Operations Management: Processes and Supply Chains, 12th Edition

Solved Problem

A photographer takes passport pictures at an average rate of 20 pictures per hour. The photographer must wait until the customer smiles, so the time to take a picture is exponentially distributed. Customers arrive at a Poisson-distributed average rate of 19 customers per hour.

1. What is the utilization of the photographer?

2. How much time will the average customer spend with the photographer?

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Solution

1. The assumptions in the problem statement are consistent with a single-server model. Utilization is

   $$\rho =\frac{\lambda }{\mu }=\frac{19}{20}=0.95$$

2. The average customer time spent with the photographer is

   $$W=\frac{1}{\mu -\lambda }=\frac{1}{20-19}=1\text{ hour}$$