The study of RQ-system with unreliable device

Abstract

The paper studies a single-line RQ Queuing system M/M/1 with an incoming Poisson flow. Requests arrive at the system input, and if the device is free, then they are serviced. If the device is busy, then the requests go to the source of repeated calls and waiting for service. After a delay in the source of repeated calls, the request tries to occupy the device again, and if it is free, the incoming request takes it for service. It is assumed that the server is "unreliable", that is, it may fail, and then it is sent for repair. An analytical and numerical solution of this system is obtained by the method of generating functions.