A genetic algorithm for cost optimization in queueing models of machining systems with multiple working vacation and generalized triadic policy

This study presents a generalized approach for implementing the Triadic control policy in queueing modeling of a redundant machining system with multiple servers. The machining system further integrates a policy for servers that allows for multiple working vacations. The fluctuation of active servers is based on the count of accumulated failed machines in the system. This alteration occurs individually at every stage of service completion or the arrival of a failed machine. The recursive approach is employed to generate analytical closed-form solutions of the system in terms of steady-state probabilities. The performance metrics of the system are determined, and their response to varying system parameters is demonstrated through tables and graphs. A cost function is proposed for the system and subsequently examined with different configurations. A Genetic Algorithm technique is used to acquire the most optimal input parameters to minimize the cost function.