$5.$ Consider $8$ nodes that use a token passing multiple access protocol to access a shared broadcast channel. The transmission rate of the channel is $16$ Mbps$.$ When a node holds the token, it is allowed to send up to $30$ Kbits. After a node has finished sending, it takes $0\mathrm{.}2$ms to pass the token to the next node. $(16$ pts$)$

$($a$)$ What is the maximum throughput that can be achieved?

$($b$)$ What is the throughput achieved if only a single node has data to send $($but that node always has something to send$)?$

$($c$)$ What is the maximum $($best$-$case$)$ throughput achieved if TDMA is used instead, and each node is statically allocated an equal share of the channel capacity?

$($d$)$ What is the throughput achieved with TDMA $($with each node statically allocated an equal share of the channel capacity$)$ if only a single node has data to send $($but that node always has something to send$)?$