ANFIS computing for $MAP/PH/1$ queueing system with server deterioration and recovery under vacation and backup server

We examine a queueing system with vacation in which the service rate deteriorates during the service and recovers the service rate during the vacation. The backup server with less service rate takes the place of the main server during the recovery time. The matrix analytic method is used to analyse the system and some performance metrics are obtained. The Adaptive Neuro-Fuzzy Inference System (ANFIS) was utilized to construct various performance measures by developing rules from input datasets. The results and the sensitivity of the model parameters are demonstrated by numerical examples.