[csail-related] TPP Re: GSB Tonight: Toilet Paper

[timbl at w3.org (Tim Berners-Lee)]

On 2010-10 -01, at 15:41, Andrew Jamoozy Correa wrote:

> Have you ever noticed how there are 2 rolls of toilet paper in each stall in the mass-toilets around CSAIL?  I've been thinking about it, and I think it has to do with two major things:
>     1) that if we use up one first, then the other, no stall will ever run out of paper (there's a backup!)

This depends on the people who use the stall using the Toilet Paper Protocol.
The TPP is:

	a) Always use the smallest roll (users)
	b) Replace empty rolls with new (maintenance crew)

The TPP is a great example of a protocol, as it has simple rules by which each participant has to abide, and rewards them by maintaining a common good, the invariant that no user is left without paper.  It is relatively resilient to a small proportion k of users not following it. A critical parameter is the ratio of the frequency ? of visits by maintenance compared to users.

For further study questions:

1) Find the probability of catastrophic failure of the protocol as a function of k and ?, stating your assumptions.

2) Find examples in the field where the TPP has been egregiously violated. What sort of people use those stalls? What do they study? Build a sociological model of the violations.

3) Compare and contrast the TPP with (a) the Golden Rule, (b) HTTP Caching, (c) The Highway Code (d) PGP (e) The Strategic Arms Limitation Treaty (SALT).



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