After checking in$,$ you take your suitcases and join the single line to take the elevator up to the room.

Because at this time of the day, all guests carry luggage, only one guest at a time can fit in the elevator with

their suitcases. There are two elevators operating at that time $($but a single line feeding both elevators$),$ and

you overhear the expert in statistics say that, of course, guests arrive to the elevator line once every $8$

minutes on average, and that the inter$-$arrival times have an exponential distribution. The expert also

observes that each elevator takes an average of $9$ minutes to go up to the room floors and back to the lobby

and that the distribution of ride times on the elevator is exponential. Based on this information, what is the

average time $($in minutes$)$ a guest has to wait in line before being able to take an elevator?

The expert tells you the following formula to solve the problem given a multi$-$server queue: given $m$ servers, the

utilization of each server is

$\frac{p}{ma}$

and the average waiting time in queue is given by