M/M/1/1 Retrial Queues with Setup Time
M/M/1/1 Retrial Queues with Setup Time
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DOI：
10.1007/978-3-319-22267-7_9
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发表时间：
2015-08
期刊：
影响因子：
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通讯作者：
Tuan Phung-Duc
中科院分区：
文献类型：
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作者：
Tuan Phung-Duc
本文考虑具有设置时间的单服务器重试队列。在基本模型中，如果服务器完成一项服务并且轨道上没有客户，则服务器立即关闭。看到服务器被占用的到达客户会加入轨道，并在一段随机时间后重复他们的尝试。我们模型的新功能是，到达的客户看到服务器关闭，在服务器处等待，然后服务器打开。服务器需要一些设置时间才能激活，以便为等待的客户提供服务。如果服务器完成服务并且轨道不为空，则它会保持空闲状态，等待新客户或来自轨道的客户。对于该模型，我们获得了联合队列长度生成函数的显式表达式。然后我们考虑一个扩展模型，其中服务器在关闭之前保持空闲一段时间，也获得了显式解。
This paper considers single server retrial queues with setup time. In the basic model, if the server completes a service and there are no customers in the orbit, the server is turned off immediately. Arriving customers that see the server occupied join the orbit and repeat their attempt after some random time. The new feature of our models is that an arriving customer that sees the server off waits at the server and the server is turned on. The server needs some setup time to be active so as to serve the waiting customer. If the server completes a service and the orbit is not empty, it stays idle waiting for either a new customer or a customer from the orbit. For this model, we obtain explicit expressions for the generating functions of the joint queue length. We then consider an extended model where the server stays idle for a while before being turned off for which explicit solution is also obtained.