Non-convex optimization and rate control for multi-class services in the Internet

• Published in: IEEE/ACM transactions on networking Vol. 13; no. 4; pp. 827 - 840
• Main Authors: Lee, J.-W., Mazumdar, R.R., Shroff, N.B.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-08-2005; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Control algorithms; Convergence; Degradation; Delay; Elasticity; Internet; IP networks; Mechanical factors; non-concave utility function; non-convex optimization; Optimization; Quality of service; Rate control; Shape; Streaming media; Studies; Utility functions; Web and internet services
• ISSN: 1063-6692; 1558-2566
• DOI: 10.1109/TNET.2005.852876

In this paper, we investigate the problem of distributively allocating transmission data rates to users in the Internet. We allow users to have concave as well as sigmoidal utility functions as appropriate for different applications. In the literature, for simplicity, most works have dealt only with the concave utility function. However, we show that applying rate control algorithms developed for concave utility functions in a more realistic setting (with both concave and sigmoidal types of utility functions) could lead to instability and high network congestion. We show that a pricing-based mechanism that solves the dual formulation can be developed based on the theory of subdifferentials with the property that the prices "self-regulate" the users to access the resources based on the net utility. We discuss convergence issues and show that an algorithm can be developed that is efficient in the sense of achieving the global optimum when there are many users.