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The infinitely bad sneeze
Zack writes to me:
You're in an airport, about to go through the security line. You sneeze, which delays you by two seconds. It doesn't just delay you by two seconds, though; it also delays everyone waiting in line behind you. And everyone who will show up while the people currently in line haven't gone through yet. In fact, if you assume that the queue is never empty, which even at 3 in the morning is true for the major airlines, we're talking about arbitrarily large quantities of wasted time.
I believe that airport queues do eventually empty out, if only at 4 a.m., so is there any setting where this result might hold? And if so, what is your obligation to produce infinitely good outcomes, say by cutting off your nose? On the philosophical side, you might find this debate relevant. By the way, here is Zack on ranking the babies.
Posted by Tyler Cowen on April 10, 2008 at 09:49 AM in Philosophy | Permalink
Comments
The airline queues never empty out? Strange, I've occasionally found the main security line totally empty at Dulles in the middle of the day. Morning flying and late afternoon flying are very popular; if you really hate security lines, take flights that are at noon and 1 and 2 pm. Yes, that's inconvenient for work, but if you truly hate security lines more than most people, it should be worth it.
Posted by: John Thacker at Apr 10, 2008 9:57:32 AM
Isn't this basically what goes on in traffic? When there's a car wreck, and everyone drives by the wreck and pauses briefly to see the wreck, it essentially creates the problems Zack is describing. The traffic externalities are the worst form of it.
Also, several years ago, Steve Landsburg posted an interesting puzzle - why do we climb stairs but only ride escalators? And I think it was either Margolis or Liebowitz (many people responded to this, but this answer was always interesting) who said that the reason no one climbs the escalator, and instead only passively rides them is because it's a general equilibrium to passively ride. If people were to walk up the escalator, they would pause slightly as they stepped off the escalator at the top or bottom. (Even though I've been riding escalators my entire life, I still mentally think about how I have to time it just right otherwise I'm going to fall on my face when I step off the moving stairwell onto the static path before me). Because they pause slightly, it causes everyone else behind them to pause, and... general equilibrium is everyone is paused and no one climbs the escalator.
Posted by: jason voorhees at Apr 10, 2008 10:08:50 AM
Turn off . Did it work?
Posted by: jason voorhees at Apr 10, 2008 10:10:10 AM
Posted by: Jacqueline at Apr 10, 2008 10:14:11 AM
And don't miss Zack's post on monetary policy.
Posted by: Rich at Apr 10, 2008 10:20:49 AM
What if the people behind you consciously speed up their process by a fraction of a second because they feel delayed by your sneeze? The effect is nullified with just a hanful of passengers. Also, aren't we assuming that the processing of people through the security line is affected (i.e. there is no slack)? That is probably incorrect.
Posted by: HeShootsAndScores at Apr 10, 2008 10:24:24 AM
There's also the possibility that when the line gets too long, they open another checkpoint. That would limit the effect somewhat.
Posted by: Phil at Apr 10, 2008 10:26:33 AM
It annoys the hell out of me when people stop on an escalator, especially if there is a li ne of people trying to go up or down. It significanly reduces the efficiency of the escalator. For this reason, escalators should always be wide enough for people who want to walk to pass.
Posted by: MS at Apr 10, 2008 10:30:07 AM
This is a fallacy. It assumes that the guards never cause a delay that is unrelated to dealing with passengers. Thus, the 2-second sneeze only delays people up until the guard(s) cause an unrelated delay that lasts 2 seconds. So, go ahead and sneeze!
Posted by: Craig at Apr 10, 2008 10:30:40 AM
I'm distracted from thinking up possible examples by the implications of this for Terminal 5 at Heathrow...
Posted by: Tim at Apr 10, 2008 11:07:42 AM
Craig,
Why isn't the guard's delay simply added on to sneeze delay?
Posted by: josh at Apr 10, 2008 11:23:17 AM
Time value of money is relevant here. Even if it does impact infinite people, with a positive discount rate this will have a finite discounted seconds wasted.
I agree with Phil above that the number of lines is endogenous to the line length, and so even if the line did last forever the delay need not last forever.
Posted by: OneEyedMan at Apr 10, 2008 11:31:32 AM
"the reason no one climbs the escalator, and instead only passively rides them...": eh? Not in London, matey.
Posted by: dearieme at Apr 10, 2008 11:39:52 AM
You have to consider the opportunity cost. The "arbitrarily large quantities of wasted time" would have otherwise been spent waiting in the terminal.
Posted by: Steve R at Apr 10, 2008 12:44:08 PM
Craig has it right. The analysis in the post assumes that the bottleneck is always how fast the passengers are walking. But ten minutes later, everyone will wait for thirty seconds for the guards to change shifts. Without the sneeze, this delay would have been 28 seconds. So in hte end, you get back to where you would've been.
Posted by: at Apr 10, 2008 12:54:08 PM
Rather, 32 seconds (not 28 seconds).
Posted by: Steve at Apr 10, 2008 12:55:13 PM
Wouldn't discounting future time lost be accounting for the time value of the money value of time?
Posted by: Steve at Apr 10, 2008 12:57:41 PM
Well, there's an average "delay due to random events" which just decreases the inflow rate from time to time, which in turn decreases average rate of flow for the line. So, if you -don't- sneeze when you're supposed to, all rates and, consequently, all costs go up because you need a marginally larger number of inspectors, assuming each inspector inspects at a constant rate. So, it's OK to sneeze.
Posted by: MattF at Apr 10, 2008 1:22:05 PM
From an Operations Research (Queueing Theory) standpoint, it probably would not make a significant difference, as mean arrival and service times, rates and distributions are what matter in most cases, and these are often stochastic. If so then 2 seconds from a single person should not make any significant difference. Of course any calculations would require data, and I don't remember much queueing theory, but I am pretty sure that this should hold, even under the assumption that the queue length is never zero, and would definitely hold if queue length can go to zero.
Posted by: ZH at Apr 10, 2008 1:55:04 PM
What if it isn’t a sneeze? What if it is a yawn that sets off a chain of social yawns with exponential growth!!! OH MY GOD!!! The Humanity!!!
And you thought American Airlines and the FCC were the Problem.
Posted by: Chris M. at Apr 10, 2008 2:47:23 PM
FAA, sorry
Posted by: Chris M. at Apr 10, 2008 2:49:17 PM
Take a "master equation" approach to the problem, a la chemical kinetics, and you'll find that if the guard is not "johnny on the spot" with flagging people through, the sneeze gets washed out.
If the person at the head of the line's reaction time is the rate-limiting step, then yes, it is correct that the two second sneeze delay is present for every traveller until the line is clear.
Posted by: Ben Kalafut at Apr 10, 2008 2:49:32 PM
Heshootsandscores is right on. Zack's effect is bogus. People are not moving at their maximum possible speed in a queue. So at any moment after the sneeze, people will speed up until they can't go further any more.
Posted by: Link at Apr 10, 2008 4:07:31 PM
If sneezing isn't working for you, consider that guy who forgets to take off his watch and then leaves his penny collection in his pocket. Or if you think the limiting step isn't queueing, it's getting stuff through the x-ray thingy (which is probably true), consider the woman who takes 18 years shedding her boots.
One-Eyed makes a good point re time discounting, but it's still going to add up to something huge.
Posted by: Dr. Zeuss at Apr 10, 2008 5:29:43 PM
No, because the line isn't constantly moving. I've found that in most lines people tend to stand a lot. The effect of sneezing could be canceled out by just stepping up a step when the line comes to a pause again.
Posted by: Nick M. at Apr 10, 2008 5:48:12 PM
