Analysis of MAP/PH1, PH2/2 Queueing Model with Working Breakdown, Repairs, Optional Service and Balking

In this paper, a classical queueing system with two types of heterogeneous servers has been considered. The Markovian Arrival Process (MAP) is used for the customer arrival, while phase type distribution (PH) is applicable for the offering of service to customers as well as the repair time of servers. Optional service are provided by the servers to the unsatisfied customers. The server-2 may get breakdown during the busy period of any type of service. Though the server -2 got breakdown, server-2 has a capacity to provide the service at a slower rate to the current customer who is receiving service when the moment of server-2 struck with breakdown. In the period of vacation/closedown of server-1 and the server-2 is in working breakdown or under repair process, the arrival of customers may balk the system due to the impatient. Stability conditions has derived for our system and the stationary probability vector was evaluated by using the matrix analytical method. This model also examined at the analysis of busy period, waiting time distribution and system performance measures. The numerical illustrations are provided with the aid of two dimensional and three dimensional graphs.