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Interarrival Times Group
June 22, 1996
- We wished to determine the distribution of service and waiting times at the counter of a local fast food restaurant.
- We also wished to see if it is possible to use service time as a predictor of total price paid and vice versa.
At a local fast food restaurant (McDonald's), our team measured the following times for each customer: time the customer entered the waiting line, time the customer began placing order, time the customer left with a complete order, and the cost of the order. All this was done very discreetly. We gathered data on Tuesday, June 18 from 11:20 AM until 12:15.
- Alternative questions: right turn on red, High St. and Hanover St. "No turn on red"
- Wendy's drive-thru-- service times not independent, too hot, risk of being apprehended for loitering
- Wendy's indoor -- prices not visible
- Weis Supermarket -- paranoid management, permission to gather data DENIED. Suggested action: "Boycott!"
- McDonald's -- no request for permission, customers blocking registers, precision of watches, one observer lingered too long observing and became a data point
Presented in table (link to dataset)
We used the time between arriving in line and arriving at the service counter as the waiting time. We used the time between arriving at the service counter and leaving with the complete order as the service time.
- Descriptive statistics of both serve and wait times
Exponential quantile plot
Comparison of serve time histogram with exponential model, using mean serve time as l
Chi-squared goodness of fit test - p-value of 0.80
Comparison of wait time histogram with exponential model - similarly good agreement, no further analysis
- Regression of price on serve time
Regression of serve time on price
- Good agreement of data with exponential model
H0 : Data follow an exponential distribution with mean l.
Null hypothesis cannot be rejected.
- Regression shows a weak (r2 = 0.315) linear relationship between price and serve time.
- Larger n
- More precise measurements
Different times of day
- Compare different restaurants
Other questions: number of customers in service area varies with time
The arrival rates were surprising -- there was a lull of approximately 10 minutes just before noon with NO customers, followed by the expected rush.
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