Question

A ticket line for the New York Yankees game: At one checking point, there are 100 fans on average in line ahead of you to buy tickets, on average 5 fans will get the tickets and leave the line in one minute. What is the average time that a ticket buyer can expect to wait in line when he/she reaches this checking point?

Solve using Little's Law (Inventory = Throughput rate x Flow time)
List each step out clearly.

Answer 1

Little's Law can be used to calculate the average time a ticket buyer can expect to wait in line at a checking point. In this case, the average time is 20 minutes.

Step-by-step explanation:

Little's Law is a formula used to calculate the average time a ticket buyer can expect to wait in line at a checking point. According to Little's Law, the average inventory or number of customers in the system at a given time is equal to the average throughput rate (number of customers served per unit of time) multiplied by the average flow time (time spent in the system by a customer).

In this case, the average number of fans in line ahead of you is 100, and on average, 5 fans are served and leave the line in one minute. Therefore, the average throughput rate is 5 fans per minute.

To calculate the average flow time, you need to divide the average inventory by the average throughput rate. So, the average flow time is 100/5 = 20 minutes.

Therefore, the average time that a ticket buyer can expect to wait in line when they reach this checking point is 20 minutes.