I do not know if you are interested in such a topic, but I've been fascinated in traveling from location A to location B as fast as I can, looking for a best "route" in the sense of costing me the least time, upon my study in the highly congested New York City.

As my personal preference of taking a subway to commute between home and school, this article would focus on traveling by New York subway while I will also talk a little about traveling using other means or combining lots of different means.

To state the problem and help you understand the situation, the start point is the Queens Plaza station and the end point is 116 St - Columbia University station. You want to find out a subway route that can take you to the destination with least time when the scenario becomes ideal. Also, when comparing with other routes, though the situation each time may not be that ideal, this route still win over and have a high expectation of saving you great amount of time.

Map apps like Apple Map and Google Map can give you guidance on such a move. Their suggestions are to be compared in real situation. My focus hence would be on exploiting the potential of these routes by saving my steps and catching the next connecting subway since there's no single subway service that can take me directly to school. As you've already found it out, the essence of the problem is how to travel efficiently in subway stations.

When visualizing the whole space time scenario, you may find the solution to the problem is locating the stairs of the next station so that you can go to the corresponding spot on the platform of this station to enter the train through the "right" door. Try to imagine it that you jumped into the train while leaving other passenger behind, who were still walking/running from a door of the last train far away from the stairs to change the platform. Advancing the work you are to do can greatly increase the chance of catching the connecting subway.

Up to now, the whole problem has been simplified to connecting the "nodes" in each "station" with shortest "line." Or you can think it this way: find a way that from the starting node to the ending node that costs you the least energy if you compare the length to weight of the edge (line). I believe you can handle such a task without much pain. The rest work is your speed of move and luck considering the subway service is not that "stable".

To sum these things up, the total cost of time is the train moving time, your walk time, and wait time. When comparing one route to another route, you hence should basically consider these stuff. If you want to be more "nerdy," try to consider the time of day to travel, the shifts of each train, and the possibility of delays. Wrangling with these additional considerations can give you scores of each route statistically. I do not want to spend too much time on this topic now, but that can be interesting to investigate in the future.

Another candidate route only requires you to change train once. However, applying the considerations I mentioned above to it, this route is more likely to ask you to walk more and cost you more time.

If you read to here, you may be interested in the topic of looking for a best route. Lots of scientists and engineers are carrying out their research in this matter. As I mentioned earlier, there are train delays. In addition, there are congestions in the city. An interesting extention of today's thoughts would be combining other means of travel. For example, when the train delays or canceled, what are some remedies? Can I go to get a Citi bike to finish the rest of my travel? Or, it is better to take a taxi? Such an extention revolves city congestion analysis which should be a live analysis that can analyze real data in real time.

I must say this is a very worthy topic to research. I would keep it moving on but today's article ends here. Thank you for reading my random thoughts.