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dc.contributor.advisorGoldberg, David
dc.contributor.authorLi, Yuan
dc.date.accessioned2018-08-20T15:27:48Z
dc.date.available2018-08-20T15:27:48Z
dc.date.created2017-08
dc.date.issued2017-05-12
dc.date.submittedAugust 2017
dc.identifier.urihttp://hdl.handle.net/1853/60118
dc.description.abstractIn the first part of this thesis, we consider the FCFS $GI/GI/n$ queue, and prove the first simple and explicit bounds that scale gracefully and universally as $\frac{1}{1-\rho}$ ($\rho$ being the corresponding traffic intensity), across both the classical and Halfin-Whitt heavy traffic settings. In particular, supposing that the inter-arrival and service times, distributed as random variables $A$ and $S$, have finite $r$th moment for some $r > 2$, and letting $\mu_A (\mu_S)$ denote $\frac{1}{\E[A]} (\frac{1}{\E[S]})$, our main results are bounds for the tail of the steady-state queue length and the steady-state probability of delay, expressed as simple and explicit functions of only $ \E\big[(A \mu_A)^r\big], \E\big[(S \mu_S)^r\big], r$, and $\frac{1}{1-\rho}$. In the second part of this thesis, we prove that when service times have finite $1 + \epsilon$ moment for some $\epsilon > 0$ and inter-arrival times have finite second moment, the sequence of stationary queue length distributions, normalized by $n^{\frac{1}{2}}$, is tight in the Halfin-Whitt regime. Furthermore, we develop simple and explicit bounds on the stationary queue length in that regime. When the inter-arrival times have a Pareto tail with index $\alpha \in (1,2)$, we prove that in a generalized Halfin-Whitt regime, for general service time distributions, the sequence of stationary queue length distributions, normalized by $n^{\frac{1}{\alpha}}$, is tight. In the third part of this thesis, when service times have a Pareto tail with index $\alpha \in (1,2)$ and inter-arrival times have finite second moment, we bound the large deviation behavior of the weak limits of the $n^{\frac{1}{2}}$ scaled stationary queue lengths in the Halfin-Whitt regime, and derive a matching lower bound when inter-arrival times are Markovian. We find that the tail of the limit has a \emph{sub-exponential} decay, differing fundamentally from the exponential decay in the light-tailed setting. When inter-arrival times have a Pareto tail with index $\alpha \in (1,2)$, we bound the large-deviation behaviors of the weak limits of the $n^{\frac{1}{\alpha}}$ scaled statioanry queue lengths in a generalized Halfin-Whitt regime, and find that our bounds are tight when service times are deterministic.
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.publisherGeorgia Institute of Technology
dc.subjectMany-server queues
dc.subjectStochastic comparison
dc.subjectKingman’s bound
dc.subjectRenewal process
dc.subjectHalfin-Whitt regime
dc.subjectHeavy tails
dc.subjectWeak convergence
dc.subjectLarge deviations
dc.subjectGaussian process
dc.subjectStable law
dc.titleStochastic comparison approach to multi-server queues: Bounds, heavy tails and large deviations
dc.typeDissertation
dc.description.degreePh.D.
dc.contributor.departmentIndustrial and Systems Engineering
thesis.degree.levelDoctoral
dc.contributor.committeeMemberMaguluri, Siva Theja
dc.contributor.committeeMemberFoley, Robert
dc.contributor.committeeMemberAyhan, Hayriye
dc.contributor.committeeMemberXu, Jun
dc.date.updated2018-08-20T15:27:48Z


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