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Comment by roel_v | Hacker News Reader

Alas, this post suffers from mathematician syndrome ("first, assume cows are spherical..."). Actual buffet queues can't be modeled like this; because of the physical constraints, they should be modeled as particle flows and hence take into account that one person cannot occupy the same space as another, and the overhead of routing, blocking etc.

While I agree that the 'default' buffet queue is inefficient, I don't agree with the proposed methodology of finding an improvement.

(also, I missed a literature study - there is so so so much research on this already)

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I do not think this is a fair criticism. The author is building a model which accurately captures a certain dynamic. Of course it isn't perfect, but it does get us to several proposed solutions.

Also, I think it is really unhelpful to quickly dismiss his analysis because you don't agree with his methods instead of showing why his proposed solutions fail when you add more realistic constraints to the simulation.

Fair enough, although I guess my point should be read more as a philosophical disagreement with the methodology rather than an 'attack'.

> hence take into account that one person cannot occupy the same space as another, and the overhead of routing, blocking

I'm not sure what you mean by this beyond what the author already implemented—people occupy space that can't overlap, several of the simulations break down because of blocking, and many of the simulations even display the routing paths that the agents are planning.

What I meant was that agent behaviour is linear and predictable, assumptions that don't hold when modeling actual people in the wild (it's fine for modeling e.g. factory queues and stuff, not knocking on queue theory as a field). Reasonable people can disagree on the assumptions made here though.

I get what you're saying here, and I agree—although you also mentioned specific objections above that don't seem to be valid.

I'll readily admit that attacking my stream of consciousness postings is like shooting fish in a barrel :)

:-)

I read a study done some time after the deaths at a Pearl Jam concert in Roskilde, Denmark. If I recall correctly (I can't seem to find the paper now) they posited that crowds could be simulated by way of particles in a fluid dynamics system, and that a common property of concert accidents such as Roskilde was the lack of pressure release "valves" for lack of a better word. If you only have one exit from the mosh pit, then pressure will mount at that choke point, possibly causing further accidents, and making it harder for emergency services to reach the injured parties. With multiple exits acting as release valves this problem is alleviated, and they used simulations of particles to prove this. Or something like that.

Point is, your comment on particle flows dug this reference up from somewhere deep in the back of my mind. It was a really interesting study, I'll try to find a link.

Yes there is lots of research on this, years ago I was in a project with a group (CASA) at UCL (Leeds) where this is one of their main topics of study - https://www.ucl.ac.uk/bartlett/casa/ . If you google e.g. 'agent based simulation pedestrian' you'll find 100's of papers doing this at various scales, as well as dedicated software packages to simulate for studies of shopping mall layout, sports stadium layout etc.

Years ago I entertained starting a business in this field - it was essentially exactly what you say, doing analysis for events as part of their risk assessment to see if event locations are safe under various patterns of (aggregate) visitor movement. At the time (15ish years ago?) that wasn't really done for anything but the largest events. The idea never really went anywhere but it's an interesting topic I still think about every now and then.

I've heard they model the crowds for the Hajj in Mecca this way as well.

> they posited that crowds could be simulated by way of particles in a fluid dynamics system

I sometimes have the same thought when traversing a particularly packed mall. Crowds appear to me to be a non-Newtonian fluid, because internal friction increases rapidly under pressure.

I think the problem is the other way around; it could be simplified further.

You don't need that much detail to model the simulation; really all you care about is that you have some distribution of arrival rates, and a distribution of processing time (to get a particular food), and some distribution of food preference, and it takes some x seconds to move to then next food. Perhaps with a food ordering as well.

The simulation could have been purely numerical with that (no need for pathing algorithms and whatnot, and avoid his day-long computations for such a simple simulation..), and the main variables to play with are:

1. Food preference

2. Food order

3. Number of instances of food stations

4. Processing time per food

But the author included pathing, and all his alternative-strategies then revolved around pathing, but really any path that isn't a simple line (or parallel lines) is probably non-viable, as they would quickly become a mess of people operating at random when they fail to understand whatever convoluted ruleset has been created unless its heavily enforced by the administration .

More likely than not, the best solutions probably would have been those that reduce processing time for high-preference food (a designated server), and increasing the number of food stations for those high-preference foods (eg split off deserts from the main food line to a new table, and add 4 locations to pick it up on that table)

It'd also address your concerns

>hence take into account that one person cannot occupy the same space as another

Modeled by the fact that its a queue, and there's only one person being processed at at time at any given station

>overhead of routing, blocking

Routing only really comes in two forms: Time to move from current station to the next one

1. and enter the queue

2. and skip the queue, and start moving to the next station

Blocking probably doesn't matter much; it's doubtful people will actually block each other off beyond the normal block of being processed, except when the buffet has overloaded and all the starving people swarm the tables, and all hell breaks loose; whatever physical blocking does occur will most likely have negligible impact on the system and if necessary, can be easily modeled in the time to switch stations

This would be my approach order and time/space/multiples of the busy stations. It’s crazy how often I see them load up the first station with things that aren’t necessary at that point but will fill up your hands and slow down the process for everyone that is putting food on their plates. Napkins and cutlery and prime examples. They should be at the end once your plate is loaded you can pick these up and move along.

I don’t think I agree with that. If we imagine people can pass through each other but must still obey the rules of the queue (one person at an item at a time) the overall wait time is not going to change much. When you think back to your buffets, I hope it’s not the physical difficult of maneuvering around people stalled at an item you don’t want that takes up the most time.

Queuing theory is very appropriate for this. It’s a queue.

But people don't obey the rules of abstract queues at buffets. People circle around, bump into each other so that both change directions, squeeze themselves between others, and so on. To model this, you need to (IMO) model them as a system of interacting particles with properties that vary as the 'pressure' in the system increases (e.g. the 'diameter' of the particle increases by people holding in their arms, their speed varies as people slow down when it gets more crowded, etc.

Buffets are not like bank teller queues. Or maybe I should just visit different restaurants.

However, they're not significantly less-ordered than bank teller queues; They're hardly a "crowd" of independent actors following no rules beyond physics + goal that would necessitate treatment as a particle simulation.

You're right if you wanted a really in-depth and granular model, but it's doubtful you'll find significantly improved insights versus treating it as a simple queue, and ignoring the fact that people are a little dynamic.

As far as I've seen, most buffets constitute a line with a little bit of people skipping around. But it's very close to well-ordered.

i'm the author – would love to read any existing literature on this if you can provide any pointers!

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