A typical TSA agent at Piedmont Triad International Airport takes approximately 1.15 minutes to screen each passenger that arrives at the security gate. During the day, a passenger arrives at the gate on average every 1.3 minutes. Both the service rate and arrival rate follow a Poisson distribution. Based on this information and the assumption that only one screening line is open at the security gate, answer the following questions. Round calculations to at least 3 decimal places. Note: Round each calculation to at least 3 decimal places. a) What is the average number of passengers waiting in line to be screened? b) What is the average amount of time (in minutes) passengers spend waiting in line? c) What is the average amount of time (in minutes) passengers spend in the screening system? d) What is percent of the time does the typical TSA agent spend actively screening passengers? e) Throughout the day, passenger arrival rates vary with the greatest number of passengers arriving about 45 minutes before a flight is expected to depart. If during this period, approximately 3 passengers arrive every minute (Poisson distributed), what is the minimum number of lines that should be open to accommodate the additional passenger traffic if each line has only one TSA agent assigned to it? You must justify your answer using data obtained through queueing analysis and show your work.
A typical TSA agent at Piedmont Triad International Airport takes approximately 1.15 minutes to screen
each passenger that arrives at the security gate. During the day, a passenger arrives at the gate on
average every 1.3 minutes. Both the service rate and arrival rate follow a Poisson distribution. Based on
this information and the assumption that only one screening line is open at the security gate, answer the
following questions. Round calculations to at least 3 decimal places.
Note: Round each calculation to at least 3 decimal places.
a) What is the average number of passengers waiting in line to be screened?
b) What is the average amount of time (in minutes) passengers spend waiting in line?
c) What is the average amount of time (in minutes) passengers spend in the screening system?
d) What is percent of the time does the typical TSA agent spend actively screening passengers?
e) Throughout the day, passenger arrival rates vary with the greatest number of passengers arriving about 45 minutes before a flight is expected to depart. If during this period, approximately 3 passengers arrive every minute (Poisson distributed), what is the minimum number of lines that should be open to accommodate the additional passenger traffic if each line has only one TSA agent assigned to it? You must justify your answer using data obtained through queueing analysis and show your work.
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