Saving the appearances: Determining a linear equation for travel time on a bus


i wanted to develop some observation based mathematics for the bus system. The purpose was to enable modeling of the bus system and evaluating proposed improvements or changes.

So I began with a "Travel time record". I generated one of these records every time I went on a bus trip. I did several versions of this form as the bus travel experience and what I could do with the data became clear.

To develop a linear travel time equation I collected these data items:

    • Start time, start location of the bus trip, measured from the door.
    • Walk time (time when I arrived at the bus stop).
    • Waiting time (time when the bus arrived, ending the wait)
    • Riding time (time when I got off the bus)
    • ... additional walk, wait and ride times for a 2 bus trip
    • Walk time (time when I walked to the destination and touched the door).
    • Destination location.
With just a few bus rides recorded, I began to see a travel time relationship emerge. For a typical bus trip: **

      • 30% of the trip time is spent walking.
      • 30% of the trip time is spent waiting.
      • 40% of the trip time is spent riding the bus.
Before even beginning a linear regression analysis, the basic characteristics of the public bus system as a network of paths, buses and walking people are beginning to emerge.

**The travel ratios presented here are subject to editing. I am hunting around in my garage for the original data. 5-28-2008

From "Carry carts" to our shared mythology

















Here are two tools for making the public bus service do more. Consider the consequences if a person could board the bus with a shopping cart.

The consequence: An entire class of domestic living activities would be possible without owning a car or hiring a taxi.

Now in thinking about why the bus systems I have studied don't carry shopping carts I finally conclude is because Americans have a mythology about individual automobiles as our primary mode of travel. The public bus system occupies a little corner of that mythology.

By mythology, I mean we have a set of shared values and ideas. For instance, here is a statement that we broadly share:

There is one mind common to all individual men. Every man is an inlet to the same and to all of the same. He that is once admitted to the right of reason is made a freeman of the whole estate. What Plato has thought, he may think ; what a saint has felt, he may feel ; what at any time has befallen any man, he can understand. Who hath access to this universal mind is a party to all that is or can be done, for this is the only and sovereign agent.

Ralph Waldo Emerson,
Essays: History, paragraph 1.

Our shared mythology is continually present and interacting with our perception of what is reasonable, what is possible in the review and development of the public bus system in the new world moving toward a low carbon emission society.


Busbook conclusion: Change bus rules of operation to allow efficent operation.


I studied the public bus system of the Los Angeles metropolitan area in 1979. Within the framework of the rules of operation extended to it, I found the Southern California Rapid Transit District was providing "transportation for those who have no other choice" in a fair manner. The District had a "service standard" to provide service and access. The District put buses on the road and did the best it could with fare income and government support.

Part of the study was I bought a 1 month bus pass and I resolved to not drive my car at any time during the month. On the last three days of the "no car" month, a neighbor offered me $100 to install a gas water heater for him. I was unemployed at the time, staying temporarily in my Dad's house, and I needed the money bad.

I had two toolboxes of plumbing tools in a storage locker 15 miles away. I had previously been in business as "Lee McKusick Water Conservation and Faucet Repair" during the 1973 water crisis. The tool boxes weighed 48 lb. and 52 lb. I decided it was not practical to walk 4 blocks, some of it up hill with this load.

So, in violation of my study discipline, I drove my 1965 Volkswagen sedan (with a bald front tire and problematic liability insurance), got my tools and made my $100.

I had just lived through a practical demonstration of the failure of the public bus system. The service rules are rigged to provide "transportation for people and their incidental baggage only."

So the conclusion of my Busbook research is: The public bus system is caught in a saddle of restrictions on what it can do with it's resources. The restrictions condemn the system to operation at a low load factor and low usability. Low load factor means the overall fraction of seats filled for the entire bus service day is below 1/3. Low usability means most people choose a car or get some other kind of ride.

The affirmation is: The mythology and legal restrictions on the public bus system need to change. The mythology is a belief that a public bus system should not be allowed to provide services offered by the private sector.

The legal restrictions that must be reduced are restrictive clauses in Federal transportation equipment bonds and suits brought by commercial transportation providers that find a bus service steals patrons from their licensed transportation service.



Advocacy: Change public bus service idea

This blog is a rewrite of my 1979 research project "Busbook - A study of the Los Angeles public bus system".

The current (year 2008) global warming and carbon dioxide crisis reminds me of my experience with the 1979 energy crisis.

My 1979 study and my 2008 experience leave me in the uncomfortable position of advocating a substantial social change in the services offered by the public bus system in America.

The public bus system should add services of carrying carts and containers of 30 to 150 pounds with the service purpose of allowing more individuals, families, and small businesses to function sometimes without the use of an automobile or truck.


The public bus systems I have studied all show a "load factor" of 33% or less. That means about 2/3 of the bus capacity is unused.

The public bus must be wedged out of it's assumption that the public bus is for "those who have no other transportation choice" and service is limited to "carry passengers and their incidental baggage only."