$17\mathrm{.}7-4.$ Marsha operates an expresso stand. Customers arrive ac$-$

cording to a Poisson process at a mean rate of $30$ per hour. The time

needed by Marsha to serve a customer has an exponential distribu$-$

tion with a mean of $75$ seconds.

$($a$)$ Use the M$/$G$/1$ model to find L$,$ Lq$,$ W$,$ and Wq$.$

$($b$)$ Suppose Marsha is replaced by an expresso vending machine

that requires exactly $75$ seconds for each customer to operate.

Find L$,$ Lq$,$ W$,$ and Wq$.$

$($c$)$ What is the ratio of Lq in part $($b$)$ to Lq in part $($a$)?$

T $($d$)$ Use trial and error with the Excel template for the M$/$G$/1$

model to see approximately how much Marsha would need

to reduce her expected service time to achieve the same Lq as

with the expresso vending machine.