Analysing M/M/1 queue dynamics with system breakdowns and unreliable repair processes

A single server Markovian queueing paradigm is studied. The server is prone to random breakdowns when delivering service or during idle periods. When the server encountered problems, the repair procedure began immediately. The likelihood of restoring the server is p(p < 1) after an exponential repair time. All present users leave the system if the server cannot be fixed. The time-dependent likelihood for a single server queue with an unreliable repairer is explicitly estimated for the first time. The results were also cross-checked with the available literature. To demonstrate the significance of parameter values, performance measures and numerical figures were also supplied.