Based on the model created on Week 3 Assignment, add the schedules, wights and processes that are closely related to your model. If it is a real scenario, or the most probably values, if it is a generic process.

Original Model

The original model was a representation of a concession stand in a movie theater. In the original version of the model, each worker at the concession stand had their own line, similar to a grocery store checkouts, which lead to unbalanced lines and inconsistent wait times for guests. The model was revised to have a single concession line with customers going to the first available concession worker.

Revised Concession Model
Revised Concession Model

Randomized Arrivals

In the original model, customers arrived with a random exponential function with mean of 60 customers per hour. In a real movie theater, movie start times are staggered based on movie length and the time needed to turn over the theater for the next showing. This staggering of start times will lead to non-uniform arrival times.

New Model

I looked up the show times of my local theater and discovered that there are 11 different movies currently showing with 34 different start times between 3:00pm and midnight. For each movie, I estimated the number of customers that could be expected to attend based on the box office numbers. I decided that movie-goers would arrive to the theater up to an hour before the start of the movie. I constructed a table to arrival rates based on these details.

Movie Start Times
Movie Start Times

I used this data to construct a rate table with 15 minute intervals for customers arriving to the theater.

Arrival Rate Table
Arrival Rate Table

The important part of the arrival table is that there are no customers expected to arrive in the last 90 minutes of the night. In the original model, customers were arriving up until close, which doesn’t make sense.

Updated Model

In the updated model, source rates were updated to use the new rate table. We also added a ticket stand where customers would purchase tickets to the movie. After the ticket booth, customers can choose to visit the concession stand, or go directly to the movie.

Updated Model
Updated Model

Comparisons

There were a number of changes that make comparing the results of the models. The most significant difference is in the substantial increase to arrival rates. In the initial model, 60 customers per hour was fixed. With the new arrival rate table, some intervals have 4 times the number of customers, and there are sustained periods exceeding 120 per hour. I don’t really know if these numbers are realistic, but it seems a theater with 12 screens, would see rates like these.

To keep waiting times down to something customers would allow, I set the number of employees in the ticket booth to 3 and the number of workers in the concession stand to 12. With these values, the model ran for 9 hours and saw 800 customers, 715 of which visited the concession stand.