Part $3-$ George The Explorer $(4*0\mathrm{.}5\backslash (=2\backslash )$ points$)$

During his extensive travels, George Burdell realized that airport security would always be a frustrating and painful experience for him. After taking MGT $3501$ and learning about the role of uncertainty in creating queues, he decided to open a consulting firm that helps different firms manage their customer queues better. This is his latest assignment.

His firm has been hired by the Atlanta airport to help with the queues at the airport security. First, George collected some data. He found that passengers arrive to the security area with a rate of $\backslash (0\mathrm{.}9/\backslash$mathrm$\{$min$\}\backslash ).$ The average time of service at a security station is $2$ min as well. The CV for arrival and service times are assumed to be equal to $1.$ For simplicity assume that each passenger waits in the queue before the passengers in front of them complete the entire service process at the security station $($the service process takes $2$ min on an average$).$ Atlanta airport has given a target for George such that, on an average no more than $8$ people are waiting in queue.

Question $7.$ Without calculating the number of security stations needed, should George recommend pooled security, where all passengers queue up for the security area and proceed to the station that is available when it is their turn, or dedicated lanes where passengers queue up for particular security stations?

a$.$ Pooled queue

b$.$ Dedicated lanes

c$.$ Two options are similar Question $8.$ How many security station should George recommend for a pooled system to satisfy the target set by the client?

Question $9.$ The Atlanta airport decides to have two security stations that are dedicated in a way that split the arriving passengers equally between the two stations $($there is no pooled queue$).$ With this arrangement, what is the average number of people waiting in queue for security at the airport?

Question $10.$ After digging deeper into the data, George finds out that $\backslash (65\backslash \%\backslash )$ of the passengers at the airport are frequent flyer gold or above status members with at least one of the airlines flying in or out of Atlanta. These passengers are also very efficient travellers and require an average service time of $1\mathrm{.}5$ min $.$ The other $\backslash (35\backslash \%\backslash )$ require an average service time of $2\mathrm{.}93$ min $.$ George's suggestion is to split the two dedicated security stations $($they cannot be pooled now as all the physical construction has been done$)$ such that one station serves all the frequent flyers and all other passengers are served by the other station. What is the average total time each customer spends from waiting in queue to pass the security station? $($as before, assume all relevant CVs to be $1,$ round up to the first decimal point$)$