In this paper, we consider a single server queueing model M/GI/GI/1/1 with two types of calls: incoming calls and outgoing calls. Incoming call enters the system and goes into service if the server is free. If the server is busy, call instantly goes to orbit, after which the call retries to go into service. The server makes an outgoing call in its idle time. We will be reviewing a system with unreliable server. In a free state and while servicing outgoing calls the server is reliable and unable to crash. If while servicing incoming call the server crashes, the incoming call stays at the server and as soon as server recovers the call goes into afterservice. For that system we’ve obtained probability distribution of server states, condition for the existence of a stationary mode and probability distribution of a number of incoming calls in the system.
Information Technologies and Mathematical Modelling. Queueing Theory and Applications : 17th International Conference, ITMM 2018, named after A. F. Terpugov and 12th Workshop on Retrial Queues and Related Topics, WRQ 2018, Tomsk, Russia, September 10-15, 2018 : selected papers. Cham, 2018. P. 213-224
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