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 , and the step size function ki(xi) = κixi, the primal algorithm (4.15) has the form (Kelly, Maulloo and Tan (1998)
where is the transmission rate at source i, κi > 0 is the control gain, is some desired value of the rate of marked packets received back at source i, and the ...