Pseudo-cyclic policies for multi-queue single server systems

In this paper we evaluate the waiting time performance of cycle-time guided algorithms in semi-dynamic polling models. In these models knowledge of the system state is used by the server in the process of on-line determination of the visit pattern. Our main focus is on pseudo-cyclic algorithms which achieve fairness by visiting every station exactly once in each cycle. It is shown that in fully symmetric systems the performance of every pseudocyclic policy is bounded between the performance of the cycle maximization and the cycle minimization strategies. In particular, stochastic dominance is shown with regard to system workload, implying dominance of mean waiting times. In a fluid approximation model the performance ratio between the two bounding policies is derived and shown to be always between 1 and 3/4 under the gated service regime and between 1 and 1/2 under the exhaustive service regime. Under both regimes, the ratio approaches 3/4 when the number of stations grows to infinity. Simulation results suggest that a similar performance ratio holds for the general (non-symmetric) stochastic model. Further, we study strategies which are guided by the cycle maximization (minimization) criteria, but which do not constrain themselves to pseudo-cyclic orders. It is shown that depending on the switch-over parameters these more dynamic policies may perform much worse than the pseudo-cyclic schemes.