Performance evaluation for production systems through queueing models

The improvement of the society highly depends on the development of industry. Besides the “hardware” (e.g., plants and machines) in a production system, the “software” (e.g., system management) is also vital to the productivity improvement. Since the last century, much effort has been made to improve production systems (e.g., maximize the throughput, reduce the mean cycle time and minimize the operation cost) and some well-known production policies and tools (e.g., JIT (Just-in-Time), TOC (Theory of Constraints)) were developed. Although the goals or methods of them may be different, all of them rely on the performance evaluation of production systems and the accuracy of performance evaluation directly impacts the quality of system control and management. Motivated by this, our study is devoted to further thoroughly analyzing, understanding and evaluating the performance of production systems. Queueing systems are employed to model production systems and an important performance measure, the mean queue time, is analyzed explicitly. Furthermore, we will first clarify the stability of queueing systems in this thesis since it is a prerequisite for the study of other performance measures (e.g., mean queue time and mean queue length). Since single-server queues are elementary building blocks of complex queueing systems, for each topic, we start from the single-server queues and then move on to the queueing networks. We not only survey the different types of stability of GI/G/1 queues but also investigate the stability conditions for queueing networks. We study the stability problem through depicting the mutual blocking effect among different job classes and generalize the concept of servers in the context of queueing networks. Besides physical stations, additional general servers can exist intangibly and have a significant influence on system stability. It is shown that a queueing network is pathwise stable if and only if the effective traffic intensity of every general server does not exceed one and this provides a unified framework for the stability of both single-server queues and multiclass queueing networks. A three-moment queue time approximation for GI/G/1 queues is developed in this study and it outperforms the traditional two-moment ones as demonstrated by extensive case studies. For queueing networks, we propose a unified approximation algorithm based on the properties (i.e., affine structure) of mean queue times in queueing systems. This approach, which makes no independence assumption, is able to provide reliable approximations as shown by the theoretical error analyses and simulation studies. This work helps us to clearly understand the properties of queueing models and presents a unified framework for the performance evaluation of production systems. It can provide meaningful managerial insights and support the managers to make better decisions.Doctor of Philosophy (MAE