Question

A campus deli serves 310 customers over its busy lunch period from 11:30 a.m. to 1:30 p.m. A quick count of the number of customers waiting in line and being served by the sandwich makers shows that an average of 12 customers are in process at any point in time. What is the average number of minutes that a customer spends in process?

Answer 1

Using Little's Law, and knowing that 12 customers are in process at any time and each customer arrives approximately every two minutes, we calculate that a customer spends on average 24 minutes in process at the campus deli.

Step-by-step explanation:

To calculate the average number of minutes that a customer spends in process at the campus deli, first understand the concept of Little's Law, which is a theorem in queueing theory stating that:

L = λW

Where:

• L is the long-term average number of customers in a stationary system.
• λ (lambda) is the long-term average effective arrival rate.
• W is the long-term average time a customer spends in the system.

For our scenario:

• L = 12 customers (average number in process at any time)
• λ = ⅓ customers/minute (since one customer arrives every 2 minutes)

We can rearrange the formula to solve for W (the average time spent in the system):

W = L / λ

So:

W = 12 customers / (⅓ customers/minute)

W = 12 customers * (2 minutes/customer)

W = 24 minutes

Therefore, a customer spends on average 24 minutes in process at the campus deli.