An M/G/1 Retrial G-Queue with General Retrial Times and Working Breakdowns
نویسندگان
چکیده
This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server breakdown, and the failed server still works at a lower service rate rather than stopping the service completely. Applying the embedded Markov chain, we obtain the necessary and sufficient condition for the stability of the system. Using the supplementary variable method, we deal with the generating functions of the number of customers in the orbit. Various system performance measures are also developed. Finally, some numerical examples and a cost optimization analysis are presented.
منابع مشابه
On the M/G/1 retrial queue subjected to breakdowns
Retrial queueing systems are characterized by the requirement that customers finding the service area busy must join the retrial group and reapply for service at random intervals. This paper deals with the M/G/1 retrial queue subjected to breakdowns. We use its stochastic decomposition property to approximate the model performance in the case of general retrial times.
متن کاملOn the Single-server Retrial Queue
In this work, we review the stochastic decomposition for the number of customers in M/G/1 retrial queues with reliable server and server subjected to breakdowns which has been the subject of investigation in the literature. Using the decomposition property of M/G/1 retrial queues with breakdowns that holds under exponential assumption for retrial times as an approximation in the non-exponential...
متن کاملDiscrete - Time / / 1 Retrial Queue with General Retrial Times , Working Vacations and Vacation Interruption
Abstract: We consider a discrete-time 1 X Geo G retrial queue with general retrial times, and introduce working vacations and vacation interruption policy into the retrial queue. Firstly, we analyze the stationary condition for the embedded Markov chain at the departure epochs. Secondly, using supplementary variable method, we obtain the stationary probability distribution and some performance ...
متن کاملAn M/g/1 Retrial Queue with Second Multi-optional Service, Feedback and Unreliable Server
An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accorda...
متن کاملAnalysis of the Number of Orbiting Customers in M/g/1 Retrial Queue with General Retrial Times
The research in the area of retrial queues focused mainly on the fact that the retrials operate under classical retrial policy, which suppose that the intervals between successive repeated attempts are exponentially distributed with total rate jθ (j is the number of customers in the orbit). There is another discipline, called constant retrial policy, where the total retrial rate does not depend...
متن کامل