[HN Gopher] Derivation and Intuition behind Poisson distribution
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       Derivation and Intuition behind Poisson distribution
        
       Author : sebg
       Score  : 32 points
       Date   : 2025-05-01 21:11 UTC (1 days ago)
        
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       | meatmanek wrote:
       | Poisson distributions are sort of like the normal distribution
       | for queuing theory for two main reasons:
       | 
       | 1. They're often a pretty good approximation for how web requests
       | (or whatever task your queuing system deals with) arrive into
       | your system, as long as your traffic is predominantly driven by
       | many users who each act independently. (If your traffic is mostly
       | coming from a bot scraping your site that sends exactly N
       | requests per second, or holds exactly K connections open at a
       | time, the Poisson distribution won't hold.) Sort of like how the
       | normal distribution shows up any time you sum up enough random
       | variables (central limit theorem), the Poisson arrival process
       | shows up whenever you superimpose enough uncorrelated arrival
       | processes together:
       | https://en.wikipedia.org/wiki/Palm%E2%80%93Khintchine_theore...
       | 
       | 2. They make the math tractable -- you can come up with closed-
       | form solutions for e.g. the probability distribution of the
       | number of users in the system, the average waiting time, average
       | number of users queuing, etc:
       | https://en.wikipedia.org/wiki/M/M/c_queue#Stationary_analysi...
       | https://en.wikipedia.org/wiki/Erlang_(unit)#Erlang_B_formula
        
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