Question

The manager of a branch office of Banco Mexicali observed that during peak hours an average of 20 customers arrives per hour and that there is an average of 6 customers in the branch office at any time. How long does the average customer spend waiting in line and being​ serviced?

Answer 1

Answer:

The average customer waits in the system for 0.3 hours or 18 minutes.

Explanation:

We can work with this as a queuing theory problem.

The observation of 20 customers arriving per hour is the rate of arrival λ=20 1/hour.

The 6 customers in the branch office is L, the mean number of customers in the system (being serviced or waiting).

We need to calculate W, which is the average time in the system (waiting or being serviced).

For that we can use the Little's rule, tha can be written as

$L=\lambda*W$

In that case,

$W=L/\lambda=6/20=0.3 \,hours$

The average customer waits in the system for 0.3 hours or 18 minutes.