Process Modeling Using Queuing Theory and Simulation

In our everyday life, we frequently encounter waiting line systems, such as checkout lines in grocery stores, airport security checkpoints, and customer service call queues. These systems share common characteristics—stochastic demand for service with stochastic arrival times, and limited service resources leading to queues. These features are prevalent not just in service industries but also in manufacturing, where raw materials, machinery, and finished products experience waiting times. The challenge for system designers lies in balancing the need for shorter wait times with the efficient allocation of service channels to optimize system performance. This balance is crucial in both manufacturing, where it affects production efficiency, and service industries, where customer satisfaction is directly impacted. In this chapter, we review the mathematical models of these waiting line systems, known as queuing theory, which provides a basis to understand and optimize system behavior. This chapter delves into the foundational principles of queuing theory and its application in systems engineering. It outlines the definition and decision factors of queuing systems, introduces basic queuing models, including the birth−death process and M/M/1 and M/M/c systems, and discusses the derivation of key model parameters. Furthermore, it explores the use of queuing models in systems design and highlights the role of simulation, specifically discrete event simulation (DES) using tools like AnyLogic, in analyzing more complex queuing scenarios. This comprehensive approach to queuing theory and simulation offers valuable insights for effectively managing and designing waiting line systems across various industries.