Optimal Control F-policy for M/M/R/K Queue with an Additional Server and Balking

Abstract

The multi-server finite queueing model with balking under admission control of customers based upon F-policy is investigated. In order to reduce the balking behavior of the customers, there is the provision of one additional server so as to shorten the queue length formed by the customers in rush hour. The noble realistic feature of the proposed Markov model is to control the admission of customers based on the threshold level ‘F’ of the queue size. According to ‘F’ policy, no more customers can be accommodated once the system is full and then after the further admission of the customers is not acceptable until the queue size drops to the predefined threshold level ‘F’. Chapman–Kolmogorov equations have been framed and are solved by using the recursive technique to establish the steady-state queue size probability distribution of the customers present in the system. A numerical example is taken to explore the various system indices. Adaptive neuro-fuzzy inference system (ANFIS) approach is applied to compare the soft computing results obtained by ANFIS with the results computed by the analytical method. The cost function is framed to determine the optimal control parameters namely threshold value ‘F’, the capacity of the system, the number of servers and service rate.