A Unified Theory of Transportation, applied to Remote Controls, Cars, Bikes and MaaS

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Why would people in one city prefer to ride bicycles more than their neighbors in the town over? Why is it that Uber is viable in some cities but not others? Can we explain the choices we make when preferring one means of transportation over another in one unified theory? Well, it turns out we can. This article starts with a simple request for the TV remote and ends with an analysis of the MAAS’s chances of replacing private ownership of cars.

A Speed-Distance-Time question

Night, indoors, Joey and Chandler’s apartment.

Joey is laid back on the recliner armchair. The TV show he was watching just ended. Joey looks around for the remote control and finally discovers it on the table, two meters away.

Joey looks at the remote, his face says deliberation. He tries to straighten out and estimates the distance between him and the remote control…

“Chandler!” He shouts, “Chandler, quick!”

Chandler enters the room, wearing a Bathrobe: “What? What happened?”

Joey: “I can’t reach the remote”

Chandler looks at the remote and back at Joey with an expression of “Are you crazy, that’s what you called me for?”

Joey returns with an expression of “I’m in THE armchair! Hey!”

Chandler looks at Joey with a “You’re out of your mind?!” look , but then his face are softens and with expression of “Yes, I guess you’ve got a point”. He goes to the table and brings the remote control to Joey.

We’ll stop here and look at the scene through my math geeks’ glasses.

On the face of it, we have a simple problem – Joey needs to get the remote. There are two possible solutions here.

  • Joey will walk 2 meters to the table and back.
  • Chandler will walk 10 meters to the room and back.

We see that in principle it is more economic that Joey will bring the remote rather than Chandler.

However, it is clear to us all that getting up from the armchair is in fact the hardest part of the task ahead, much more than doing the walking. The real model therefore needs to be similar to the one we use when calculating energy required for a movement with friction. We need to overcome the static friction – getting up from the couch; and the dynamic friction along the way – the walking part.

The energy (the hassle required) that we need to invest to get the remote is therefore: The hassle it takes to get up (overcome the static friction) + The hassle it takes to make one step, multiplied by The number of steps required.

We now can draw the two options in a simple graph and discover that there is a point of equilibrium at 20 meters. Below that point it is best for Chandler to get the remote, above it Joey should just get his ass off the couch.

Uber Vs. Private car

This is actually the way to compare traffic in different cities. Have you ever thought about why Uber manages to become a meaningful transportation option in one city and not in another? Or what would encourage commuters to take the bus or bicycle to work? Which formula should applied and what value should be maximized in order to compare different transportation alternatives? We already know it’s not just the price that is a factor here.

Let’s start for example by comparing an Uber ride to a driver using his own car for a trip of 5 miles within the city.
On first glance, both means seems to be the same. In both cases it’s a car, using the same road with the same traffic lights, the same traffic jams etc. So why are there cities where Uber is so successful and others where it has no chance?

Let’s look at the formula we have built above and claim that our passenger wants to spend a minimum amount of hassle (energy).

  • Uber hassle = Uber Static hassle + Uber dynamic hassle per mile * 5 mile
  • Private car hassle = car Static hassle + car dynamic hassle per mile * 5 mile

We’ll start with the assumption that the hassle per mile of travel is almost the same – if there’s a traffic jam, it affects both options, if the fuel price rises it affects both. So in fact the difference that determines which solution will be selected is not the trip itself, but rather the Static Hassle – the actions before and after the trip. Let’s look at these, what is the static hassle in each option:

  • Uber – you need to find a driver and wait for the car to arrive to you on point of ride origin.
  • Private car – you need to walk to the place where you have parked your car at the starting point + find parking at the end point and go on foot to your destination.

That’s it, that’s the whole ordeal. This is what determines if Uber succeeds or not in a particular city, not the ride but rather the parking.
For a person with private parking at home and at work, a private car would be the best option. For someone that doesn’t have reserved parking at work or near his residence, Uber is better.

Now let’s consider the complete model and different price (hassle) per mile. it’s easy to discover that there is a distance above which private car will be the best option even if the initial static hassle for it is high.

On a city scale, in cities like Metropolis, where there is almost no parking Uber will be successful while in cities with plenty of parking, like Smallville it can’t be a viable transportation solution.

