Product form networks with negative and positive customers
Product form networks with negative and positive customers
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产品与负面和正面客户形成网络
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
E. Gelenbe
中科院分区：
文献类型：
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作者：
E. Gelenbe
我们引入了一类新的排队网络，其中顾客要么是“消极的”，要么是“积极的”。如果队列长度为正，则到达队列的负客户将使该队列中的总客户数减少1；如果队列为空，则没有任何作用。消极的顾客得不到服务。顾客离开一个队列去另一个队列，要么变得消极，要么保持积极。积极的客户表现得像普通的排队网络客户一样，接受服务。我们表明，该模型具有指数服务时间，泊松外部到达，通常的服务时间独立性假设，以及队列之间的马尔可夫客户移动，具有产品形式。在通常意义上，它是准可逆的，但在更广泛的意义上，它不包括所有客户的破坏，在一组离开。讨论了（非线性）顾客流方程解的存在唯一性，从而讨论了产品形式解的存在唯一性。
We introduce a new class of queueing networks in which customers are either "negative" or "positive". A negative customer arriving to a queue reduces the total customer count in that queue by one if the queue length is positive; it has no effect at all if the queue is empty. Negative customers do not receive service. Customers leaving a queue for another one can either become negative or remain pos itive. Pos itive customers behave as ordinary queueing network customers and receive service. We show that this model with exponential service times, Poisson external arrivals , with the usual independence assumptions for service times , and Markovian customer movements between queues , has product form. It is quasi-reversible in the usual sense, but not in a broader sense which includes all destructions of customers in the set of departures. The existence and uniqueness of the solutions to the (non-linear) customer flow equations, and hence of the product form solution, is discussed.