A Common Model for the Approximate Analysis of Tandem Queueing Systems With Blocking

• Published in: IEEE transactions on automatic control Vol. 61; no. 7; pp. 1780 - 1793
• Main Authors: Li, Lei, Qian, Yanling, Yang, Yongmin, Du, Kai
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aggregation; Analytical models; Approximation; Approximation methods; Automatic control; Blockage; Blocking; Cascades; Computational modeling; Decomposition; Equilibrium equations; Mathematical model; Mathematical models; Production; Production lines; Queueing analysis; Queueing theory; Tandem queueing systems; Throughput; Throughput analysis; Uniqueness; Aggregation; production lines; decomposition; tandem queueing systems; blocking; throughput analysis
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2478127

This work proposes a common model that unifies several approximate methods for the analysis of tandem queueing systems with blocking. Two abstract functions are introduced to characterize the relationship between starvation and blockage in neighboring machines. Using the functions, the equilibrium equations are determined, and a general procedure is developed to solve them. The sufficient conditions for the existence and uniqueness of a solution are obtained. More generally, the proposed model leads to the concept of a bidirectional cascade system, in which each subsystem has both forward and backward inputs and forward and backward outputs. Finally, the theory of the common model is applied to specific systems to demonstrate its applicability.