A Robust Formulation Of A Multi Class Queueing Network Control Problem

Author : Yi Zheng
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

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Download or read book Stochastic Control and Stability for Queueing Networks in Random Environments written by Yi Zheng and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The service systems, such as data centers and healthcare systems, are usually of large scale which makes the system more sensitive to environments and more vulnerable to interruptions. It is thus important to better design the system and develop optimal scheduling policies that will help to minimize the cost in random environments and prevent interruptions. On the other hand, the control of jump diffusions has attracted much attention due to its vast applicability to stochastic networks, mathematical finance, telecommunications, etc. The primary goal of this dissertation is to study the stability and optimal scheduling of large-scale stochastic networks in random environments and address control problems of jump diffusions. I study multiclass many-server queues for which the arrival, service, and abandonment rates are all modulated by a common finite-state Markov process in the "averaged" Halfin-Whitt regime. I establish a functional central limit theorem for the diffusion-scaled queueing process and show that the limiting process is a controlled diffusion. I address the infinite-horizon discounted and long-run average (ergodic) optimal control problems and establish asymptotic optimality. The ergodic properties of a class of Markov-modulated general birth-death processes under fast regime switching are studied. I show the ergodic properties of the properly scaled joint Markov process with a parameter that is taken large. Under very weak hypotheses, it is shown that if the averaged process is exponentially ergodic for large values of the parameter, then the same applies to the original joint Markov process. The ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process is studied. I provide a full characterizations of optimality via the Hamilton--Jacobi--Bellman (HJB) equation, for which the regularity of solutions under mild hypotheses is established. In addition, I show that optimal stationary Markov controls are a.s. pathwise optimal. I show that one can fix a stable control outside a compact set and obtain near-optimal solutions by solving the HJB on a sufficiently large bounded domain. The optimal scheduling problems for multiclass many-server queues in an alternating renewal random environment in the Halfin-Whitt regime are studied. Assuming that the downtimes are asymptotically negligible and only the service processes are affected, I show that the limits of the diffusion-scaled state processes are controlled jump diffusions driven by a compound Poisson jump process. I establish the asymptotic optimality of the infinite-horizon discounted and ergodic problems for the queueing dynamics.