multithreading - Chance of the same worker getting X tasks out of Y total (in a pool of Z workers) -


this probability theory question, rusty can't seem wrap head around start.

i have pool of z workers. each worker has limit, x, how many tasks must perform before recycled. each new task grabbed worker @ random (1/z chance of worker grabbing it).

after y tasks has been given, odds 1 worker has reached x threshold?

i wish calculate because need perform "cleanup" periodically, , instead of picking number @ random, related number of workers , task limit (which may tweak @ later point), i'll clean-up once there's 25-30-35% chance 1 worker done for.

consider worker w. each time task enters system, there 1/z chance w grabs task. total of y tasks enter system.

y tasks, each grabbed probability 1/z: number of grabbed tasks, g_w, random variable binomial distribution.

the probability worker w has reached x threshold after y tasks p(g_w >= x).

you can approximate distribution , probability using normal distribution mean y/z , variance y(z-1)/z^2. can use function evaluates normal distribution's cumulative distribution, available in every programming language.


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