in Chapter 7 introduced the model of a TCP/IP router whose

Chapter 8, Problem 51

(choose chapter or problem)

Problem 64 in Chapter 7 introduced the model of a TCP/IP router whose packet-drop probability is controlled by using a random early detection (RED) algorithm (Hollot, 2001). Using Figure P8.3 as a model, a specific router queue's open-loop transfer function is

G(s) = \(\frac{7031250 L e^{-0.2 s}}{(s+0.667)(s+5)(s+50)}\)

The function \(e^{-0.2 s}\) represents delay. To apply the root locus method, the delay function must be replaced with a rational function approximation. A first-order Padé approximation can be used for this purpose. Let (e^{-s D} \approx 1-D s\). Using this approximation, plot the root locus of the system as a function of L.

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