Optimal resource allocation algorithms for cloud computing

Cloud computing is emerging as an important platform for business, personal and mobile computing applications. We consider a stochastic model of a cloud computing cluster, where jobs arrive according to a random process and request virtual machines (VMs), which are specified in terms of resources such as CPU, memory and storage space. The jobs are first routed to one of the servers when they arrive and are queued at the servers. Each server then chooses a set of jobs from its queues so that it has enough resources to serve all of them simultaneously. There are many design issues associated with such systems. One important issue is the resource allocation problem, i.e., the design of algorithms for load balancing among servers, and algorithms for scheduling VM configurations. Given our model of a cloud, we define its capacity, i.e., the maximum rates at which jobs can be processed in such a system. An algorithm is said to be throughput-optimal if it can stabilize the system whenever the load is within the capacity region. We show that the widely-used Best-Fit scheduling algorithm is not throughput-optimal. We first consider the problem where the jobs need to be scheduled nonpreemptively on servers. Under the assumptions that the job sizes are known and bounded, we present algorithms that achieve any arbitrary fraction of the capacity region of the cloud. We then relax these assumptions and present a load balancing and scheduling algorithm that is throughput optimal when job sizes are unknown. In this case, job sizes (durations) are modeled as random variables with possibly unbounded support. Delay is a more important metric then throughput optimality in practice. However, analysis of delay of resource allocation algorithms is difficult, so we study the system in the asymptotic limit as the load approaches the boundary of the capacity region. This limit is called the heavy traffic regime. Assuming that the jobs can be preempted once after several time slots, we present delay optimal resource allocation algorithms in the heavy traffic regime. We study delay performance of our algorithms through simulations

Nitrification performance of a modified aerated lagoon

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on October 30, 2007)Includes bibliographical references.Thesis (M.S.) University of Missouri-Columbia 2007.Dissertations, Academic -- University of Missouri--Columbia -- Civil engineering.The performance of a modified wastewater lagoon and the factors affecting the treatment process are discussed. This study was conducted over a period of twelve months at the Kingdom City, Missouri lagoon. A polyethylene fixed film media was incorporated in the lagoon to modify its waste treating ability. However, further study of the performance of the lagoon would be required to assess the effectiveness of the media in treating the wastes. The study recognizes the affect of seasonal changes on the treatment process. Analysis of various characteristics of wastewater such as ammonia, biochemical oxygen demand (BOD₅), nitrites, nitrates, total suspended solids (TSS), volatile suspended solids, chemical oxygen demand, and alkalinity were performed during the study period. The parameters of pH, dissolved oxygen concentration, and temperature were monitored at the time of sample collection in the field. Results indicate that the average ammonia removal rate was 87% and 98% removal rates were achieved during the summer. It was observed that nitrification is greatly influenced by temperature. Eighty four percent of BOD₅ was removed on an average and the lagoon was able to maintain low BOD₅ values during 2006. The concentration of nitrate was consistent with nitrification levels. An average of 86% of TSS was removed from the lagoon during the study period. The study provides good preliminary data for evaluating the performance of a lagoon. The advancement of wastewater treatment technology in lagoons with the help of fixed films can be achieved by further studies and monitoring of the lagoon based upon the current observations

On Optimal Weighted-Delay Scheduling in Input-Queued Switches

Motivated by relatively few delay-optimal scheduling results, in comparison to results on throughput optimality, we investigate an input-queued switch scheduling problem in which the objective is to minimize a linear function of the queue-length vector. Theoretical properties of variants of the well-known MaxWeight scheduling algorithm are established within this context, which includes showing that these algorithms exhibit optimal heavy-traffic queue-length scaling. For the case of $2 \times 2$ input-queued switches, we derive an optimal scheduling policy and establish its theoretical properties, demonstrating fundamental differences with the variants of MaxWeight scheduling. Our theoretical results are expected to be of interest more broadly than input-queued switches. Computational experiments demonstrate and quantify the benefits of our optimal scheduling policy