Question

At a fashion retailer, there are 3 cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It has been estimated that the arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 20 minutes. Suppose that customers form a single line. What is the average length of the line (i.e., average number of customers in the waiting line)?

Answer 1

The average length of the line (i.e., average number of customers in the waiting line) at the fashion retailer is 2 customers.

Step-by-step explanation:

In order to find the average length of the line, we need to calculate the average number of customers in the waiting line. This can be done using Little's Law, which states that the average number of customers in the system is equal to the average arrival rate multiplied by the average time spent in the system. In this case, the average arrival rate is 1 customer every 6 minutes, and the average checkout time is 12 minutes.

Therefore, the average length of the line (average number of customers in the waiting line) can be calculated as:

Average length of line = Arrival rate imes Average checkout time = 1/6 imes 12 = 2 customers

So, on average, there are 2 customers in the waiting line.