Analysis of tandem queues with finite buffer capacity

ABSTRACT

Tandem queues with finite buffer capacity commonly exist in practical applications. By viewing a tandem queue as an integrated system, an innovative approach has been developed to analyze its performance through insight from Friedman's reduction method. In our approach, the starvation at the bottleneck caused by service time randomness is modeled by interruptions. Fundamental properties of tandem queues with finite buffer capacity are examined. Without the assumptions of phase-type distributions and stochastic independence, we show that, in general, the system service rate of a tandem queue with a finite buffer capacity is equal to or smaller than its bottleneck service rate, and virtual interruptions, which are the extra idle period at the bottleneck caused by the non-bottlenecks, depend on arrival rates. Hence, the system service rate is a function of arrival rates when the buffer capacity of a tandem queue is finite. Approximations for the mean queue time of a dual tandem queue are developed using the concept of virtual interruptions.

KEYWORDS:

• Queueing theory
• tandem queue
• finite buffer capacity

Acknowledgments

The authors wish to express their deep gratitude to the referees for the careful review and valuable comments.

Funding

This research is supported in part by the GSK-Singapore Partnership for Green and Sustainable Manufacturing under Grant M406884.

Additional information

Notes on contributors

Kan Wu

Kan Wu is an Assistant Professor in the School of Mechanical & Aerospace Engineering at Nanyang Technological University (NTU). He received a B.S. degree from National Tsinghua University, M.S. degree from the University of California at Berkeley, and Ph.D. degree in industrial and systems engineering from Georgia Institute of Technology. He has 10 years of experience in the semiconductor industry, from a consultant to an IE manager. Before joining NTU, he was the CTO and founding team member of a startup company in the United States. His Ph.D. dissertation was awarded third place in the IIE Pritsker Doctoral Dissertation Award in 2010. His current research interests are primarily in the areas of queueing theory, with applications in the performance evaluation of supply chains and manufacturing systems.

Yichi Shen

Yichi Shen is currently a Ph.D. student at the School of Mechanical and Aerospace Engineering, Nanyang Technological University. He holds a B.S. degree (2011) in mathematical statistics and an M.S. degree (2014) in operations research from the Department of Mathematics, Nanjing University. His primary research interests are queueing theory, industrial engineering, and manufacturing systems.

Ning Zhao

Ning Zhao is an Assistant Professor in the Faculty of Science at Kunming University of Science and Technology. She received an M.S. degree in applied mathematics from Shanghai Jiaotong University and a Ph.D. in business information systems from the University of Macau. Her research interest is in queueing theory.