Unreliable Single-Server Queue with Two-Way Communication and Retrials of Blocked and Interrupted Calls for Cognitive Radio Networks

Abstract

In this paper, we consider an M/GI/GI/1/1 retrial queue where incoming fresh calls arrive at the server according to a Poisson process. Upon arrival, an incoming call either occupies the server if it is idle or joins an orbit if the server is busy. From the orbit, an incoming call retries to occupy the server and behaves the same as a fresh incoming call. After some idle time, the server makes an outgoing call to outside. We consider the system with an unreliable server. In a free state and while servicing outgoing calls the server is reliable and unable to crash. If while servicing an incoming call the server crashes, the incoming call goes into the orbit. The service time of such an interrupted call follows the same distribution as that of an incoming call. For that system we obtained probability distribution of the states of the server, the condition for the existence of a stationary mode and probability distribution of a number of calls in the system.