The lady in the taxi - a parable of metrics

Once upon a time there was a lady in a taxi. It took such a long time for the lady to get to her destination in the taxi that she went to the town hall and told the man from the council. The man from the council wanted to figure out why the taxi journey was so slow, so he placed cameras at all the traffic lights in the town to measure how many cars went past, and how quickly. The traffic light cameras would click every time a car went past the lights.

He wanted to speed up the rate of cars, so he changed the layout of the town. He figured if he introduced a one-way system the traffic flow would be more efficient. This confused the taxi drivers and they started to get lost. The taxi driver would go past a light, click, discover he couldn’t go the way he wanted, try to find a way through and find himself going back past the same light, click, realise he had been this way before, turned around and drive back through the light, click, and would still not find his way to the lady’s destination. The new one-way system was good at moving cars around - it just wasn’t very easy to navigate. And just as the taxi drivers were learning the new layout, the man from the council would try a new layout just in case.

What a lot of clicking, thought the man from the council, and what a lot of cars must be driving through my town. How efficient this is! I shall invite more cars into this town because it is so efficient at moving cars around.

So he invited more cars into the town, which of course just clogged up the streets. Every time the light would go green, a line of cars, nose-to-tail, would crawl through the lights: click, click, click! When they were past the lights, they would sit stuck in traffic. Sometimes the taxi drivers would get so fed up they would just abandon the journey and make the lady get out of the taxi. Of course she would have to pay for the journey so far. And wait for another taxi. And get in and try to resume the journey. (She often had to go a way back up the road to find another taxi.) Same lady, same journey, different taxi, back through the same lights. Click, click.

The taxi drivers realised they were losing money by spending all day in traffic jams, so they decided to have two kinds of tariff. When the taxi was moving they would charge by the mile. When the taxi was stopped, they would charge for waiting. What a clever idea!

This made the lady very upset. It is taking me longer than ever to get to my destination, she thought, and it is getting more and more expensive because it is costing me money just to sit here.

She sighed and looked out of the taxi window, and saw the cameras at the traffic lights. Then she realised what was happening. The poor man from the council thought that each time the same taxi went past the light, it was a different vehicle! He thought that when different taxis were taking the same lady to the same destination, that it was different jouneys! He probably figured that having lots of cars going through the lights meant they were travelling quickly!

Then she had an idea. I shall take a camera in the taxi she thought, and I shall show the film to the man from the council. So she took a camera in the taxi (and cleverly recorded the taxi meter at the same time). Look at this, she said to the man from the council. Ths shows you my experience as a passenger in the taxi. I move from red traffic light to red traffic light, crawling through the lights in a little batch of cars, queued up behind the next traffic light. I don’t mind paying for the mileage, but I don’t think I should have to pay just to sit waiting to go forwards. And to make matters worse, the journey to my destination is taking longer and longer!

Oh my! said the man from the council. I’ve been looking at the wrong thing all along. Instead of trying to maximise the amount of cars that go through a particular light, I should try to minimise the amount of time it takes you to get to your destination! How silly of me.

Oh, and perhaps I should pay you if you have to sit there in a taxi because my town is all backed up with traffic. At least then there would be an incentive for me to work on the most blocked-up parts of the town. Perhaps they are the only places I should be concerned with anyway, because by unblocking the most constrained parts I will probably have a better flow of traffic altogether. And perhaps when a particular street is backed up, I should stop more traffic coming in and causing traffic jams.

Thank you! said the lady. I now feel like you really are going to be able to help me to get to my destination quicker. I know it won’t happen overnight, but I am sure that over time my journeys will be faster. That’s quite alright, said the man from the council. Thanks for teaching me to look from the point of view of a passenger in the taxi, and not just to take snapshots from the different stages of the journey.

And they all lived happily ever after.

Thanks to Oliver Schreck for the idea that led to this story.