Cost optimization and ANFIS computing for M/M/(R+c)/N queue under admission control policy and server breakdown

Abstract

This study focuses on a finite queueing model with multiple servers, incorporating an admission control F-policy and considerations for customers’ balking and server breakdown. The F-policy concept is used to control the flow of incoming customers, making the model formulation more realistic. Implementing the admission control F-policy, along with adding additional servers, can effectively alleviate congestion issues for customers by reducing the formation of queues and decreasing the frequency of customers opting out of the queue due to extended waiting time. In order to conduct a mathematical analysis of the model and establish probability distributions, we formulate the steady-state Chapman–Kolmogorov (C–K) equations and solve them using a recursive technique. The probability distributions allow us to develop several system performance measures, including the expected system size, the expected number of busy permanent servers, the probability of server breakdown, etc. These measures are utilized to assess the effectiveness of the model. The impact of system input parameters on several performance measures in the multi-server queueing model is presented using a numerical example. The accuracy of the results of performance measures is validated by implementing the adaptive neuro-fuzzy inference system (ANFIS) approach, enhancing the reliability and robustness of the findings. The non-linear cost function is also created to compute the optimal values of the decision variables, including the number of permanent servers, admission control threshold, service rate, and joining probabilities of customers. Grey wolf optimization (GWO) and particle swarm optimization (PSO) algorithms are applied to deal with the cost optimization problem. A comparative study of the GWO and PSO algorithms for cost optimization is also conducted. This optimization enables decision-makers to efficiently manage the system’s operations and resources. The findings of the study suggest that the proposed model can be applied in diverse real-life scenarios, such as electric vehicle charging stations (EVCSs), restaurants, and various other locations.