A problem of massive parallelism is considered, where $N$ processor units
are used for large-scale simulation or computation. Processor unit $i$
has its accumulated local time variable $z_{i}(t)$. At Poisson time moments
$t_{k}^{i}$, it gets a job and chooses randomly $I$ other units. If its
local time does not exceed the local times of the chosen $I$ units, then
$z_{i}(t_{k}^{i})$ is augmented by an independent random variable $\eta_{ik}$.
In the large $N$ limit we obtain a deterministic nonlinear PDE for the
density of local times. Subsequent corollaries are a travelling wave solution,
the linear time growth of the mean local time etc.

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