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I doubt that this model of a queue and the processing of its items by overlaying two independent poisson processes is statistically valid (one for items arrivin

I doubt that this model of a queue and the processing of its items by overlaying two independent poisson processes is statistically valid (one for items arriving, the other for processing those items). The processing starts only after the respective item arrived in the queue - so it's not independent - and this needs to be modeled accordingly or it requires a proof that this is equivalent to the suggested overlaying approach - that wouldn't be obvious or trivial.

travisjungroth 2y ago
It might be trivial if you consider it a window of an infinite process.
- 2-3-7-43-1807 2y ago
  the infinite process only solves the problem of having a processed event happen before anything to process has entered the queue - as far as I can tell.
ocular-rockular 2y ago
As an introduction to the topic it functions very well though. It doesn't matter whether it's valid or not. In fact, I would say that diving immediately into the validity of some bullshit independence assumptions and other nonsense is where you lose most students (it definitely lost me). I think flawed examples lead to a great way of scaffolding towards the "true" nontrivial answer in a teaching setting at least... I am still exceptionally bitter at how I was taught and forced to learn stochastics and it was very much through a purely theoretical, proof driven, abstract lens with very crappy examples that were more of an afterthought... because of course the theory is all you need to make sense of it!
- 2-3-7-43-1807 2y ago
  This bullshit independence is one of the most fundamental and important concepts of probability theory and that other nonsense is also relevant cause especially with statistics it's easy to concoct a model which only seems to be correct ... but in fact isn't.
  - ocular-rockular 2y ago
    Exactly my point, hence why at least from the learning side it works well towards making something that is actually correct. What I was aiming at is that too often people teaching this stuff get lost in the weeds without any clear motivation for what is actually being taught.
carlmr 2y ago
>The processing starts only after the respective item arrived in the queue Further you can't process anything if the queue is empty. So it breaks down in this most obvious of cases.

travisjungroth 2y ago

It might be trivial if you consider it a window of an infinite process.

2-3-7-43-1807 2y ago
the infinite process only solves the problem of having a processed event happen before anything to process has entered the queue - as far as I can tell.

ocular-rockular 2y ago

As an introduction to the topic it functions very well though. It doesn't matter whether it's valid or not. In fact, I would say that diving immediately into the validity of some bullshit independence assumptions and other nonsense is where you lose most students (it definitely lost me). I think flawed examples lead to a great way of scaffolding towards the "true" nontrivial answer in a teaching setting at least... I am still exceptionally bitter at how I was taught and forced to learn stochastics and it was very much through a purely theoretical, proof driven, abstract lens with very crappy examples that were more of an afterthought... because of course the theory is all you need to make sense of it!

2-3-7-43-1807 2y ago
This bullshit independence is one of the most fundamental and important concepts of probability theory and that other nonsense is also relevant cause especially with statistics it's easy to concoct a model which only seems to be correct ... but in fact isn't.
- ocular-rockular 2y ago
  Exactly my point, hence why at least from the learning side it works well towards making something that is actually correct. What I was aiming at is that too often people teaching this stuff get lost in the weeds without any clear motivation for what is actually being taught.

carlmr 2y ago

>The processing starts only after the respective item arrived in the queue Further you can't process anything if the queue is empty. So it breaks down in this most obvious of cases.