M/M/1 Queue with Server Breakdown, Single Working Vacation, State Reliant Customers and Feedback

Our article deals with M/M/1 queue with server breakdown, single working vacation, state reliant customers and feedback. The service times of two distinct service rates are exponentially assigned. Service times during the vacation period, service times during the service period as well as vacation times are all exponentially distributed. Arrival follows Poisson process with three different arrival rates. Assuming the queue length expands, the server goes from working vacation to ordinary busy period. At the point whenever the server could open to abrupt breakdown and after it should to be repaired and goes to ordinary service. After getting a service, incomplete or unsatisfied customer decide to leave the system with some parameter or continue the system with its compliment. Customer continuing the system with feedback have join the queue tail and get the service as primary customer. This kind of model examined utilizing Matrix Geometric Approach (MGA). We also provide some numerical examples by taking particular values to the parameters. Using that probability vectors, we also derived some performance analysis.