。在假设额外批次到达时节点空的假设下，在一定的稳定性条件下，证明了队长的平稳分布在节点上具有几何乘积形式当且仅当额外到达满足一定的条件。这给出了一类具有易于处理的平稳分布的排队网络，同时也证明了乘积形式在没有额外到达的情况下为相应排队网络的平稳分布提供了一个随机上界。
We introduce a batch service discipline, called assemble-transfer batch service, for continuous-time open queueing networks with batch movements. Under this service discipline a requested number of customers is simultaneously served at a node, and transferred to another node as, possibly, a batch of different size, if there are sufficient customers there; the node is emptied otherwise. We assume a Markovian setting for the arrival process, service times and routing, where batch sizes are generally distributed. Under the assumption that extra batches arrive while nodes are empty, and under a stability condition, it is shown that the stationary distribution of the queue length has a geometric product form over the nodes if and only if certain conditions are satisfied for the extra arrivals. This gives a new class of queueing networks which have tractable stationary distributions, and simultaneously shows that the product form provides a stochastic upper bound for the stationary distribution of the corresponding queueing network without the extra arrivals.