Section $2$

Back when I was in college, McDonald's $($across from the McNeese campus$)$ only had one order queue and one window queue. For this two$-$step process, a customer arrives and waits in the order queue $($where a single server in an M$/$M$/1$ layout makes the entire order$---$of course there are more people in reality, but since it happens simultaneously, we will consider an $\frac{M}{M}\frac{?}{1}$ for simplicity$),$ then proceeds to an M$/$M$/1$ window queue $($wrapping$,$ packaging, and payment$)$ before exiting the system. The manager has provided us with an arrival rate of $=0\mathrm{.}75$ customers per minute and the following metrics:

McDonald's queuing metrics

Order queue Window queue

Queue structure one $\frac{M}{M}\frac{?}{1}$ queue one $\frac{M}{M}\frac{?}{1}$ queue

Arrival rate

$$ per minute

$$ per minute

Service time

$E[1]=1\mathrm{.}25$ minutes

$]=0\mathrm{.}8$ minutes

What is the mean service rate ${}_{\text{o}\text{r}\text{d}\text{e}\text{r}}($in customers per minute$)$ for the order queue?

a$.0\mathrm{.}5$ customers per minute

b$.0\mathrm{.}75$ customers per minute

c$.0\mathrm{.}8$ customers per minute

d$.1\mathrm{.}25$ customers per minute