Heavy-traffic asymptotics of a priority polling system with threshold service policy

•The heavy-traffic behavior of a polling system with threshold policy is discussed.•The scaled queue-length of the critically loaded queue is exponentially distributed.•Approximations of queue lengths of the stable queues are provided.•The decay rates of the stable queues are the same decay rate as the classical preemptive priority queues.

In this paper, by the singular-perturbation technique, we investigate the heavy-traffic behavior of a priority polling system with three queues under threshold policy. It turns out that the scaled queue-length of the critically loaded queue is exponentially distributed, independent of that of the stable queues, which possess the same distributions as a two-class priority queue with N-policy vacation. Further, we provide an approximation of the tail queue-length distribution of the stable queues, which shows that it has the same prefactors and decay rates as the classical two-class preemptive priority queue. Stochastic simulations are taken to support the results.