Question $4$

$($Total: $20$ marks$)$

All airplane passengers at the Lake Regional Airport must pass through a security

screening area before proceeding to the boarding area. The airport has three

screening stations available, and the security manager must decide how many to open

at a particular time. The service rate for processing at each screening station is $3$

passengers per minute. On Friday morning, the arrival rate is $5\mathrm{.}4$ passengers per

minute.

Assume that the processing times at each screening station follow an Exponential

distribution and arrival follows a Poisson distribution.

a$)$ Suppose two of the three screening stations are open on Friday morning. Compute

the operating characteristics for the screening facility.

b$)$ Security manager set a goal to limit the average number of passengers waiting in

line to $10$ or fewer. Will the two$-$screening station system be able to deliver the

goal?

c$)$ What is the average time required for a passenger to pass through security

screening?