Cost optimization and machine learning-based prediction of waiting time for fault-tolerance machining system with general vacation and F-policy

Abstract

This study focuses on the queueing management, performance analysis, and cost optimization of a fault tolerance machining system (FTMS) that incorporates the multiple vacations of repairman and admission control F-policy (ACFP). The ACFP is an effective tool for managing the congestion problem that arises due to the arrival of failed machines for repair jobs in a system. This effectively controls the influx of failed machines and enhances the efficiency of the repair process. Furthermore, when there are no failed machines available in the system (i.e., the system is empty), the repairman may choose to take a vacation. After returning from vacation, if there are no failed machines available for repair, the repairman can take another vacation. For the mathematical analysis of the proposed model, the Chapman–Kolmogorov (C-K) steady-state equations are constructed and solved. This is achieved by introducing supplementary variables corresponding to vacation times, followed by using the Laplace-Stieltjes transform (LST) and recursive method to establish probability distributions. Furthermore, using the established probability distributions, various performance measures are developed to gain insights into the system’s behavior. These performance measures include the expected number of failed machines in the system, waiting time, machine availability, and other relevant metrics. Numerical simulation is carried out to assess the influence of input parameters on performance measures. Moreover, a machine learning approach employing regression methods is employed to predict the waiting time for failed machines to initiate their repair within the system. This combination of numerical simulation and machine learning analysis provides a comprehensive understanding of the system’s performance and enables accurate predictions of waiting times. Cost optimization is also performed for the FTMS using trapezoidal fuzzy numbers as cost elements by employing meta-heuristic techniques based on particle swarm optimization (PSO) and artificial bee colony (ABC) algorithms.