--- Jonathan Kalbfeld <[EMAIL PROTECTED]> wrote: "So we've noticed that wherever we go it seems as if the lines seem to grow exponentially: book store, post office, bank. Is there some economic precept to describe this growth?"
There may well be; however, the problem has also been addressed from the perspective of the traffic engineer. You may benefit by searching the internet. The traffic forum, www.trafficforum.de, may be a start. It can tend to be highly technical, e.g. physics papers on granular flows and stuff like that, but it may point the way to better lay explanations. I note this because I'll probably botch the explanation as I understand it. I think it stems from the facts that arrivals are not evenly distributed and that people can be serviced only so quickly. Traffic engineers estimate the service time of a stop sign to be about five seconds per car. Therefore a stop sign can service about 60*60/5 = 720 cars per hour, or 12 cars per minute. If cars arrived in 5 second intervals there would always be a car at the sign, but no line waiting to offically stop. But cars don't arrive evenly spaced. (Arrival rates are described by a Poisson distribution, if I recall correctly.) If there are a couple minutes in a row where more than 12 cars show up, let's say 16 & 20, then at the end of the second minute there are 12 cars left waiting to be serviced. That's a full minute to clear the waiting cars. Now the cars could pile even faster if you have a couple of greater-than-twelve minutes, or it could clear (slowly) with a some of less-than-twelve minutes. I think it's clear that this can quickly get out of hand with a little bad luck (from the perspective of the poor slob at the end of the line...). Of course, you can say that my explanation doesn't account for the frequency with which things get out of hand. That's fair. I would respond by suggesting that you keep track for a while. This is a memorable experience and humans commit the "availability hueristic," that is we estimate probabilities based on how memorable an event is. Just for kicks I went to a shark-fishing java applet here: http://www.math.csusb.edu/faculty/stanton/m262/poisson_distribution/Poisson.html and ran the experiment for three sets of five trials each. The results were: 1: 14 13 15 16 10 2: 10 16 17 21 14 3: 10 6 11 10 11 Trial 1 gives a line of 8 cars after 5 minutes; trial 2 gives 18; trial 3 gives zero cars in line. So maybe my explanation is plausable. Also interesting is that your perspective is from one who's *not* in line! By definition your odds of being in a line are greater since there's more people in lines--otherwise there'd be no line. We should go drinking together...I hate waiting in line for a beer at the bar. I hope that made sense, was accurate, and not too confused, -jsh ===== "...for no one admits that he incurs an obligation to another merely because that other has done him no wrong." -Machiavelli, Discourses on Livy, Discourse 16. __________________________________________________ Do You Yahoo!? Yahoo! Finance - Get real-time stock quotes http://finance.yahoo.com
