Limitations of Calculating Theoretical Solutions for Closed BCMP Queueing Networks and Verification of Alternative Theoretical Values by Parallel Simulation

Abstract

Abstract The global spread of the new coronavirus has caused people to rethink their ideas about waiting. In terms of building design, facilities must consider infection control measures and whether evaluations can be performed using queueing theory. Flexible definitions of queueing networks, such as Baskett, Chandy, Muntz and Palacios (BCMP) queueing networks, must be applied to large-scale models that exist in the real world, to evaluate congestion levels. This study applied a closed BCMP queueing network to a real-world model and examined the limitations of the theoretical solution calculation and the possibility of substituting theoretical values by parallel simulation. Parallel computing was applied to the mean value analysis method. Calculations were performed in a large-scale computing environment, enabling calculations on a much larger scale than with conventional models. The results also showed the computation time and required computing resources for the calculation. Since a larger customer class places a greater burden on computational resources, we conducted simulations on models for which a theoretical solution is required and assessed the accuracy of these simulations to confirm that they are sufficiently accurate as an alternative method to the theoretical solution. We proposed a process to calculate performance evaluation indices such as the average number of people in the system in parallel simulations and confirmed that the performance evaluation indices are sufficiently accurate for models with large customer classes. The study findings contribute to both social practicality and academic significance by making it possible to conduct mathematically supported congestion assessments in real-world models and to propose application scenarios for queueing theory.