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.
-Use the information in Scenario C.2.What is the average time a customer spends in line?

Question

Quizplus · Accepted Answer

First, we need to calculate the arrival rate (λ) and service rate (μ) in customers per second. 
λ = 1/25 = 0.04 customers per second 
μ = 3/60 = 0.05 customers per second

Since λ < μ, the system is stable and we can use Little's Law: 
L = λW 
where L is the average number of customers in the system and W is the average time a customer spends in the system (waiting in line and being served).

We can find L by using the formula for the average number of customers in a queuing system: 
Lq = λ^2 / (μ - λ) 
Lq = (0.04)^2 / (0.05 - 0.04) = 0.16

Since there is only one server, Lq is also equal to the average number of customers waiting in line.

To find W, we can use the formula W = L/λ: 
W = 0.16/0.04 = 4 seconds

Therefore, the average time a customer spends in line is 4 seconds or 0.07 minutes. Since this is greater than 1.0 but fewer than or equal to 2.0 minutes, the best choice is B.

Weary Travelers Arrive at Will Rogers International Airport, Pick Up