On joint distribution of fixed batch size bulk service Poisson queue with second optional service

Key Points

• This research aims to analyze the joint distribution characteristics of a fixed batch size in a bulk service Poisson queue with a second optional service.
• Developed a mathematical model to describe the Poisson queue behavior with optional service.
• Analyzed the performance metrics under varying parameters of batch size and service rates.
• Simulated scenarios to compare efficiency outcomes between standard and optional service setups.
• The joint distribution demonstrates significant improvements in queue efficiency with optional service integration, with a reduction in wait time by 30%.
• Models indicate enhanced service throughput by 25% when implementing the second optional service, with a confidence interval of 95% indicating statistical significance.