Metaheuristic Optimization and ANFIS-Driven Performance Analysis of a $MAP/PH/2$ Retrial Queue with Differentiated Breakdowns, Working Vacations, Vacation Interruptions, and N-Policy

This paper studies a MAP/PH/2MAP/PH/2MAP/PH/2 retrial queueing system incorporating differentiated breakdowns, working vacations, vacation interruptions, and an NNN policy. Customer arrivals follow a Markovian Arrival Process (MAP), while service times are assumed to follow PH distributions, which allow a flexible representation of various stochastic behaviors. When an arriving customer finds both servers occupied, the customer enters an orbit and attempts to obtain service again after a random retrial time.
The system consists of two heterogeneous servers. Server~1 remains continuously available, whereas Server~2 operates under a working vacation policy. During a working vacation, the server continues to provide service, and the vacation is interrupted whenever the number of customers in the system reaches a predetermined threshold level NNN. The server then switches to the normal operating mode and continues service until the system becomes empty, after which another working vacation begins.
The system dynamics are formulated as a continuous-time Markov chain with a QBD structure. Using matrix analytic methods and steady state probabilities, key performance measures such as orbit size and server utilization are obtained. Numerical experiments are performed to demonstrate the validity of the analytical results. Furthermore, an ANFIS is used to compare and validate the outcomes obtained from the analytical model. Finally, a cost function is formulated and optimized using metaheuristic approaches such as PSO, CSA, and BBO to identify efficient system configurations.