Polling Models with Unequal Service Rates under Limited Service Policies—Sharp Asymptotics

Abstract

We derive asymptotic expressions for the distribution of the total queue length in a polling model with two classes of customers and unequal service rates. The server employs a scheduling policy that alternately visits each queue, with the maximum number served in each visit potentially being different for each queue. We provide sufficient conditions for the behaviour to lie in one of two regimes, depending on the system parameters. The first regime, called codominant, has both queues tending to grow as the total system size grows. The single-class dominant regime has only one queue tending to grow as the total system size grows. Finally, we present numerical results that demonstrate that the developed conditions are only sufficient and comment on the implications of this observation.

Keywords:

• Polling systems
• tail asymptotics