Professor Eckstein

Simulation Variable Arrival Rates and Staffing Levels

You manage a store that operates 24 hours per day. Customers arrive at the checkout line as follows:

- 12:00am-5:00am: average of 5 per hour
- 5:00am-7:00am: average of 12 per hour
- 7:00am-10:00am: average of 20 per hour
- 10:00am-4:00pm: average of 16 per hour
- 4:00pm-9:00pm: average of 20 per hour
- 9:00pm-11:00pm: average of 13 per hour
- 11:00pm-12:00am: average of 6 per hour

A single line is shared between all cashiers. The time required for customer checkout is well modeled by a triangular distribution with a minimum value of 1 minute, a most likely value of 5 minutes, and a maximum value of 8 minutes. You currently staff cashiers in 4-hour time blocks, as follows

- 12:00am-4:00am: 1 cashier
- 4:00am-8:00am: 2 cashiers
- 8:00am-8:00pm: 3 cashiers
- 8:00pm-12:00am: 2 cashiers

Simulate 50 days of operation. What is the average time waiting in line for a cashier?