Large deviations analysis of scheduling policies for a web server

With increasing demand and availability of bandwidth resources, there has been tremendous growth in the scale and speed of web servers. In web servers, scheduling plays an important role in resource allocation (for instance, bandwidth allocation, processor allocation, etc). However, as the scale of a system increases so does the number of activities/events in the system (e.g., job arrivals), as a consequence of which the analysis of scheduling becomes increasingly harder. In particular, the possible ways in which scheduling failure (e.g., queue overflow, excessively large delay, instability of a system) can occur becomes increasingly greater, thus making it more difficult to understand the behavior and develop design rules for scheduling algorithms. However, a well-known observation from large devi viations theory that large scale systems fails in a “most likely way” can potentially be used to simplify the design and analysis of scheduling. In this thesis, we study the implications and applications of this effect on scheduling in a web server accessed by a large number of sources. We analyze the delay distribution of scheduling policies for web servers under a many sources large deviation regime which models web servers in a large scale system well. Due to the difficulties brought on considering a large number of sources, only a small number of scheduling policies, such as First-Come-First-Serve (FCFS), General-ProcessorSharing (GPS), and Priority Queueing policies have been analyzed under the many sources regime. In particular, in a single queue single server setup the delay characteristics of only FCFS, Shortest-Job-First (SJF), and Longest-Job-First (LJF) has been analyzed. In this thesis, we study the Two-Dimensional-Queueing (2DQ) framework, a unifying queueing framework that allows the identification of the “most likely way” in which delay occurs, to analyze the delay of various unexplored scheduling policies. In conjunction with the 2DQ framework, we develop a new “cycle based” technique for understanding the large deviations tail probability of more complex policies. Using the combination of the 2DQ framework and the cycle based analysis, we first analyze two interesting scheduling policies, i.e., Shortest-Remaining-Processing-Time (SRPT) policy (which is mean delay optimal) and Processer-Sharing (PS) policy (which is a “fair” policy). We derive the asymptotic delay distributions (rate functions) of both policies and study their behavior across job sizes. Next, we address three problems in implementing the aforementioned scheduling policies: (i) end receivers may have bandwidth constraints that are not taken account in SRPT, (ii) the remaining processing time information might not be available to the web-server, and (iii) most actual implementations are variants of SRPT to reflect other implementation constraints and/or to jointly optimize other metrics in addition to delay, i.e., jitter, fairness, etc. To address these, we first develop finite-SRPT that takes into account the bandwidth constraint at the end receiver, and show that the policy shifts between SRPT and a PS-like policy depending on the bandwidth constraint. Second, we study the Least-Attained-Service (LAS) policy which is viewed as a good substitute for SRPT when the remaining job size is not available and we analyze the penalty associated with not using the remaining size information directly. Lastly, we analyze a class of scheduling policies known as SMART that contains many variants of SRPT with different fairness properties and show that all policies in the class have the same tail probability of delay across job sizes for a many sources regime. The results of this thesis facilitate the understanding of various scheduling policies under the many sources regime and provides an analytical queueing framework that can be used to understand other scheduling policies.Electrical and Computer Engineerin

Functional limit theorems, branching processes and stochastic networks

This manuscript describes some of the work I have been doing since 2010 and the end of my PhD. As the title suggests, it contains three main parts. 1. Functional limit theorems: Chapter 2 presents two theoretical results on the weak convergence of stochastic processes: one is a sufficient condition for the tightness of a sequence of stochastic processes and the other provides a sufficient condition for the weak convergence of a sequence of regenerative processes; 2. Branching processes: in Chapter 3, scaling limits of three particular types of branching processes are discussed: 1) Galton-Watson processes in varying environments, 2) binary and homogeneous Crump-Mode-Jagers processes and 3) Crump-Mode-Jagers processes with short edges;3. Stochastic networks: Chapter 4 presents three results on stochastic networks: 1) scaling limits of the M/G/1 Processor-Sharing queue length process, 2) study of a model of stochastic network with mobile customers and 3) heavy traffic delay performance of queue-based scheduling algorithms

Applications of robust optimization to queueing and inventory systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 105-111).This thesis investigates the application of robust optimization in the performance analysis of queueing and inventory systems. In the first part of the thesis, we propose a new approach for performance analysis of queueing systems based on robust optimization. We first derive explicit upper bounds on performance for tandem single class, multiclass single server, and single class multi-server queueing systems by solving appropriate robust optimization problems. We then show that these bounds derived by solving deterministic optimization problems translate to upper bounds on the expected steady-state performance for a variety of widely used performance measures such as waiting times and queue lengths. Additionally, these explicit bounds agree qualitatively with known results. In the second part of the thesis, we propose methods to compute (s,S) policies in supply chain networks using robust and stochastic optimization and compare their performance. Our algorithms handle general uncertainty sets, arbitrary network topologies, and flexible cost functions including the presence of fixed costs. The algorithms exhibit empirically practical running times. We contrast the performance of robust and stochastic (s,S) policies in a numerical study, and we find that the robust policy is comparable to the average performance of the stochastic policy, but has a considerably lower standard deviation across a variety of networks and realized demand distributions. Additionally, we identify regimes when the robust policy exhibits particular strengths even in average performance and tail behavior as compared with the stochastic policy.by Alexander Anatolyevich Rikun.Ph.D

Extended Abstracts: PMCCS3: Third International Workshop on Performability Modeling of Computer and Communication Systems

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryThe pages of the front matter that are missing from the PDF were blank

[Activity of Institute for Computer Applications in Science and Engineering]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science