The use of Metamodel-based Evolutionary Optimizer for multi-server queuing system design

Queuing systems play a vital role in various aspects of our daily lives, from banks and supermarkets to traffic lights, call centers, and production processes. However, many queue systems often fail to work in an efficient way. Traditionally, the design of such systems has relied on models that oversimplify reality. On the other hand, dynamic simulation models can be developed to reflect reality more closely with the possibility of introducing multiple scenarios to analyze the effect of the changes in given parameters. Despite their advantages, the optimization of simulation models of queuing systems is typically achieved through trial-and-error or by means of a large amount of simulation runs obtained through traditional design of experiments techniques. However, this process can be time-consuming and computationally expensive. This research presents an approach for designing an optimum multi-server queuing system applying a surrogate-based optimization algorithm. The said approach aims at speeding up the design of an optimal queue system with stochastic variables. To evaluate the proposed approach, a case study that models a cashier system is conducted. The case study considers stochastic events such as the arrival rate of customers, the number of products they buy, a diversity of prices, and the time each cashier takes to process the purchases. The cashier system is modeled and simulated using the FlexSim simulator software. Several scenarios are analyzed, including different types of cashiers with multiple servers and multiple queues, a single queue with multiple servers, and "fast cashiers” for customers buying a smaller amount of products. The goal is to determine the number of servers (cashiers) required to maximize the Net Present Value (NPV). The proposed approach is compared to two other approaches: experimental design-based optimization (directly with FlexSim simulator), and the Bayesian optimization algorithm. A statistical analysis is carried out for multiple runs of the algorithm to evaluate the proposed approach.