How Many Vehicles in a Continuous Convoy?

My friend Jim asked a penetrating question about Continuous Convoys: how many vehicles do you need to make all 18 stops? And how does the number grow with the number of stations? This question takes us deep into what the Transportation System of the Future will be.

2 + 16 = 18 Vehicles:  to get started let’s think through a simple case:  assume that for each station at least one passenger wants to get on and at least one wants to get off. Also assume that the number of passengers entering or exiting at any station is less than the capacity of a single vehicle.  The simplest solution is that you need two vehicles at the first station:  all the passengers going to station number 2, the next station, get in the rear vehicle and everyone else gets in the front vehicle. Then you need one vehicle at each of the other stations except the last one, for a total of 18 vehicles for 18 stations.  As the Convoy approaches a station, the rear vehicle detaches, and the vehicle that was stopped at the station accelerates and joins at the front of the Convoy, then everyone getting off at the next station goes to the rear vehicle (previously the front vehicle J), and everyone going farther on moves to the new front vehicle.  One problem with this solution is that for every station that you want to pass by you have to move forward to the vehicle that was added at the station you just passed.    

17 + 16 = 33 Vehicles:  A simple solution to the problem of having to move from one vehicle to the next is to have 17 vehicles at the first station, so as soon as you get on the convoy, you just go to the vehicle that will stop at the appropriate station (the rear vehicle for the next station, the one in front of that for the after that for station 3, and so on). This means you need 33 vehicles for 18 stations, almost twice as many as the minimum case above.  This solution is relatively inefficient because you don’t need the capacity of the 16 vehicles you collect along the way.  In the case of commuter trains going from Long Branch to New York City, this solution isn’t as inefficient as it sounds because not that many people get on at any intermediate station, but a lot of passengers get off in New York City, so you need the capacity of the vehicles you collect along the way.

Let’s relax some of the assumptions and see how the solutions change. Suppose more passengers want to get on or off at a station than one vehicle can accommodate.  That’s easy to handle, you just have more than one vehicle stop or start from that station. In the Long Branch to New York City commuter case, a lot of people get on and off at Newark, which is the station just before you go under the Hudson to get to New York City. A lot of passengers get on and off because it is both a major transportation hub and a city with jobs, etc. So the capacity of the vehicles that accumulated at the front of the Convoy coming from Long Branch is needed to drop off passengers.  And those vehicles can then carry the passengers who want to join the next Convoy.

The challenge here is how do you know how many vehicles you need for each station.  The approach today is to predict the load using previous experience based on time of day and day of the week.  I’ll describe better approaches based on things like real-time data (for example, if you haven’t left your house by 8 am, we know you won’t be on the 8:05 am train like you usually are), and plans that you enter in your calendar (you will have lots of reasons to enter your plans, including getting much better estimates of when to leave to get you to your destination on time).  An advantage of these approaches is they provide many other features that we will talk about.

We will talk about more approaches in a few more posts.

You start to see the fascinating opportunities of the Transportation System of the future, both how we can make it faster, cheaper, and easier, as well as how this will fit together with other things you want to do.  Hopefully you also see why I enjoy playing with the future, and why I want to share it with you.