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We study an optimal-control problem of polling systems with large switchovertimes, when a holding cost is incurred on the queues. In particular, weconsider a stochastic network with a single server that switches betweenseveral buffers (queues) according to a pre-specified order, assuming that theswitchover times between the queues are large relative to the processing timesof individual jobs. Due to its complexity, computing an optimal control forsuch a system is prohibitive, and so we instead search for an asymptoticallyoptimal control. To this end, we first solve an optimal control problem for adeterministic relaxation (namely, for a fluid model), that is represented as ahybrid dynamical system. We then "translate" the solution to that fluid problemto a binomial-exhaustive policy for the underlying stochastic system, and provethat this policy is asymptotically optimal in a large-switchover-time scalingregime, provided a certain uniform integrability (UI) condition holds. Finally,we demonstrate that the aforementioned UI condition holds in the followingcases: (i) the holding cost has (at most) linear growth, and all service timeshave finite second moments; (ii) the holding cost grows at most at a polynomialrate (of any degree), and the service-time distributions possess finite momentgenerating functions.

Asymptotic Optimality of the Binomial-Exhaustive Policy for Polling Systems with Large Switchover Times