Question $2(24$ points$)$: Multiple choice question, $1$ point each.

A call center has $6$ phone lines and $3$ castomer service represeutatives. Suppose that culls artive at

the center according to a Poisson process with rate of $15$ calls per hour. The time to process each call is

exponential with a mean of $10$ minutes. If all the service representatives are busy, in arriving cunturat

is pliced on hield, but ties up one of the phone lines. If afl of the phone lines are tied up$,$ the calstimice

eceives a busy signal, and the call is lost.

Whit is the Kendall's notation for the above system?

A$.\frac{M}{G}\frac{?}{?}\frac{3}{o}\frac{?}{6}$

B$.\frac{M}{M}\frac{?}{?}\frac{3}{a}\frac{c}{6}$

C$.\frac{M}{M}\frac{?}{?}\frac{3}{6}\frac{?}{2}$

D$.\frac{M}{M}\frac{?}{?}\frac{3}{s}\frac{?}{o}$

E$.$ None of the above

Arrivals to an airport are all directed to the same runway. At a certain time of the day, these arrivals

form a Poisson process with a rate of $30$ aircraft per hour. The time to land an aircraft is a constant $125$

seconds with variance of zero. What is the steady state average time the airplane spends in the air

waiting to land?

A$.13\mathrm{.}02$ minutes

B$.23\mathrm{.}95$ minutes

C$.26\mathrm{.}041$ minutes

D$.15\mathrm{.}69$ minutes

E$.$ None of the above

A hospital has two doctors and a single waiting line $(\frac{M}{M}\frac{?}{2}$ queuing system$).$ If the average service

time per patient is $20$ minutes and the arrival rate is $15$ patients per hour, what is the utilization for each

doctor?

A$.50\%$

B$.250\%$

C$.125\%$

D$.75\%$

E$.100\%$

The mean arrival rate to a coffee shop is $10$ customers per hour. If one server needs on average $5$

minutes to serve a customer, arrival and service follow exponential distribution. Is one server enough to

make the average waiting time in the queue less than $27$ minutes?

A$.$ No$,2$ servers are needed.

B$.$ No$,$ more than $2$ servers are needed.

C$.$ Yes, one server is enough.

D$.$ The number of servers is not affecting the waiting time in the queue.

E$.$ More information is required to answer.