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Multiple Server Scheduling: We consider a cluster of heterogeneous servers, modeled as M/G/1 first-come first-serve queues with different processing speeds. A dispatcher that assigns jobs to the servers takes as input only the size of the arriving job and the overall job-size distribution. We show that there exist optimal strategies that are deterministic, fixing the server to which jobs of particular sizes are always sent. We prove that the optimal strategy for systems with identical servers assigns a non-overlapping interval range of job sizes to each server, and that when server processing speeds differ, it is necessary to assign each server a distinct set of intervals of job sizes in order to minimize expected waiting or response times. An undergoing research project is to extend the result to the scenario that the dispatcher receives the current queue lengths (in terms of the total amount of work) of all servers as input when making decision, in additional to the job size information.
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Old Projects
Server Collectives: in [VR03], we analyzed when it made sense for independent service providers to form collectives, pooling resources to host one another's content. Our queueing analyses showed that as long as the intensities (ratio of demand to service capacity) of the providers was similar, they could all benefit from sharing, but slight deviations would make the collective unappealing to the more heavily-loaded providers. We showed that setting tresholds (limiting how much of a provider's resources would be shared) increased this deviation, but it still remained small. The work was extended in [VR05]. An interesting read/write variant of this problem involving the consistency of information across servers was explored in [VMRS06].
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Self-Tuning Web Server Control: Managing the performance of multiple-tiered Web sites under high client loads is a critical problem with the advent of dynamic content and database-driven servers on the Internet. This work proposes a control-theoretic approach for admission control in multi-tiered Web sites that prevents overload and enforces absolute client response times while still maintaining high throughput under load. We use classical control theoretic techniques to design a Proportional Integral (PI) controller for admission control of client HTTP requests. In addition, we present a processor-sharing model that is used to make the controller self-tuning, so that no parameter setting is required beyond a target response time. Our controller is implemented as a proxy, called Yaksha, which operates by taking simple external measurements of the client response times. The controller design is non-invasive and requires minimal operator intervention.
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