Steady-state Analysis of an M /M / 2 Queueing System Operating in a Multi-phase Random Environment Subject to Disaster and Repair

In this research article, an M /M / 2 queueing system operating in a multi-phase random environment subject to disaster and repair is studied. The random environment discussed here has N phases and the k - th phase is exponentially distributed with mean 1 , k 1,2,..., N. k  = The queueing system behaves like ( ) / ( ) / 2 k k M  M  while in the k - th phase. At the end of the k - th phase, a disaster occurs where the servers are taken for repair and all the customers in the system are wiped out. Both the servers are repaired jointly and the repair time is exponentially distributed with mean 1 , 0  Immediately after the repair completions, the system goes to phase k with probability k q . During repair time, Customers are permitted to enter the queueing system. The probabilistic behaviour of the system is studied in steady state by using probability generating function technique. Some performance measures of this queueing model are also obtained.