Restricted Adaptivity in Stochastic Scheduling

We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee ?((log m)/(log log m)). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of ?-delay and ?-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an ?(log log m)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any ?-delay and ?-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy

New benchmarking techniques in resource allocation problems: theory and applications in cloud systems

Motivated by different e-commerce applications such as allocating virtual machines to servers and online ad placement, we study new models that aim to capture unstudied tensions faced by decision-makers. In online/sequential models, future information is often unavailable to decision-makers---e.g., the exact demand of a product for next week. Sometimes, these unknowns have regularity, and decision-makers can fit random models. Other times, decision-makers must be prepared for any possible outcome. In practice, several solutions are based on classical models that do not fully consider these unknowns. One reason for this is our present technical limitations. Exploring new models with adequate sources of uncertainty could be beneficial for both the theory and the practice of decision-making. For example, cloud companies such as Amazon WS face highly unpredictable demands of resources. New management planning that considers these tensions have improved capacity and cut costs for the cloud providers. As a result, cloud companies can now offer new services at lower prices benefiting thousands of users. In this thesis, we study three different models, each motivated by an application in cloud computing and online advertising. From a technical standpoint, we apply either worst-case analysis with limited information from the system or adaptive analysis with stochastic results learned after making an irrevocable decision. A central aspect of this work is dynamic benchmarks as opposed to static or offline ones. Static and offline viewpoints are too conservative and have limited interpretation in some dynamic settings. A dynamic criterion, such as the value of an optimal sequential policy, allows comparisons with the best that one could do in dynamic scenarios. Another aspect of this work is multi-objective criteria in dynamic settings, where two or more competing goals must be satisfied under an uncertain future. We tackle the challenges introduced by these new perspectives with fresh theoretical analyses, drawing inspiration from linear and nonlinear optimization and stochastic processes.Ph.D