Optimal Control of Arrival Rates in a Queueing Model with Stochastic and Time Dependent Demand

Objectives: Examining a queueing model for production and service systems with stochastic and time-dependent demand is the aim of this research. In order to maximize the system’s net benefit while preserving dependable and efficient system performance, the major objective is to optimize throughput revenue, backlog expenses, and arrival rate control costs. Methods: An optimization framework for assessing performance over time is developed using an 𝑀/𝑀/1 queueing model in conjunction with the Piecewise- Stationary Approach (PSA). The objective function is formulated using three key components: the backlog penalty cost, the expected throughput income, and the cost of dynamically changing arrival rates. The goal of the model is to maintain analytical simplicity while capturing time-varying demand behavior. Finding: In time-dependent and stochastic situations, the proposed approach offers a useful framework for managing arrival rates. It is appropriate for MTO production and service systems with varying demand since it promotes better operational decision-making by striking a balance between system utilization and service efficiency. Novelty: This study allows time-dependent queue performance evaluation with flexible computing complexity by merging an arrival-rate control optimization framework with the Piecewise-Stationary Approach (PSA). Keywords: 𝑀/𝑀/1 queuing model; Optimization; MTO (Make-to-order) manufacturing system; Piecewise-Stationary Approach (PSA)