Time-Dependent Analysis of a Single-Server Queueing System with Disasters and Unreliable Repairs: A Probabilistic Approach to System Resilience

A single server Markovian queueing paradigm is studied. The server is prone to disaster when delivering service or during idle periods. When the server encountered problems, all waiting customers will be flushed away and the repair procedure began immediately. Arrivals are allowed to join the queue during the repair time. The likelihood of restoring the server is p(p<1) after an exponential repair time. All waiting users leave the system if the server cannot be fixed. The time-dependent likelihood for a single server queue with disaster and an unreliable repairer is explicitly estimated for the first time. To demonstrate the significance of parameter values, performance measures and numerical figures were also supplied.