On Competitive Analysis for Polling Systems

Abstract

Polling systems have been widely studied, however most of these studies focus on polling systems with renewal processes for arrivals and random variables for service times. There is a need driven by practical applications to study polling systems with arbitrary arrivals (not restricted to time-varying or in batches) and revealed service time upon a job's arrival. To address that need, our work considers a polling system with generic setting and for the first time provides the worst case analysis for online scheduling policies in this system. We provide conditions for the existence of constant competitive ratio for this system, and also the competitive ratios for several well-studied policies such as cyclic exhaustive, gated and l -limited policies, Stochastic Largest Queue policy, One Machine policy and Gittins Index policy for polling systems. We show that any policy with (1) purely static, (2) queue-length based or (3) job-processing-time based routing discipline does not have a competitive ratio smaller than k, where k is the number of queues. Finally, a mixed strategy is provided for a practical scenario where setup time is large but bounded.