Limit theorems for continuous time Markov chains and applications to large scale queueing systems
This thesis discusses limit theorems for density dependent families of continuoustime Markov chains and their application to the stochastic analysis of large scalecloud computing environments and data centers. On the purely theoretical side, wereview the classic functional strong law of large number...
| Autor: | |
|---|---|
| Formato: | tesis de maestría |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | Uruguay |
| Recursos: | Universidad de la República |
| Repositorio: | COLIBRI |
| Idioma: | inglés |
| OAI Identifier: | oai:colibri.udelar.edu.uy:20.500.12008/21041 |
| Acesso em linha: | https://hdl.handle.net/20.500.12008/21041 |
| Access Level: | acceso abierto |
| Palavra-chave: | Markov chain Strong law of large number Fluid limit Central limit theorem Diffusion approximation Queueing theory Heavy traffic Feedback control Cloud computing Data center |
| Resumo: | This thesis discusses limit theorems for density dependent families of continuoustime Markov chains and their application to the stochastic analysis of large scalecloud computing environments and data centers. On the purely theoretical side, wereview the classic functional strong law of large numbers and central limit theoremdue to Kurtz, which characterize the asymptotic behavior of density dependentfamilies in terms of their drift. In the case of the central limit theorem we provide extensions in two directions: to consider small order perturbations in the transitionrates of the family and non-differentiable drifts. The classic theorems and the latterextensions are used to study the dynamic right sizing of capacity in large scalecloud environments and data centers, aimed at the adjustment of this capacity toan uncertain workload. Under a central queue scheme and Markovian assumptions,we design a policy that eliminates queueing almost completely, at the expense of aslight over-provisioning; ifρthe traffic intensity, then the over-provisioning scales as O(√ρ) whenρ→∞. In this sense our policy automatically adjusts the system’scapacity according to the well-known square root staffing rule. |
|---|