I think it’s similar to that, with some critical point at which the behavior makes a discontinuous change — as seen from the examples: - the gambler goes broke

I think it’s similar to that, with some critical point at which the behavior makes a discontinuous change — as seen from the examples: - the gambler goes broke - a sink carrying over 100% capacity can jam In general, if you have some kind of system where there’s a “critical threshold” and a discontinuous (or even non-linear) result for crossing it, then approaching that boundary will be increasingly dominated by that effect, as the distribution of events starts to cross into that regime. For the example of a queue, the odds of a packet failing due to delay suddenly spikes as you approach “full capacity” because the variation in packet timings causes it to “cross over” that boundary for brief periods, the closer the mean of the distribution moves to the critical threshold.