Optimizing Facilities by Adjusting Node and Server Numbers in a Closed BCMP Queueing Network

Queueing theory is a mathematically sophisticated discipline, and there is currently an expectation to apply it to optimization problems using computational results. To achieve the overall optimization of facilities, it is essential to consider selects in the number of service nodes, the availability of nodes, and the relationships with neighboring nodes. In this research, we construct a model to perform simultaneous optimization of the number of service nodes and the number of service points at each node, given the number of people classes and the number of people within the system, in a closed network constructed using closed BCMP. The theoretical calculation of closed BCMP utilizes the mean value analysis method. We employ a genetic algorithm for optimization, where the objective function considers both the standard deviation of the mean number of people within the system and the cost of installing servers at nodes, aiming to distribute congestion effectively within the network. Constraints are implemented to ensure that the mean number of people at each node does not exceed its maximum allowable capacity. Additionally, if a specific node is not used, the number of servers at that node becomes zero. The total maximum allowable capacity of all nodes is subject to specified conditions. This approach allows for the effective dispersion of congestion within the network, prevents excessive increases in the number of people at each node, and minimizes the cost of servers installation.