Thursday, December 20, 2007

Path Optimization

When you're walking from one place to another, do you path-optimize? That is, do you try to determine the quickest way to get to your destination? i'm not talking just about crossing the parking lot instead of walking along the sidewalk around the parking lot, though that might be part of it. In my life, it's a little more pervasive. Here's an example:

On most days, i bring a lunch to work with me. It's fairly easy and definitely cheaper than going out to eat. On those days when i don't, though, i usually end up going to a block where there are a bunch of food carts (usually for Thai, but next time i'm going to try the Bosnian cart). They're all relatively cheap for a good meal. The carts are, from the door of my building, 2.5 blocks north and 2 blocks west. i'm pretty much forced to go the 0.5 block north, so i don't have to make any decisions until i have 2 blocks north and 2 blocks west. For completeness (because you must know this), i also have to cross 3 streets in each direction, all one-ways.

So when i come to an intersection, should i cross north or west? The streets running east/west (that i have to cross going north) tend to have more traffic on them and do not have stop signs, whereas those running north/south (cross west) have stop signs and less traffic. Therefore it is more likely that, coming on any given intersection, it will be easier for me to cross west than north. So, if i have the opportunity, i cross north first. Let's beat a dead horse examine a hypothetical example. <needlesslyLongExplanation skipIf="itBoresYou">i leave my building and head north to the first intersection, where i find myself at the southeast corner (needing to cross both north and west). There is no traffic coming on the east/west street, so i cross north and continue northward to the next intersection (i do not cross westward even though i could). At the next intersection, there is traffic on the e/w street so i cross west. By the time i've crossed, the traffic has lessened and i can cross north again. i do so and continue northward to the next intersection. Once there, my only crossing option is to cross north, but there is traffic, so instead i turn and walk down the block westward. At each intersection i come to, i again check the traffic and cross north if possible. Once i make that northward crossing, i am on the same side of the street as the carts, so i only need to travel west until i reach them (unless i haven't been able to cross until i am already as far west as the carts, in which case i'm already there).</needlesslyLongExplanation>

i make similar decisions when i walk home from the Max station after work, but i also have a goal, which is to get as north as soon as possible because the walk is nicer there. So i'm not completely enslaved to optimization. Good thing, too, because otherwise i would have a hard time going for walks with Michelle and Gavin ("You mean we're going for a walk to nowhere in particular and will end up right back here? But we're already here! We're done!").

i also know that, in downtown Portland, if i walk briskly against the flow of (vehicular) traffic i can hit all the walk signs. It works going north/south as well as east/west, meaning all the lights are timed approximately the same. i'm not even sure why i noticed this, but it aids significantly when i need to walk more than just a few blocks downtown (by myself - i wouldn't subject someone else to my frantic pace).

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