Here's a basic queuing theory fact that may have behavioral/psychological implications.

If customers take on avg 10 minutes to serve and arrive randomly at a rate of 5.8 per hour, then with one bank teller working, expected wait is 5 hours. With two tellers, 3 minutes.

I learned this from…

The reason for the counterintuitve difference is that 5.8/hour means customers arrive on average 10.3 min apart, so there's little slack. If they arrived equispaced, everything would be fine. W/ random arrivals, pileups are awful.

Two speculative implications for the self-managed knowledge worker. First, if you accept tasks subject to the rule that inflow < outflow (so that your queue does not grow unboudedly), BUT you make inflow nearly EQUAL to outflow, you'll sometimes have huge delays.

The counterintuitive example works because the system behaves very badly when the expected time between arrivals is nearly equal to the completion time. If you stay away from that regime (leave 20% of time as planned slack), your delays/stress go down by WAY more than 20%.

My second implication is more speculative, but maybe more interesting, and I'll phase it as a question.

Can patterns of self-management change whether a single knowledge worker looks more like one or two bank tellers?

The problem with one bank teller is that it has to wait until a slow, problem customer is handled before calling "next."

That reminds me of how I feel when one hard or unmotivating task is getting done very slowly, blocking normally-arriving new tasks.

It seems to me that the kind of work practices advocated by Terry Tao here alter the queueing regime to look more like a multi-teller one, with several tracks where some things are guaranteed to be accomplished.…

PS/ Big thanks to @sogawasan for the pointer that led to this!

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More from @ben_golub

5 Oct
Imagine you give a prize for achievement, and you also have some values you care about promoting.

It seems like it wouldn't be optimal for you to give the prize based exclusively on achievement all the time. The prize earns reputation with the strongest winners,

which gives you latitude to promote values you care about some of the time, even when that "distorts" the allocation relative to what would be chosen by someone who did not want to promote the same values.

For the persuasion story to work, it must be that the uncontroversial measure of quality is better observed by you, the prize-giver, than the public. Only then can you shift beliefs about some winners' quality relative to the hypothetical "unbiased prize."

Read 6 tweets
1 Oct
A few observations to add, in the form of common mistakes.

A. "The audience as computer" aka "important things need to be written to memory once." In fact, nobody learns anything except the simplest things the first time. Important points should persist across a few slides.

E.g. if there is an important, longish Bellman equation, DON'T just put it up once and move on. Have it hanging around on several slides.

Blackboards talks are better because of persistence. Most speakers using slides ignore that things take time to absorb.

B. "Literature details before content."

It's amazing how often you hear, at minute 7, "but our eigenvalue condition will actually be in terms of the Laplacian matrix, rather than the usual adjacency matrix as in XYZ (2014)"
before anyone can follow this.

Read 9 tweets
17 Sep
Hard to convey my excitement at seeing an argument by @ojblanchard1 for a networks perspective on three seemingly distinct kinds of fragility.

This is something that I have worked on for a few years now, and I hope that network theory can really help.

I think it's right that there are commonalities between the fragility of

(i) production when institutions are shocked;
(ii) financial systems when asset values are shocked;
(iii) supply when shipping technology is shocked.

One perspective that network theorists have been especially interested in is that there is something qualitative about some collapses: it's not just a matter of some things working worse, but the whole system entering a crisis.

Read 16 tweets
2 Sep
A real-world high stakes game of experimentation with externalities:

Last night at 10, my car was at the front of several miles of cars on the Garden State Parkway all stuck behind a segment of road 3-5 feet underwater. You could try to drive through if you wanted,
but most people were dissuaded by the half dozen stalled/flooded cars in the water.

For about three hours, one vehicle every 15 minutes or so would go for it. Whether it succeeded depended on its type, the path it took, and the water depth.
The interesting thing is that a failed experiment (trying and having your car stall in 3 feet of water) has considerable private cost: deeply flooded cars are totaled, and the cost of even a lucky recovery in such a case is more than a few thousand dollars.
Read 8 tweets
29 Aug
Sometimes faculty complain about the stubborn Ph.D. student, who seems unaffected by advice. Talent and energy are risk factors for this disease, and, worse, is closely related to personality traits of many successful academics.

A few random thoughts.

What "bad stubborn" looks like from the advisor perspective is that you thoughtfully engage with the work, repeatedly say something (that you feel is) REALLY IMPORTANT that should affect the project, and perceive it not to be affecting the project or the student's thought.

A friend wishes they could tell students one cheat code for success. When faculty say, "This seems like a question you can answer in your project and people would really care about the answer," *actually try to do that*, or at least have serious conversations about it.

Read 11 tweets
14 Jun
An applied mathematician I know thinks it's hilarious that economists care about formal rigor so much more than, e.g., applied physicists do.

Rigor, he says, is valuable, but other inputs currently seem to have a much higher return for advancing economic theory.

For example, if our theorizing about long-run outcomes of social learning falls short of our potential, it's not because we forgot to check a subtle condition in applying the martingale convergence theorem in our model of their Bayesian behavior.

(their = the agents').

"His people" (applied mathematicians, applied physicists) would not worry about that. Instead, they would quickly work through much more "theory," but without great rigor, and use the results to refine the collective decision about how to continue.

Read 10 tweets

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