Proposal for optimizing number of servers in closed BCMP queueing network

In this study, we use a closed BCMP queueing network model designed for multiple customer classes and servers to optimize the number of servers at each node. This optimization is achieved by setting an upper limit on the number of servers and using an objective function that combines the standard deviation of the average number of customers in the system with the server installation cost. We use a genetic algorithm with parallel computations for the optimization process. Our findings demonstrate that this approach is viable for closed BCMP network models that require extensive computational resources. The optimal server count is validated by comparing the optimization results with the maximum number of servers utilized. Node popularity is predetermined, and a gravity model is employed to generate transition probabilities, rendering the model applicable to real-world scenarios. Our optimization results indicate that both the node popularity and distance between nodes influence the server count. Furthermore, simulations were conducted to evaluate the effect of the number of servers on the optimization outcomes. Allowing variations in the node count, location, and popularity makes this study flexible and adaptable to various real-world scenarios, such as transportation systems, healthcare facilities, and commercial spaces. Moreover, by providing an efficient and scalable solution, this study serves as a cornerstone for future research in this field and offers a practical tool for facility managers aiming to minimize both congestion and operational costs.