# Puzzling Adventures: How to Make Buses More Attractive Than Cars?

Image: Cloe Liane Shasha

Like many cities of the North American Sunbelt, Las Gridas is a big grid of two-way roads (three lanes for each direction), some going east-west and some north-south. Most people get around by driving their cars. But gridlock and energy costs have finally driven the normally car-loving culture to reconsider its disdain for buses.

To go from corner (x,y) to (x',y') one could imagine taking a bus first to (x',y) and then to (x',y'). An alternative is to go first to (x,y') and then to (x',y'). Of course less direct routes involving three or more buses are also possible.

It takes one time unit (about 2.5 minutes) to go from one intersection to another in a dedicated bus lane (or for a car on a traffic-free road).

As the city planner, you would like to make the bus more attractive than the car. Commuter surveys indicate that if you can make any bus trip take at most eight time units more than a traffic-free car trip, then you can convince the public to switch.

For cost and congestion reasons, you want to minimize the number of buses you purchase. You may assume the buses will arrive at each street corner on the second they should.

1. Assume that the same number of east-west and north-south roads. How can you achieve the eight-unit guarantee no matter when a commuter arrives at the bus stop? You can ignore the time to get on and off and to go from one bus to another at the same intersection. (There will be a center island at each intersection where all buses stop.)

Warm-Up:

Would it be enough to put buses four units apart on each east-west road and four units apart on each north-south road?

Solution to warm-up:
Sure. The commuter would have to wait at most four units at each bus stop. But note that this solution does not take advantage of the dedicated bus lanes or the precise arrival times.

Can you achieve the same guarantee with fewer buses?

### ABOUT THE AUTHOR(S)

Dennis's most recent puzzle book, Puzzles for Programmers and Pros, was published in May 2007 by John Wiley and Sons/Wrox

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1. 1. Hugh Jones 05:11 AM 5/1/08

I had to check my "Websters" to make sure you weren't discussing kissing. I've been reassured that busses and buses are both the correct spelling. I'm really not sure what point this article is trying to make, but I'll say one thing is certain; I used to ride buses as a kid, and if a recent experience is any indicator, the comfort level has gone down the toilet.

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2. 2. milo gudgel 02:23 PM 5/1/08

the cost pf buses and drivers pales in comparison to the cost of a car for each passenger or the roads necessary for so many cars.

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3. 3. firstrobin 05:31 PM 5/1/08

Buses are unattractive because they may be full and require you to stand. I do not prefer to stand while going from one place to another.

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4. 4. Hugh Jones 06:32 PM 5/1/08

I lived in San Francisco during the 1960s. I rode the Muni Streetcar down Market Street to work. It was the most comfortable & relaxing ride I had ever experienced in public transportation. Nowadays, buses have fiberglass seats. If they ever want to coax the general population out of their cars, they've got a long ways to go.

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5. 5. javogh 08:50 PM 5/1/08

I have been wondering if the "straight down the road" model is the most time efficient, or if a small loop, or a large loop, or some form of zig-zag might be better. I am at work, and I don't work on planning bus routes, so I have not spent any real time on it. I also thought that in a real world situation, there would be all sorts of modifying situations - population centers, dead-end streets, diagonal streets, rush periods, but it would be nice to work up a really efficient model for the basic grid. A bus arriving every 3 time units means a max wait of 7.5 min at each stop, plus the transit time, plus 2 more time units to get from the last stop to wherever you are going makes a worst case scenario of 8 time units extra - better if you happen to have a shorter wait at either or both stops, or a shorter walk to the end destination. That would mean that you have 1 bus every three city blocks on each main street. Not bad.

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6. 6. Peggylynn 10:26 AM 5/2/08

Buses would be more attractive with vidio screens showing the news or movies and with better colors inside ie seat covers and the walls and frames and with seat belts and more comfortable seats.

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7. 7. Steve D 07:24 PM 5/2/08

If I lived in this town, I'd gladly take the bus everywhere. In my town, and most others, buses don't run down every street, or at close intervals, especially on nights and weekends. That's why everybody drives.

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8. 8. JamesM 05:25 PM 5/6/08

The problem is both one of synchronization, or lack of it, and the reality that bus systems are made up of both the bus and the stops.
If the stop is a nice place to be, like a coffee shop, you don't mind waiting there, on the other hand if it is on the side of a road in the weather then it can be miscible.
A new model built on a spoked system with comfortable transit nodes may make it a lot more attractive. If you can do grocery shopping while waiting for the next connection you may be regretting the buss coming so soon.
Technology needs to be implemented to alert people who are enjoying the transition point to gather at the bus boarding point prior to the arrival of the bus.
We can see how we treat transit guests in airports, and how modern bus routs often intersect at the edge local shopping malls, but what would happen if you planned the bus system first? Then built the supporting services and infrastructure around the bus system?
The mathematical model to make grids useful is interesting. I worked on this years ago when programing for buss and para-transit routing systems. Unfortunately it is only a temporary solution and approaches the real problem from the wrong direction.

For example, after work it is common for people drive from work to home, then drive from home to the store, then back to home, then out to a movie, then back to home.
Can you build a comunity to change that pattern? Where you bus from work to a central comunity resource center where you can join up with your family, take in a movie, collect the groceries and then bus home? This model would have less commuting, both in personal driven miles and in personal time spent commuting.
We live in cities but act like we are on a farm, making trips out, several times a day, for every thing we need.
Designing bus routes to mimic car trips is a failure because cars go point to point and a bus does not. But designing communities and life styles where the bus goes where you want to go, that's the real solution. Think Disney World, but with less walking.

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