Optimal nodes placement using a closed BCMP queueing network

In this study, a closed BCMP queueing network, which is one of the most flexible queueing models relative to customer class and multiple service types that can be selected, was used for optimal node placement. Although the closed BCMP queueing network offers flexibility, it is computationally expensive when calculating performance evaluation quantities, such as the average number of customers in a system. Thus, the application of the closed BCMP to large-scale problems is considered challenging. In this study, an optimal node placement model, which uses a genetic algorithm to select the nodes where customers are not concentrated and are appropriately distributed, was implemented using a computational engine that calculated the performance evaluation quantity of a closed BCMP queueing network in real time. Two types of objective functions were designed: a penalty type, which applied a penalty when customers were concentrated at a node, and a variance type, which minimized the standard deviation of the average number of customers to equalize the average in the system. The features of this study, including the large-scale application of the closed BCMP queueing network and optimal node placement model, find application as a general-purpose model for node allocation planning in numerous situations and have high academic significance in the application of queueing theory to the real world.