New Bounty Edit (2 days remaining on the Bounty):
To point out that the only answer given at this time cannot be considered an answer, because it simply gives a hint on how to formally model the problem, which is not what I was looking for, considering I wrote it informally on purpose. Still looking forward to some analyses of this problem!
I was wondering about the following problem.
Assume the following.
- you have to find a parking spot for your car in a very busy saturday night to go in a restaurant;
- you search for this parking spot by basically going around (literally) in the hope to get a spot;
- of course, (the saturday night is really busy) other people are in the same situation as you are and they are running in circle like you are;
- the direction of the movement is only one (again, you literally go around);
- the time frame of the problem lies between 20:00 and 00:00. Finally (of course!);
- when you start your search at 20:00 there are no free parking spots.
What is the best strategy you can use to find a parking spot?
Should you stop in a place and wait until one of the cars that you can cover with your eyesight leaves?
Or is it better to move around in the hope to find a free parking spot?
I was thinking about the following few variables that I think should essentially change the nature of the problem:
Cardinality of the set of parking spots (countable vs. uncountable);
Cardinality of the set of agents involved in this situation (countable vs. uncountable);
Probability of having a car that already occupies a parking spot leaving that lot in function of time (normally distributed, uniformly distributed, etc);
Farsightedness of the agents (extreme cases: one place ahead of you, whole circle ahead of you)
Hence, a solution should be explicit about what is assumed concerning those variables.
[Notice that the in general I assume that the space where you are looking for a spot is homeomorphic to a circle]
Any feedback as always is most welcome.
PS: As you can guess, where I live it is very (very!) difficult to find a parking spot on Saturday nights...
As in the bounty text, I would like to know what are reasonable answers to this question (without considering as options using the bus, the tram, a bicycle or an helicopter...).