Analysis of dual tandem queues with a finite buffer capacity and non-overlapping service times and subject to breakdowns

Abstract

Tandem queues with a finite buffer capacity are the common structures embedded in practical production systems. We study the properties of tandem queues with a finite buffer capacity and non-overlapping service times subject to time-based preemptive breakdowns. Different from prior aggregation and decomposition approaches, we view a tandem queue as an integrated system and develop an innovative approach to analyze the performance of a dual tandem queue through the insight from Friedman's reduction method. We show that the system capacity of a dual tandem queue with a finite buffer and breakdowns can be less than its bottleneck-sees-initial-arrivals system due to the existence of virtual interruptions. Furthermore, the virtual interruptions depend on job arrival rates in general. Approximate models are derived using priority queues and the concept of virtual interruptions.

Keywords:

• Queueing systems
• applied probability
• manufacturing systems modeling

Funding

This research is supported in part by the Singapore MOE Academic Research Funding Tier 1 Grant M4011107.

Additional information

Notes on contributors

Kan Wu

Kan Wu is an Assistant Professor in the School of Mechanical & Aerospace Engineering at Nanyang Technological University. He received a B.S. degree from National Tsinghua University, an M.S. degree from the University of California at Berkeley, and a Ph.D. degree in Industrial and Systems Engineering from the Georgia Institute of Technology. He spent 10 years in the semiconductor industry, progressing 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 for the IIE Pritsker Doctoral Dissertation Award in 2010. His current research interests are primarily in the performance evaluation of supply chains 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. degree in Business Information Systems from the University of Macau. Her research interest is in queueing theory.