Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement

Abstract

The present study deals with the admission control policy for the single server finite capacity queueing model with discouraged customers and general distributed retrial times. The arriving customer is forced to join the retrial orbit on finding the server busy. From the orbit, the customer can retry for the service again after sometime. Due to the long queue in front of the server, the customers may be discouraged and leave the system without receiving the service. The noble feature of proposed study is to control the arrivals in the system based on F-policy according to which as soon as the system capacity becomes full, no more customers are permitted to join the system until the system capacity again drops to threshold level ‘F’. The steady state queue size distribution of the system size is evaluated by introducing the supplementary variables corresponding to remaining retrial times and framing Chapman–Kolmogorov equations. The recursive and soft computing based artificial neuro fuzzy inference system (ANFIS) approaches are applied to solve governing equations and to establish various performance indices. Furthermore, a cost function is also constructed to evaluate the optimal service rate and the corresponding expected cost of the system. Genetic algorithm (GA) and quasi-Newton method (QNM) are used to minimize the expected cost of the system to decide the optimal decision parameter corresponding to service rate.