Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
-Use the information in Scenario B.2. What is the average number of customers in the system?

Question

Quizplus · Accepted Answer

Given that the interarrival times and service times are exponentially distributed, and the processing rates follow a Poisson distribution, this scenario can be modeled as an M/M/1 queue. The average arrival rate ($\lambda$) is 1 traveler every 25 seconds, or $60/25 = 2.4$ travelers per minute. The service rate ($\mu$) is 3 travelers per minute. The average number of customers in the system ($L$) for an M/M/1 queue is given by $L = \lambda / (\mu - \lambda)$. Substituting the given values, $L = 2.4 / (3 - 2.4) = 2.4 / 0.6 = 4$. Therefore, the average number of customers in the system is greater than 3.0 but fewer than or equal to 5.0.

Scenario B.2 Weary Travelers Arrive at Will Rogers International Airport, Pick Up