Asymptotic optimality of threshold control in a stochastic network based on a fixed-point approximation

ABSTRACT

In Li and Yao [5], a stochastic network with simultaneous resource occupancy is studied, and a threshold control policy is proposed based on a fixed-point approximation. Here, we establish the asymptotic optimality of this control policy under fluid and diffusion scaling.

REFERENCES

• 1: Tian Bu , Don Towsley, Fixed point approximations for TCP behavior in an AQM network, Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems, p.216-225, June 2001, Cambridge, Massachusetts, United States
• 2: Chen, H. and D. D. Yao, Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization. Springer-Verlag, New York, 2001.
• 3: Gallego, G. and G. J. van Ryzin, A Multiple Product Dynamic Pricing Problem with Applications to Network Yield Management. Operations Research, 45 (1997), 24--41.
• 4: Gibbens, R. J., S. K. Sargood, C. Van Eijl, F. P. Kelly, H. Azmoodeh, R. N. Macfadyen, N. W. Macfadyen, Fixed-Point Models for the End-to-End Performance Analysis of IP Networks. 13th ITC Specialist Seminar, IP Traffic Measurement, Modeling and Management, Sept. 2000, Monterey, California.
• 5: Xuan Li , David D. Yao, Control and pricing in stochastic networks with concurrent resource occupancy, ACM SIGMETRICS Performance Evaluation Review, v.32 n.2, September 2004 [doi>10.1145/1035334.1035354]
• 6: Kalyan Talluri , Garrett Van Ryzin, An Analysis of Bid-Price Controls for Network Revenue Management, Management Science, v.44 n.11, p.1577-1593, November 1998
• 7: Talluri, K. and G. van Ryzin, The Theory and Practice of Revenue Management, Kluwer, Novell, MA, 2004.
• 8: Williamson, E. L., Airline Network Seat Control, PhD Thesis, MIT, Cambridge, MA, 1992.
• 9: Ye, H. Q. and D. D. Yao, Heavy-Traffic Optimality of a Stochastic Network under Utility-Maximizing Resource Control. Preprint, 2006.