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math.PR2005★ 41 cited
On the power of two choices: Balls and bins in continuous time
Malwina J. Luczak, Colin McDiarmid
Suppose that there are n bins, and balls arrive in a Poisson process at rate λn, where λ>0 is a constant. Upon arrival, each ball chooses a fixed number d of random bins, and is pl…
math.PR2004★ 1 cited
Strong approximation for the supermarket model
Malwina J. Luczak, James Norris
We prove three strong approximation theorems for the `supermarket' or `join the shortest queue' model -- a law of large numbers, a jump process approximation and a central limit th…