Analysis of adaptive queueing policies via adiabatic approach

We introduce an adiabatic framework for studying adaptive queueing policies. The adiabatic framework provides analytical tools for stability analysis of slowly changing systems that can be modeled as time inhomogeneous reversible Markov chains. In particular, we consider queueing policies whose service rate is adaptively changed based on the estimated arrival rates that tend to vary with time. As a result, the packet distribution in the queue over time behaves like a time inhomogeneous reversible Markov chain. Our results provide an upper bound on the time for an initial distribution of packets in the queue to converge to a stationary distribution corresponding to some pre-specified queueing policy. These results are useful for designing adaptive queueing policies when arrival rates are unknown, and may or may not change with time. Furthermore, our analysis is readily extended for any system that can be modeled as a time inhomogeneous reversible Markov chain. We provide simulations that confirm our theoretical results.