Math and Bus Routes

Have you ever travelled by bus around town?  I have but usually when I'm off traveling.   Of course, bus schedules and the actual times buses arrive are not always the same. Some folks did a mathematical study to see why buses often arrive in groups of two or three rather than being spaced out as planned. The official name for it is "Bus Bunching". 

This is a problem that transit companies have been trying to solve for decades. Overtime, researchers have been using mathematical models to work on understanding why it happens and how to prevent it. Unfortunately bunching causes riders to wait longer and more variable. In addition, bunching makes the system itself more unreliable and off schedule.  This makes people change to other forms of transportation.

It was discovered that the bunching occurs because bus routes are inherently unstable. At first, when buses are on time, everything works well. The bus makes it's stops, people get on and off, and the world is great but once the bus gets behind, it is almost impossible for it to catch up. In fact, once the bus is behind schedule, it gets even more behind as time passes until the second one catches up to the first one. The same thing happens when a bus starts out on time but gains time so it is early and early until it catches up with the bus ahead of it. One slows till it meets the one behind and one speeds to catch up with the one ahead.

The time between buses is referred to as bus headway so when it begins to run late, more people arrive at the stop and the time needed to load and unload passengers increase making the bus run later. On the other hand, when the bus is early, there are fewer passengers waiting so the time needed for the stop decreases and the bus travels the route quicker.  Either way, one bus ends up catching up or slowing down to another.

Proposals to solve this issue include skipping stops if no one is there or needs to get off or limit the number of people who get on the bus as ways to help make up time for late buses. A different strategy is to build additional time into the schedule referred to as slack to help allow for the variable travel times. For buses that run early, companies instruct buses to wait at stops to use up some of the extra top. Unfortunately, slack doesn't always help buses running late. Skipping or adding slack tends to reduce the speed at which people move along the routes.

Modern technology has helped with these issues.  Transit companies are now able to provide real time feedback as the buses are observed operating in real time.  Buses can be directed to skip stops, slow down, speed up, or stop a few minutes to get them back onto schedule.  Researchers have created programs containing algorithms which monitor individual buses and can provide information to dispatchers who relay the appropriate information.  

It is hoped that one day, these algorithms will get rid of the bunching issue, help buses run on time so everything happens as projected.  Let me know what you think, I'd love to hear.  Have a great day.