The Petcock Problem

Many years ago, I worked for the small town where I grew up. My title was Street Commissioner. This is a very small town, and I was a part time employee with one helper. Basically, I was the guy what fixed things. We had a very old network of water pipes that supplied water from several wells. The water system leaked in many places. Occasionally, a small leak turned into a big leak, and something had to be done about it.

You might think that the first response to a big water leak would be to close the water valves in order to isolate the leak and prevent the loss of valuable water. Not so fast!

First of all, in an interconnected network that had been upgraded and patched by piecework for many decades, it wasn’t always possible for small localized segments to be isolated, and turning off the water for a large area would inevitably lead to discord.

Second, closing even a single valve caused pressures throughout the system to change. Any pressure change anywhere in the system had the potential to cause new failures at weak points, which would just compound the problem.

Furthermore, at some point repairs could be counterproductive and completely replacing parts of the network would be the best option. This would require time for the town council to approve the funds, and for contractors to be hired, and for the work to be scheduled and completed — all while the leaking water is causing collateral damage to the roadway and inconveniencing the affected residents with low water pressure.

Eventually the big leak had to be repaired, and the water had to be turned off somewhere before the repair could be completed. The decision about where and how to accomplish this was not a simple decision, due to the competing factors involved, and the practical realities a small town is faced with.

I call this problem the Petcock Problem. Imagine petcock valves scattered throughout a network of pipes. I call this the Petcock Problem because petcock valves typically have three positions, analogous to the notion of closing, opening, or redirecting connections on the network in order to isolate a fault.

The Petcock Problem would apply in many situations involving complex networks, such as when a tree knocks down a power line or when an internet router dies. Sometimes the best solution is to isolate the fault to the most localized part of the network possible, thereby inconveniencing the least number of people at the expense of putting the larger network at greater risk of a much larger catastrophe. Sometimes the best solution is to shut down the entire network temporarily, thereby inconveniencing everybody that relies on the network, but removing any risk of further degradation while repairs are completed. Most of the time the best solution is somewhere in between these extremes. As the network ages and faults become more commonplace, at some point the best solution is to scrap the entire network and build a new one.

This is the Petcock Problem, or “How do you stop the bleeding?”. The solution involves balancing several variables, some of which are known quantities, some of which are wild guesses, and some of which are potentially very chaotic (in that a small change in value could have an unpredictable impact on the outcome).

[Disclaimer: I’m sure that the study of network topologies has its own terms of art and well researched algorithms for describing and solving these types of problems. I’m not claiming to have some new revelation about networks here. This is just my own little custom worldview.]

In a future post I will explain how the Petcock Problem applies to something as diverse as the Vernor lawsuit.