Given that throughput of pure Aloha $($Chapter $12)$ network is:

$=(1)2(1)$

Where S is the throughput of the network, N is the number of stations in the network, p is the

probability that a station has a frame to transmit during the frame transmission time. Write a

program in a language of your choice to perform the following task:

$$ Compute throughput values and plot five graphs for N$=1,2,3,4,5$ where each graph

has throughput $($S$)$ is on y$-$axis and probability $($p$)$ on x$-$axis with values of p$=\mathrm{.}01,\mathrm{.}05,\mathrm{.}1,$

$\mathrm{.}15,\mathrm{.}2,\mathrm{.}25,\mathrm{.}3,\mathrm{.}35,\mathrm{.}4,\mathrm{.}45,\mathrm{.}5,\mathrm{.}55,\mathrm{.}6,\mathrm{.}65,\mathrm{.}7,\mathrm{.}75.$

From the observation of these five graphs, answer the following questions:

i$.$ At what probability value $($p$),$ throughput is maximum in each of the five plots.

ii$.$ Explain clearly why throughput increases linearly for N$=1$ as probability $($p$)$ of

transmission increases.

iii. Explain clearly for N $=2,3,4,$ and $5,$ why maximum throughput occurs in your graphs at

a lower probability of transmission $($p$)$ values as number of stations increase from $2$ to $5$

in the network.

Deliverables

In a single PDF document, provide the following items in the given order:

$1.$ Five plots for part $($i$).$

$2.$ Explanation of part $($ii$)$

$3.$ Explanation of part $($iii$)$

$4.$ Code that you wrote for completing the assignment.