Sunday, February 28, 2010

Urinal Queueing Theory

It is difficult to explain how we develop a life-long curiosity about certain things. For me it is a curiosity about why living things behave the way they do. I can listen to someone speaking but irrespective of what they say I am more interested in why they say it the way they do. I imagine this is simply wired into our brains in the self-preservation section to detect intention, deception or threat.

We must remember that as complex as our systems are they still must obey the laws of physics. If we jump off of a building it doesn't matter what we think, rare naked physics is in control. Newton's fundamental principle of motion states that an object in motion will remain in motion until it encounters an equal force. Now if we want to get picking we could invoke the law of vectors we can account for angles, differing masses and velocities etc... but for this discussion a game of billiards exemplifies the concept of mass in motion.

Another example of this would be a drop of oil on a smooth sea surface. The molecules will expand until the molecular cohesion balances with the force of gravity. We exist in an expanding universe where entropy rules. The existence of any entity is regulated by the balance of forces but in the end everything loses it's existence the closer it all gets to equilibrium and the ultimat heat death of all things.

This applies to organisms. Even in calculus we do problems like determining the growth of bacteria in a petri dish where its growth is countered once it reaches the limits of the petri dish. This applies on even grander scales of human endeavor such as politics, business, sports, relationship and war. All of these are based on queuing behavior of organisms searching for equillibrium.

Now I did not have to go to a university to observe this behavior though I did study it decades later mathematically in computer data structures class. I worked in a manufacturing yard cutting angle iron on this big saw next to a road outside. Across the street was a run of phone lines on poles. I noticed that birds of the same species would queue up on the line evenly spaced. Usually the first bird or two landed towards the middle giving them an optimal distance on either side. The more birds the less the distance between them but the more evenly spaced they became.

Additionally I noticed another behavior as the line became crowded. If a bird of the same species tried to land in between two other birds a territorial fight would start. But if a bird of another species did the same thing they simply sat there as if that bird didn't exist.

We humans do the same thing. It can be observed on any commute as drivers defend their position and seek an optimum distance between potential threats. All of this observation has not been in vain. After many decades of diligent observation I devised my Urinal Queuing Theory. At first I thought I had stumbled on something original but later discovered I wasn't the first to notice this behavior. But every man knows it without having ever been taught it.

Suppose there is a public restroom with 5 urinals labeled A,B,C,D,E. Doesn't matter if we go right to left or left to right. A man enters a restroom and finds the following situations, what are his valid options?

1. A is occupied. Valid options: C,D,E
2. A & C are occupied. Valid options: E
3. A,B,C are occupied. Valid option: E
4. A & D are occupied. Valid options: Decision based on who appears to be finishing.
5. C & D are occupied. Valid options: A
6. C is occupied. Valid options A, E
7. 4/5 occupied. Valid options: the available urinal or an unoccupied stall.

There is an exclusion depending on what degree of familiarity exists between competitors. If a guy is out with his buds and they make a coordinated assault it doesn't matter the order.

If a man finds himself alone and stranger comes up in the adjacent stall he becomes a bit uncomfortable.

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