Single server retrial queues with setup time
Single server retrial queues with setup time
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DOI：
10.3934/jimo.2016075
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发表时间：
2016-10
影响因子：
1.3
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，其中服务器知道重试客户的存在。在基本模型中，当系统变空时，服务器会立即关闭，以节省能耗。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，则它将保持空闲状态，等待新客户或重试客户。在服务时间和建立时间任意分布的假设下，我们得到了联合队列长度生成函数的显式表达式。我们还获得了计算队列长度矩的递归公式。然后，我们考虑一个扩展模型，其中服务器在关闭之前有一个关闭时间，并且还获得了显式解。
This paper considers single server retrial queues with setup time where the server is aware of the existence of retrying customers. In the basic model, the server is switched off immediately when the system becomes empty in order to save energy consumption. 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 or retrial customer. Under the assumption that the service time and the setup time are arbitrarily distributed, we obtain explicit expressions for the generating functions of the joint queue length. We also obtain recursive formulas for computing the moments of the queue length. We then consider an extended model where the server has a closedown time before being turned off for which an explicit solution is also obtained.