Consider a single server process with a buffer. Possible customer arrivals are $0,1,$ and $2$

per minute with equal probability. The average service time is half minute $(0\mathrm{.}5$ minute$)$ per

customer. The average number of customers being served in a minute is:

A$.\frac{1}{4}$

B$.1/2$

C$.1$

D$.2$

E$.$ None of above

Facing with unpredictable arrival rates, what can we do to increase throughput

A$.$ Add buffer

B$.$ Reduce variability

C$.$ Add capacity

D$.$ A and C only

E$.$ A$,$ B and C

Which of the following$($s$)$ about PK formula is $($are$)$ true?

I. It shows that higher utilization implies higher queue length

II$.$ We can relate it to OM triangle

III. It shows that without variability the queue length will be zero

A$.$ I

B$.$ II

C$.$ I and II

D$.$ II and III

E$.$ I, II and III

In a G$/$G$/1$ queue, the average arrival rate is $10$ customers per hour and the standard

deviation of inter$-$arrival times is $12$ minutes. The service time is $3$ minutes per customer

and its standard deviation is zero. The average queue length is:

$($Hint: $I_q=\frac{{}^2}{1-}\frac{C_a^2+C_s^2}{2})$

A$.\frac{1}{3}$

B$.\frac{1}{2}$

C$.1$

D$.2$

E$.$ None of the above