Here is the question. Suppose one bit stream arrives at a buffer. The rate of the bit stream is a periodic

function of time with period T $=1$ second. During $[0,$ T$/4],$ the rate is equal to $10$ Mbps and during $($T$/4,$

T$),$ it is equal to zero. A transmitter with rate R bps serves the buffer by sending the bits whenever

available.

$($a$)$ Draw a diagram that shows the occupancy of the buffer as a function of time, for different ranges

of values for R$.$

$($b$)$ What is the minimum value R$0$ of R so that this occupancy does not keep growing?

$($c$)$ For $10$ R $$ R$0,$ express the average delay D$($R$)$ per bit as a function of R$.$

$($d$)$ For $10$ R $$ R$0,$ express the average buffer occupancy $($over time$)$ L$($R$)$ as a function of R$.$

$($e$)$ Show that L$($R$)=$ D$($R$),$ where $=2\mathrm{.}5$ Mbps is the average arrival rate of the bits. This is an

example of the Little$$s Formula