Performance of Fuzzy Bulk Queueing Models with Performance Measures and Cost Optimization

AbstractThis paper investigates a bulk service queueing model under a fuzzy environment to reflect real world uncertainties in in service and arrival patterns. Traditional queueing model rely on precise numerical data, which are often unavailable in practical systems like telecommunication manufacturing and transportation. To address this limitation, this study applies fuzzy set theory, representing the arrival rate, service rate and batch size configuration as fuzzy numbers. The primary objective is to analyze key system performance measures and optimize the total operational cost. We derive explicit analytical expressions for critical performance metrics, including the expected queue length, waiting time in the queue server utilization and system throughout.