Additional assumptions:

Overall demand rate to the system is $100$ passengers per hour.

It takes $5$ minutes for a CBP officer to process a U$.$S$.$ resident in the

traditional process.

Question $2$:

Assume there are $12$ CBP officers working in the system in total. What is

the impact of doubling the usage of the new kiosks on the implied

utilization of CBP officers?On a typical day, more than a quarter of a million passengers

and crew members arrive at U$.$S$.$ airports, requiring the attention

of U$.$S$.$ Customs and Border Protection $($CBP$).$ For many years, this

process was organized as follows. Passengers would move from their

landing gates to the CBP officers. Passengers would then join one

of two lines. U$.$S$.$ citizens and permanent residents would be

welcomed by one set of officers. Visitors from other countries

would join another line leading to a separate set of officers.

Typically, waiting times were longer for visitors than for

citizens, though this could change depending on the day, and a

substantial waiting time was possible for citizens as well as

visitors. Because all visitors are fingerprinted, they take longer

to be processed by the CBP$.$ In the early $2000$s$,$ the United States

and Canada instituted the NEXUS program $($initially known as the

Trusted Traveler Program$).$ The program allows eligible travelers

who have been prescreened to bypass the lines using self$-$service

technology at a number of kiosks. At the kiosks, the passenger

answers a couple of questions, the passport and NEXUS membership

card are scanned, fingerprints are scanned and compared to

fingerprints on record, and a photo is taken. From there, most

travelers can proceed directly to the luggage area. Only a randomly

selected sample of passengers must be seen by a CBP officer. In

$2014,$ several airports, including Los Angeles $($LAX$),$ introduced an

additional technology to streamline the process at CBP$,$ creating a

third flow of travelers. LAX, together with $20$ other U$.$S$.$ airports,

allows eligible travelers to seek out a self$-$service kiosk. U$.$S$.$

citizens and permanent residents are eligible, and so are travelers

from $38$ nations that are part of the U$.$S$.$ waiver program. Similar

to NEXUS, at the kiosks, passengers answer a couple of questions,

their passport is scanned, fingerprints are scanned for non$-$U$.$S$.$

citizens, and a photo is taken. At the end of their self$-$check$-$in$,$

customers receive a printout that they then must personally present

to a CBP officer. Passengers who have taken advantage of the kiosks

require less time with the CBP officer, creating an overall

increase in capacity and hence a reduction in waiting times. For

the following calculations, assume that It takes the CBP officer

twice as long to process a visitor compared to a U$.$S$.$ citizen or

permanent resident. This is true for the traditional process, the

randomly chosen passengers in the NEXUS process, and the new kiosk

process. Eighty percent of the passengers use the traditional

process, $10$ percent use the NEXUS process, and $10$ percent use the

new kiosks. In each of these processes, the share of U$.$S$.$ citizens

and permanent residents is about $50$ percent. Passengers spend no

time with a CBP officer in the Nexus process except when they are

randomly sampled for an inspection. In that case, they spend the

same amount of time with the CBP officer as in the traditional

process. Five percent of passengers are randomly chosen for

inspection $($independent of being visitors or U$.$S$.$ residents$).$

Compared to the traditional process, passengers spend $50$ percent

less time when using the new kiosks $($though U$.$S$.$ residents still

only spend half the time with the CBP compared to visitors$).$

Question $1$: Evaluate the impact of increasing the usage of the new

kiosks. To do this, first draw a process flow diagram that combines

the three different flows $($traditional process, NEXUS program, new

kiosks$).$ Then, compute by what percentage the workload of the CBP

officers would decrease if the usage of the new kiosks doubled

$($from the current $80$ percent, $10$ percent, and $10$ percent for

traditional, NEXUS, and new kiosks to $70$ percent, $10$ percent, and

$20$ percent$).$