Question

Passengers arriving into Pearson International Airport are to have their temperature check before leaving the airport. Any passengers with a fever are required to go into quarantine.  Three Nurses perform the check.  An average of 3.84 passengers per minute arrive at the checkpoint and wait in a single line.  They are checked by the first available nurse.  It takes on average 25 seconds to check a passenger.  Assume that inter-arrival times and service times are exponential distribute, FCFS, infinite queue, infinite population size.

 

(a)  What is the probability that a passenger will not have to wait when they arrive at the checkpoint?  

(b)  On average, how many passengers will be at the checkpoint (waiting & being scanned)?  

(c) When the passenger finally reaches the checkpoint, what is the probability it will take 20 seconds or less to check their temperature?  

(d) What is the probability there will be more than 2 passengers arriving to the checkpoint in a one min time period. 

(e) As nurses performing the check risk getting infected with the Covid-19 virus, the airport has decided to setup a separate automated self-check scanning machine. Passengers that “think” they may have the virus are asked to go to the self-check machine.  Management estimates of the 3.84 passengers/minute that arrive, 20% of them will use the self-check.  It takes an average of 30 sec (exponential dist) for a passenger to perform the self-check.  What is the probability a passenger will not have to wait when they get to the self-check? What is the expected time (seconds) a passenger will spent at the self-check (waiting in line and doing the check)?