Deterministic cyclic limit conjecture for polling systems with renewal arrivals

Let a cyclic polling system have general renewal arrival processes and deterministic switch-over times. The system is considered in the regime where the deterministic switch-over times tend to infinity. Renewal-arrival deterministic-limit conjecture. The cyclic polling system converges to a deterministic cyclic system in this limit. The conjecture proposes that the limiting behaviour previously established for Poisson arrivals remains valid for general renewal arrivals, for which corresponding results were not known at the time of the paper.