Retrial queues with server subject to breakdowns and repairs
Retrial queues with server subject to breakdowns and repairs
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DOI：
10.1007/bf01158474
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发表时间：
1990-11
期刊：
影响因子：
1.2
通讯作者：
V. Kulkarni;B. Choi
中科院分区：
文献类型：
--
作者：
V. Kulkarni;B. Choi
在本文中，我们考虑了一个单服务器重试队列中的服务器是受故障和维修。新客户到达服务站根据泊松过程和需求i.i.d.服务时间。如果服务器处于空闲状态，则会立即开始为传入客户提供服务。如果服务器忙碌，则进入的客户在指数时间量之后进行重试。重审客户的行为相互独立。服务器保持指数时间，然后失败。维修时间具有一般分布。服务器空闲时的故障/修复行为与服务器忙碌时不同。两种不同的模型被认为是。在模型I中，故障服务器不能被占用，其服务被中断的客户必须离开系统或重新加入重试组。在模型II中，服务被故障中断的客户留在服务器上，并在修复完成后重新启动服务。模型II可以作为模型I的特例来处理。对于模型I，我们利用马尔可夫再生过程的工具，导出了系统的稳定性条件，并研究了系统的极限行为。
In this paper we consider a single server retrial queue where the server is subject to breakdowns and repairs. New customers arrive at the service station according to a Poisson process and demand i.i.d. service times. If the server is idle, the incoming customer starts getting served immediately. If the server is busy, the incoming customer conducts a retrial after an exponential amount of time. The retrial customers behave independently of each other. The server stays up for an exponential time and then fails. Repair times have a general distribution. The failure/repair behavior when the server is idle is different from when it is busy. Two different models are considered. In model I, the failed server cannot be occupied and the customer whose service is interrupted has to either leave the system or rejoin the retrial group. In model II, the customer whose service is interrupted by a failure stays at the server and restarts the service when repair is completed. Model II can be handled as a special case of model I. For model I, we derive the stability condition and study the limiting behavior of the system by using the tools of Markov regenerative processes.