An adiabatic approach to analysis of time inhomogeneous Markov chains : a queueing policy application Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/rj4307471

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  • In this thesis, convergence of time inhomogeneous Markov chains is studied using an adiabatic approach. The adiabatic framework considers slowly changing systems and the adiabatic time quantifies the time required for the change such that the final state of the system is close to some equilibrium state. This approach is used in Markov chains to measure the time to converge to a stationary distribution. Continuous time reversible Markov chains on a finite state space with generators changing at fixed time intervals are studied. This characterization is applied to a Markovian queueing model with unknown arrival rate. The time inhomogeneous Markov chain is induced by a queueing policy dependent on uncertainties in arrival rate estimation. It is shown that the above convergence happens with high probability after a sufficiently large time. The above evolution is studied via simulations as well and compared to the bounds suggested by the analysis. These results give the sufficient amount of time one must wait for the queue to reach a stationary, stable distribution under our queueing policy.
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