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

Jang Won Lee, Ravi R. Mazumdar, Ness B. Shroff

Research output: Contribution to journalArticlepeer-review

121 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)827-840
Number of pages14
JournalIEEE/ACM Transactions on Networking
Issue number4
Publication statusPublished - 2005 Aug

Bibliographical note

Funding Information:
Manuscript received February 9, 2004; revised July 25, 2004; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor S. Low. This work was supported in part by the National Science Foundation under NSF Grants ANI-0073359, ANI-9805441, and ANI-0207728. This research was conducted when J.-W. Lee and R. R. Mazumdar were at Purdue University.

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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