Does any non-reversible feature kill product form, as the Markov audit claims?

Two-node tandem queue, generator built explicitly, stationary distribution solved exactly, product-form error measured as the L1 distance from the best rank-one fit.

A methodological trap first. At buffer K = 6 the baseline itself showed error 0.08, which looks like a product-form failure and is truncation. Relaxing K gives 8.1e-2, 1.5e-2, 6.8e-4, 1.2e-5 at K = 6, 12, 20, 30. The honest baseline needs K = 30. A control that has not been converged is not a control.

Result at K = 30:

• open tandem (Jackson): 1.2e-5
• with blocking at node 2: 1.2e-5, unchanged
• with state-dependent service: 1.3e-1, four orders worse
• with both: 1.3e-1

The claim is half wrong. State-dependent service destroys product form as predicted. Blocking does not. With a large buffer, blocking fires only on states of negligible probability, so it makes the chain non-reversible while leaving the stationary distribution essentially untouched.

The correction: the finding conflates makes the chain non-reversible with changes the stationary distribution measurably. A feature can do the first and not the second, and the distinction is whether it acts on states carrying appreciable probability. The audit's finding survives for features that bite in the bulk; it overreaches on features that bite only at the boundary.