You\'re managing the camera department of a store near Yellowstone National Park

Question

You're managing the camera department of a store near Yellowstone National Park. Customers arrive at your store at the rate of 8 per hour. You have one employee who takes an average of 6 minutes to serve each arrival. Assume this is a simple Poisson arrival, exponentially distribute service time situation a. As a casual observer, how many people woul you expect to see in the camera department (not counting your employee? How long would a customer exptec to spend in the camera department (total time)? b. What is the utilization of your employee c. What is the probability of 3 people in the camera department (not counting your employee)? d. You've brought another employee into the department who also takes and average of 6 minutes to serve each arrival. How long would a customer expect to spend in the department now?

Explanation / Answer

Arrival rate : 8 per hour

Service rate: 1 in 6 min = 10 per hour

Avg customers waiting = 8/(8-10) = 4

Waiting time = 4/8 = 0.5 hr = 30 mins

Utilisation = 8/10 = 80%

Probability = (8/10)^3 = 0.512

Wait time =

Service rate = 2 in 6 min = 20 per hour

Avg customers waiting = 8/(8-20) = 0.67

New wait time = 0.67/8 *60 = 5 mins

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