Q$1.$ Name at least one entity, three attributes $($related to the defined entity$),$ two activities $($related to the defined entity$),$ four events, and three state variables for the following systems $($put it in a Table$)$:

$1-$ KFUPM students Restaurant.

$2-$ Dental clinic.

$3-$ Airport.

Chapter $6$

Q$2.$ A two$-$runway $($one runway for landing, one runway for taking off$)$ airport is being designed for propeller$-$driven aircraft. The time to land an airplane is known to be exponentially distributed, with a mean of $1\mathrm{.}5$ minutes. If airplane arrivals are assumed to occur at random, what arrival rate can be tolerated if the average wait in the sky is not to exceed $3$ minutes?

$($Hint: arrival rate follows exponential distribution$)$

Q$3.$ The Port of Trop can service only one ship at a time. However, there is mooring space for three more ships. Trop is a favorite port of call, but, if no mooring space is available, the ships have to go to the Port of Poop. An average of seven ships arrive each week, according to a Poisson process. The Port of Trop has the capacity to handle an average of eight ships a week, with service times exponentially distributed. What is the expected number of ships waiting or in service at the Port of Trop?

Q$4.$ At Metropolis City Hall, two workers $$pull strings$($make deals$)$ every day. Strings arrive to be pulled on an average of one every $10$ minutes throughout the day. It takes an average of $15$ minutes to pull a string. Both times between arrivals and service times are exponentially distributed. A$)$ What is the probability that there are no strings to be pulled in the system at a random point in time? B$)$ What is the expected number of strings waiting to be pulled? C$)$ What is the probability that both string$-$pullers are busy? D$)$ What is the effect on performance if a third string$-$puller, working at the same speed as the first two, is added to the system$$ Solve A$,$ B and C with c$=3?$