A local diner is interested in understanding the flow of customers (5 pm to 9 pm). Customers arrive in parties of 1 or 2 with probabilities 0.4, and 0.6, respectively. The time between arrivals is exponentially distributed with a mean of 2.4 minutes. Customers must arrive prior to 9 pm in order to be seated. The dining area has 50 tables. Each table can seat at most 2 people. Each arriving group gets in line to be seated. If there are already 6 parties in line, the arriving group will leave and go to another restaurant.
The time that it takes to be served is triangularly distributed with parameters (14, 19, 24) in minutes. The time that it takes to eat is normally distributed with a mean of 26 minutes and a standard deviation of 8 minutes. When customers are finished eating, they go to the cashier to pay their bills. The time that it takes the cashier to process the customers is gamma distributed with a mean of 1.5 minutes and a standard deviation of 0.5 minutes.
Develop a model for this situation. Simulate 30 days of operation. Make a table like the following to summarize your results.
Number of customers served
Number of waiting parties
Number of busy tables