Comparing walking, cycling and driving

Walking has no static hassle. We start and stop walking without “paying” for it. On the other hand, the dynamic hassle, the “cost” per kilometer is high. We hate walking.

Bicycles are a means of reducing the dynamic hassle of walking. Even more so when it comes to electric bicycles or scooters. Here the hassle per mile is quite low compared to walking. The static hassle is a little higher. You have to get the bike and unlock it. You should also lock it at the end of the ride

Our dynamic hassle when using a car is the lowest. We love our cars, with the air conditioning and the music we love … the static hassle however is high – we have to find parking at the end of the ride and the car is never located exactly at the origin or end point of our journey.

The result is a graph that will look like this.

I’ll explain it by asking you this: You are sitting at home, it’s 10 PM and  you have just found out that you are out of cigarettes (condoms, milk… pick your poison). The closest store is 500 meters away, say 6 minutes of walking. Will you walk there? Will you ride a bike? Would you choose to take the car?

I’ll bet your answers depends on the cities you live in. If you are in a suburb where parking is easy, most of you will take the car. Five minutes and you’re home. If however you live in Tel Aviv, most of you will walk or choose the bike because finding parking in Tel Aviv in 10 PM is a nightmare.

That is to say, the choice you made for the means of transportation was related to the Static Hassle much more than anything else.

You can see that this method allows us to compare rental of docked bikes. Dock-less bikes and privately owned bikes. The model explains why it is better for cyclists to build the bike lanes at the expense of the parking lanes rather than on the sidewalk. It can also give you an idea why the difference between bicycles and e-bikes is so dramatic.

About Hassle Distance

I want to talk a bit about the elusive concept of “hassle.” When I write here in the blog about “hassle” or “hassle distance” I am referring to the overall considerations a person is taking when a trip required to obtain a product or a service. Yes, it is very personal. I may think that taking a plan and investing in a 3 day trip to get to the Champions League finals is reasonable while others may find it a total waste. Some would send their children to a nearby school, while others would be willing to travel an hour each day for “better education”. One way or another, as a group, we can see that our considerations are not affected by price alone and not only by distance, we can still construct fundamental graphs and understand the behavior of the human swarm in the city.

There are many factors that affect our perceived hassle. My sister, for example, refrained from entering Tel Aviv with her private car before she began to use Waze. For her, the hassle of navigating in the city was so great that she preferred to use the bus despite the fact that the journey took twice as long.

Cyclists today include the risk of riding alongside cars in their perceived hassle. As the speed of the journey decreases and intersections become safer, the perceived hassle of riding bikes descends and we will see more and more of them.

Private cars Vs. Maas

The simple model I am presenting here is not revolutionary, but it allows us to focus and to better understand how to examine different means of transportation. It also enables us to examine and compare urban areas, to understand why  certain means of transport is popular in a particular area, and what needs to be done in order to encourage different ones.

Try to predict for example in which cities Mobility as a Service will be better than private ownership? What is the static and dynamic hassle of the private MaaS model versus a private ownership model?
Private MaaS is getting a service like taxi, similar to our private car and unlike public MaaS where we share the ride with others and is more like a bus.

Yep, it is very similar to Uber. MaaS can never be a better option than private cars globally, only in the denser cities.


Look at the graphs above …

How does congestion pricing affect the perceived hassle? Does it make a significant difference between a private car ride and an Uber ride or is it just a small shift in the equilibrium point (like rising fuel prices)?

How does public transportation and specifically buses look like in this graph? What is the static hassle of a bus ride? How can it be reduced? In which cities we will not be able to find buses as the preferred option in all trip ranges? What should we do to make it a preferred option?

And… oh yea, do me a favor, if you’re already standing, bring me the remote.

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2 thoughts on “A Unified Theory of Transportation, applied to Remote Controls, Cars, Bikes and MaaS”

  1. Hi Yuval, I think you have a Mistake in a couple of graphs. I explained that Uber and private car had the same dynamic hassle – in that case, on the scorned and third graphs their slope should be the same. The same applies to the last graph.

  2. Hi,

    Sorry for the late response.

    Uber and private cars do not have the same dynamic hassle. Maybe I have not explained it correctly.
    They suffer from the same traffic jams, ride the same roads, but Uber costs more.

    Uber has lower Static Hussale (in dense cities) but higher Dynamic hassle.

    Thanks, for the comment, Yuval

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