Problem $2\mathrm{.}2$

A ramp meter is being considered at an entrance to a freeway. Currently, rush hour traffic arrives at the on$-$ramp at a rate $q_1$ from time $t=0$ to time $t=t^{**}.$ After $t=t^{**},$ vehicles arrive at a $($lesser$)$ rate $q_2.$

$($a$)$ Assuming that drivers will not change their trips, draw and label an inputoutput diagram showing a metering $($i$.$e$.,$ departure$)$ rate of $(W_{\text{m}\text{a}\text{x}})\frac{W_{\text{m}\text{a}\text{x}}}{2}$