Stability and convergence of moments for multiclass queueing networks via fluid limit models

• Published in: IEEE transactions on automatic control Vol. 40; no. 11; pp. 1889 - 1904
• Main Authors: Dai, J.G., Meyn, S.P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.1995; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Communication networks; Convergence; Exact sciences and technology; Fabrication; Manufacturing systems; Operational research and scientific management; Operational research. Management science; Performance analysis; Queuing theory. Traffic theory; Semiconductor device modeling; Solids; Stability; Steady-state; Sufficient conditions; Markov process; Queue length; Stability; Moment; Simulation; Manufacturing process; Fluid model; Communication network; Queueing network; Failures; Delay; Convergence
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/9.471210

The subject of this paper is open multiclass queueing networks, which are common models of communication networks, and complex manufacturing systems such as wafer fabrication facilities. We provide sufficient conditions for the existence of bounds on long-run average moments of the queue lengths at the various stations, and we bound the rate of convergence of the mean queue length to its steady-state value. Our work provides a solid foundation for performance analysis either by analytical methods or by simulation. These results are applied to several examples including re-entrant lines, generalized Jackson networks, and a general polling model as found in computer networks applications.< >