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This problem refers to section 3.3 where we applied the fluid flow approximation to a multiplexer carrying voice traffic.
Consider the case of $N=2$ voice sources, with ${1 \over \alpha}=1 sec$ and ${1 \over \lambda}=1.5 sec$ .

\begin{enumerate}
\item Find $C,J_0$ and $J_u$ for two cases $\rho=0.5, 0.75$ and $\rho=0.85$. Indicate all three values on state diagram as in figure 3-5 of the textbook.
\item Find and compare the eigenvalues of equation 3-18 for the two cases in the previous case $1$. Show that in both cases one eigenvalue is always 0 as expected!
\item Find the eigenvectors for all cases.
\item Derive the cdf $F(x)=Prob(X \leq x))$ for the queuesize. Compute the $G(x)=Prob(X > x))$. Also approximate the $G(x)$ using the dominant eigenvalue and verify that this eigenvalue is given by equation 3-42 in the text. Plot $G(x)$ and its approximations as a function of $x$ for the different loads $\rho$.
\end{enumerate}

You may wish to use Matlab for your calculations. Feel free to collaborate. Your report should include your code with enough documentation.



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