Transient behaviour of an M/M/2 queue subject to disasters and repairs - A new approach

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Abstract
We consider an M / M / 2 queueing system subject to disasters and repair. Disasters occur only when there are active servers in the system. Whenever a disaster occurs, all customers in the system are washed out and the available servers in the system get failed. The failed servers are immediately taken to a repair facility and the repair starts immediately. Immediately after the repair, the server becomes active as new as it was before in the operable state and is now ready to render service to the available customers in the system. The repair facility is not affected by the occurrence of disasters. Customers are allowed to join the system at any time. For this model, we provide a transient analysis and deduce the steady-state distribution of the system size. We also provide some performance measures of the system. A numerical illustration is also provided to highlight the system behaviour.