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On Solvability of the Rate Control Problem in Wired-cum-Wireless Networks

In: Optimization and Optimal Control

Author

Listed:
  • Won-Joo Hwang

    (Inje University)

  • Cong Loi Le

    (Inje University)

  • Rentsen Enkhbat

    (National University of Mongolia)

Abstract

Summary In a wired-cum-wireless network, the rate control problem is a difficult optimization problem. This chapter addresses the solvability of the optimization problem, where the optimization variables are both end-to-end session rates and wireless link transmission rates. The convergence of all algorithms on solving the rate control problem in wireless or wired-cum-wireless networks has been shown in [2, 5, 8, 9, 10, 11]. But existence of a unique solution in the problem has not been studied so far. Although the problem is a nonconvex optimization problem, the unique solvability of the end-to-end session rates of the problem has been shown. In addition, we also prove that there exist infinitely many corresponding values of the wireless link transmission rates which are optimal solutions of the rate control problem. Simulation results are provided to illustrate our approach.

Suggested Citation

  • Won-Joo Hwang & Cong Loi Le & Rentsen Enkhbat, 2010. "On Solvability of the Rate Control Problem in Wired-cum-Wireless Networks," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 463-478, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-89496-6_22
    DOI: 10.1007/978-0-387-89496-6_22
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