In edge computing, tasks must be placed on servers of finite capacity before workloads are realized, often with only workload means and variances known. An assignment balanced on expected load can still leave a server with more fluctuations than its residual capacity can absorb. Per-server risk constraints can enforce a prescribed overload tolerance but do not distinguish the assignments that meet it by how close the riskiest server comes to the limit. We show that, for independent tasks, placement preserves a period's total variance and total residual capacity, and decides only how fluctuation, measured by standard deviation, is paired with residual capacity across servers. The risk ratio, the ratio of fluctuation to residual capacity, parameterizes a server's worst-case overload probability over all aggregate workload distributions with given mean and variance. We minimize the largest risk ratio, attained at the risk bottleneck. Risk-Bottleneck Placement (RBP) places tasks in descending order of standard deviation, each on the server with the smallest post-assignment risk ratio, and refines the assignment with relocations and swaps within a finite per-period online budget. On small instances solved exactly by enumerating every assignment, minimizing the maximum expected utilization leaves the largest risk ratio 25.66-29.19% above its exact minimum on average, even with risk-minimizing tie-breaking, and the corresponding gap for RBP is 1.77-2.64%. In trace-derived multi-period simulations at two workload pressures, RBP reduces the worst-server overload probability by 26.0% and 18.0% relative to the best baseline and remains the lowest at every tested pressure and scale.

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