Unreliable Single Server Double Orbit Retrial Queue with Balking

The single unreliable server double orbit Markovian retrial queue with customers’ balking behavior has been investigated. The arriving customers may not wish to proceed for the service when the system seems overcrowded. On joining the system, if the server is busy then customers are forced to join ordinary orbit or executive orbit as per their demand. It is assumed that the server is unreliable and subject to breakdown and repair. For the steady-state analysis of the system, Chapman–Kolmogorov steady-state equations are framed and then solved by using probability generating function. Furthermore, various performance metrics are derived explicitly. An illustration is taken to analyze the effects of the system parameters on the performance metrics. ANFIS technique is implemented to authenticate the steady-state results. Further, a nonlinear cost function is also formulated which is then minimized by using the quasi-Newton method.