Scenario B.1
A single ticket taker can tear tickets and direct movie patrons to their seats at a rate of 90 per hour.Customers arrive every minute for assistance and always wait,regardless of how long the line gets.Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
-Use the information in Scenario B.1.What is the average time a customer must wait in line?
A)0.66 minute
B)1.33 minutes
C)2.00 minutes
D)3.00 minutes

Question

Quizplus · Accepted Answer

We can use Little's Law to calculate the average time a customer must wait in line. Little's Law states that the average number of customers in a system (L) is equal to their arrival rate (λ) multiplied by the average time they spend in the system (W).

L = λW

We know that the ticket taker can serve 90 customers per hour, so their service rate (μ) is 90/60 = 1.5 customers per minute. The arrival rate (λ) is also given as one customer per minute. Therefore, the utilization rate (ρ) of the ticket taker is λ/μ = 1/1.5 = 0.67.

Using the formula for the exponential distribution, we can find that the average time a customer spends in the system (W) is 1/μ = 2/3 minute.

Plugging in the values for λ and W into Little's Law, we can solve for L:

L = λW = 1 * 2/3 = 0.67

This means that on average, there is only one customer in the system at any given time. Therefore, the average time a customer must wait in line is equal to the average time they spend in the system, which is 2/3 minute or 1.33 minutes.

Scenario B.1 A Single Ticket Taker Can Tear Tickets and Direct Movie