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Comment by spapas82 | Hacker News Reader

I remember queueing theory from the "Automatic telephony" class we had at the university. It was used to solve the problem of how many operators you needed on your call center to have a waiting time of s seconds considering an average call time of s1 seconds and a poisson distribution of incoming calls with a rate r1. Of course queueing theory had various other applications (like the buffers of routers) but the call center one is the most interesting for me.

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> a poisson distribution of incoming calls with a rate r1

This is what always confuses me about queueing theory. The analysis is valid assuming a particular distribution, but the justification given for using that distribution was very weak, if at all given.

So how is the choice of a distribution justified?

I think that a poisson distribution is the easiest for the problem to be solved. It may not be the most accurate incoming distribution for all cases but it should be good enough for most cases.

Poisson is the limit distribution you converge to when n people each flip a coin with probability p to do something, when you drive n to infinity but keep np constant.

It is well justified and models the world reasonably well. The parameter changes - e.g. when there’s a service outage, the proportion of people likely to call and report it, does change; but the number of calls per unit time within e.g. the first hour, indeed is Poisson with a higher-than-usual parameter.

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