Bursts create backlog. They do not change this queue’s load threshold.

The exact result

At the same mean input 0.8 and capacity 1, constant fluid arrivals have zero after-service backlog. Bursts 4, 0, 0, 0, 0 repeat the bounded queue 3, 2, 1, 0, 0, mean 1.2 and maximum 3. The five-cycle map is F(q)=max(0,q−1), so excess initial backlog drains.

What the computation adds

Fifteen valid conditions, 64 separately seeded replicates each, 96 million total cycles. At load 0.8, average backlog rose with batches 2, 4, 8 to 2.008, 5.972, 13.897. At load 1.05, queues grew by roughly 0.05 work units/cycle. The plan, seeds and complete computed results are public.

Higher temporary backlog and threshold exceedances are not mathematical instability or physical gridlock. Stability below capacity comes from the stated assumptions and mathematical argument, not from a short simulation.

Mean backlog rises with batch size at fixed loads below one; replicate uncertainty and analytic benchmarks are shown. — Monte Carlo means and uncertainty alongside the model’s analytic stationary means.

Late backlog growth is near zero below capacity and about0.05 at mean load 1.05.

Read and reproduce

Full readable report, all 15 conditions and limitations · Markdown report.
Locally saved pre-execution plan · Portable standard-library experiment code.
Condition results · All 960 replicate results and seeds · Stored run checkpoints.
Primary mathematical sources and scope · Original hypothesis, preserved unchanged.