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Frequency-Domain Analysis and Design of Distributed Control Systems by Yu-Ping Tian

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Chapter 5

Congestion Control: Stability and Scalability

The net of Heaven has large meshes but yet it lets nothing through.

—Lao Dan (580–500 BC), Tao Te Ching

A distributed congestion control system with diverse propagation delays enjoys symmetry property in the frequency domain. This chapter applies the stability and scalability results presented in Chapter 2 and Chapter 3 to derive scalable stability criteria for the congestion control algorithms introduced in Chapter 4. The mechanism of time-delayed feedback control in the stabilization of distributed congestion control systems is also investigated.

5.1 Stability of the Primal Algorithm

5.1.1 Johari–Tan Conjecture

With the choice of utility function img, and the step size function ki(xi) = κixi, the primal algorithm (4.15) has the form (Kelly, Maulloo and Tan (1998)

(5.1) equation

(5.2) equation

where img is the transmission rate at source i, κi > 0 is the control gain, img is some desired value of the rate of marked packets received back at source i, and the ...

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