Question

Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 0.6 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)?

Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.

Answer 1

Arrival rate (A) = 100 seconds per passenger or 60/100 passengers per minute = 0.6 passengers per min

Service rate (S) = 0.6 min per passenger or 1/0.6 passengers per min = 1.67 passengers per min

Average number of passengers in line (Lq) = A^2/(S*(S-A)) = 0.6^2/(1.67*(1.67-0.6)) = 0.2015

Average waiting time = Lq/A min = Lq/A*60 sec = 0.2015/0.6*60 = 20.15 seconds

Ans = 20.15 seconds