Time Dependent solution of a two homogeneous servers Markovian Queueing system with Feedback, Environmental, Catastrophic and Restoration effects

In this paper we consider a finite capacity Markovian feedback queueing system with two identical servers under two environmental conditions. Change in environmental conditions also affects the state of the queueing system. Further the system is also suffered by randomly occurring disasters, which destroys all the present customers of the system in both the environmental conditions. Then a repair process is started and after the successful repair the system is ready for working. Here, repair time is known as the restoration time. After completion of their service the served customer either join at the end of the queue with probability p or permanently leave the system with probability q =1−p, this phenomenon is known as customer feedback. We modeled this queueing system and obtained the transient state solution by using probability generating function technique.