ИСТИНА

Queueing models with repeat orders, or retrial queues, are characterized by the following feature: a customer that cannot receive full service (due to balking, impatience, server failure, etc.) leaves the service area but after some random time repeats his demand until the required service is provided. It is also possible that after several unsuccessful attempts the customer decides to abandon further attempts and leaves the system without service. Such systems can be used in performance analysis of ordinary telephone networks, cellular mobile networks, wavelength-routed optical networks, e-mail systems, Internet protocols, call centers, etc. Other applications include stacked aircraft waiting to land, and queues of retail shoppers who may leave a long waiting line hoping to return later when the line may be shorter. We consider a single server retrial queueing system with the server subject to breakdowns. It is assumed that fresh customers join unlimited queue and then are served in a FCFS discipline. But if the server fails while servicing a customer, the customer leaves the server, joins a retrial group and in random intervals repeats attempts to get service (independently of other customers in the retrial group). If the server is free and non-failed when a repeat order is placed, the respective customer from the retrial group starts to be served; otherwise the customer has to try his luck later on. This model can be used, for example, to evaluate the influence of returning customers on performance of a computer network streaming multimedia applications. We introduce the notions of a service cycle and a server busy period and use them to find the joint distribution of the server state, the number of customers in the queue and the number of customers in the retrial group in steady state when both the service time and the server recovery period have general distributions.