

\subsection{\bf Example of Birth/Death Process---I}

\begin{slide}
\begin{itemize}
\item Consider a telephone exchange with an infinite number of lines
and let $E_n$ be state ``$n$ lines are busy.''

\begin{description}
\item{$\bullet$} Then we apply above formalism with 
\item{$\bullet$} $\mu_n = n\mu$ where $\mu$ is fixed ($1/\mu$ is average 
length of call), 
\item{$\bullet$} but $\lambda_n = \lambda$ independent of $n$.
\end{description}

\item One can find the steady state solution---independent of both $t$ and
initial state:
\[
P_n (t) = e^{-\lambda/\mu} \frac{\left( \frac{\lambda}{\mu}
\right)^n}{n!}
\]
as probability of $n$ lines being busy.
\end{itemize}
\end{slide}

