Modeling the Restaurant

In the scenario, they indicate that it takes about 164 seconds, on average, to serve a customer during the busy lunch-hour period. Put yourself in the seat of your car getting food at the FS restaurant. Let's assume you are using the drive-through window and that you will pick up the food and take it home to eat with some friends.

You drive into the restaurant lot and notice there is a line of cars that has formed at the order kiosk. You wait for your turn to talk to the Customer Service Champion so that you can place your order. The menu is sitting there in clear view, so you can see exactly what you want. Soon it is your turn and you quickly place your order, learn what the bill will be, and move your car to the line at the drive-through window. While waiting, you get your money out and count out the exact change you will need. After a short time, it's your turn at the window and you give the Service Champion your money, take your drink and food, and carefully drive out of the parking lot.

Think about what happened at the restaurant. First, you waited in two lines. The first was at the order kiosk and the second at the drive-through window. Next, consider the work that the restaurant needed to complete to process your order. The Service Champion took your order and entered it in the POS system, prepared your drink, and then when the food was ready, collected your money, and delivered your drink and food. One of the Food Champions prepared your food using information from a screen that shows orders as they are entered by the Service Champion.

The total time it takes between when you arrive at the restaurant until you leave is made up of the following elements:

1. The service time for the Service Champion to process your order
2. The service time for the Food Champion to prepare your order
3. The waiting while the Service Champion and Food Champion served other customers

To model this using the queuing models in the chapter, assume that you have two totally independent service processes. The first process is the Service Champion and the second is the Food Champion. Each process has potentially a different mean service time per customer. The Service Champion must serve each customer and they arrive at a particular rate. The Food Champion prepares the individual items on the order such as a burrito, taco, chalupa, or gorditas taco. As the orders are taken, each individual item appears on a monitor telling the Food Champion what should be made next. The average time for a customer to run through the system is the sum of the average service times (time to take the order by the Service Champion and time to make the order by the Food Champion) plus the sum of the expected waiting times for the two processes. This assumes that these processes operate totally independent of each other, which might not be exactly true. But we leave that to a later discussion.

Assume that the queues in front of each process are large, meaning that there is plenty of room for cars in the line before and after the order kiosk. Also, assume there is a single Service Champion and two Food Champions each operating independently and working just on the drive-through orders. Also, assume that the arrival pattern is Poisson, customers are handled first come, first served, and the service pattern is exponential.

Given this, answer the following questions:

1. Draw a swimlane diagram of the process. There will be three 'lanes' (i.e. functions)

2. Save as a .JPEG file or take a screenshot and save as a .JPEG