This is a fun final project that my friend, Jordan Hoffmann, and I did for AM 205: Numerical Methods. Many thanks to Jordan for being an amazing project partner and long-term friend since high school. Project report can be viewed here.
We investigate the efficiency of the Boston Red Line during the 2:00 pm to 8:30 pm period of a weekday. Using minute-by-minute entry data, we extract the rate at which people enter 12 different stops on the MBTA Red Line. From this data, we are able to get an accurate estimate of the number of commuters hoping to take the T at any given time. Using this data, we employ two different models:  We assume that commuters instantly load onto a train with infinite capacity.  We assume that the number of train cars that can be put into use is fixed and equally divided amongst some number of trains. Furthermore, we assume that people load onto the train at a rate that decreases as the capacity of the train is reached. We then optimize a departure time table that attempts to minimize the total number of minutes spent waiting by commuters. While in model  we find that with an optimal time table we are only reduce wait times by up to 3%, in model  we are able to reduce wait times by up to 30%. We conclude that the main inefficiencies from the regularly dispatched trains that the T currently use arise not from the fact that inflow and outflow rates are not constant during the day, but rather because trains tend to enter shocks and cluster when people take time to load on the train.