The Hog BBQ Joint is interested in understanding the flow of customers for diner (5-9 pm). Customers arrive in parties of 2, 3, 4, or 5 with probabilities 0.4, 0.3, 0.2, or 0.1, respectively. The time between arrivals is exponentially distributed with a mean of 1.4 minutes. Customers must arrive prior to 9 pm to be seated. The dining area has 50 tables. Each table can seat two people. For parties, with more than two customers, the tables are moved together. Each arriving group gets in line to be seated. If there are already six 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 lognormally distributed with a mean of 24 minutes and a standard deviation of 5 minutes. When customers are finished eating, they go to the cashier to pay their bill. 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 an Arena model for this situation. Simulate 30 days of operation. Make a table like the following to summarize your results.

Average Half-width

Number of customers served

Number of busy tables

Number of waiting parties

Number of parties that depart without eating

Utilization of cashier

Customer system time (in minutes)

Probability of waiting to be seated >5 minutes