Stationary and transient analysis of \(M/M/1\) G-queues (Q1753788)

Summary: An \(M/M/1\) queueing model subject to disaster and subsequent failure is analysed under stationary and transient regime. When the system is met with a disaster, all customers (including those waiting) are lost forever and the system goes to the repair state. However, customers are allowed to join the queue even when the system is under repair. The repair times also follow exponential distribution. Explicit expressions for both steady state and time dependent probabilities are obtained using Laplace transform and generating function techniques. Various other system performance measures are also derived analytically and illustrated in the form of graphs.