The linearized model of a particular network link working under TCP$/$IP and controlled

using a random early detection $($RED$)$ algorithm can be described by Figure $13$ where

$G(s)=M(s)P(s)$;$H(s)=1,$ and $($Hollot$,2001)$

$M(s)=\frac{0\mathrm{.}005L}{s+0\mathrm{.}005}$;$P(s)=\frac{140625e^{-0\mathrm{.}1s}}{(s+2\mathrm{.}67)(s+10)}$

Figure $13$ Simplified block diagram

In the TCP$/$IP network link, let $L=0\mathrm{.}8,$ but assume that the amount of delay is an

unknown variable.

e$.$ Plot the Nyquist diagram of the system for zero delay, and obtain the

phase margin.

f$.$ Find the maximum delay allowed for closed$-$loop stability.