ANFIS computing and cost optimization of an M/M/c/M queue with feedback and balking customers under a hybrid hiatus policy

Abstract

The present investigation studies a hybrid hiatus policy for a finite-space Markovian queue, incorporating realistic features such as Bernoulli feedback, multiple servers, and balking customers. A hybrid hiatus policy combines both a working hiatus and a complete hiatus. As soon as the system becomes empty, the servers switch to a working hiatus. During a working hiatus, the servers operate at a reduced service rate. Upon completion of the working hiatus and in the absence of waiting customers, the servers enter a complete hiatus. Once the complete hiatus period concludes, the servers resume normal operations and begin serving waiting customers. In the context of Bernoulli feedback, the dissatisfied customer can re-enter the system to receive another service. By utilizing the Markov recursive approach, we examined the steady-state probabilities of the system and queue sizes and other queueing indices, viz. Average queue length, average waiting time, throughput, etc. Using the Quasi-Newton method, a cost function is developed to determine the optimal values of the system’s decision variables. Furthermore, a soft computing approach based on an adaptive neuro-fuzzy inference system (ANFIS) is employed to validate the accuracy of the obtained results.