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

Statistical Service Guarantees for Traffic Scheduling in High-Speed Data Networks

School of Electrical and Computer Engineerin

Delay analysis for wireless applications using a multiservice multiqueue processor sharing model

The ongoing development of wireless networks supporting multimedia applications requires service providers to efficiently deliver complex Quality of Service (QoS) requirements. The wide range of new applications in these networks significantly increases the difficulty of network design and dimensioning to meet QoS requirements. Medium Access Control (MAC) protocols affect QoS achieved by wireless networks. Research on analysis and performance evaluation is important for the efficient protocol design. As wireless networks feature scarce resources that are simultaneously shared by all users, processor sharing (PS) models were proposed for modelling resource sharing mechanisms in such systems. In this thesis, multi-priority MAC protocols are proposed for handling the various service traffic types. Then, an investigation of multiservice multiqueue PS models is undertaken to analyse the delay for some recently proposed wireless applications. We start with an introduction to MAC protocols for wireless networks which are specified in IEEE standards and then review scheduling algorithms which were proposed to work with the underlying MAC protocols to cooperatively achieve QoS goals. An overview of the relevant literature is given on PS models for performance analysis and evaluation of scheduling algorithms. We propose a multiservice multiqueue PS model using a scheduling scheme in multimedia wireless networks with a comprehensive description of the analytical solution. Firstly, we describe the existing multiqueue processor sharing (MPS) model, which uses a fixed service quantum at each queue, and correct a subtle incongruity in previous solutions presented in the literature. Secondly, a new scheduling framework is proposed to extend the previous MPS model to a general case. This newly proposed analytical approach is based on the idea that the service quantum arranged by a MAC scheduling controller to service data units can be priority-based. We obtain a closed-form expression for the mean delay of each service class in this model. In summary, our new approach simplifies MAC protocols for multimedia applications into an analytical model that includes more complex and realistic traffic models without compromising details of the protocol and significantly reduces the number of MAC headers, thus the overall average delay will be decreased. In response to using the studied multiservice multiqueue PS models, we apply the MPS model to two wireless applications: Push to Talk (PTT) service over GPRS/GSM networks and the Worldwide Interoperability for Microwave Access (WiMAX) networks. We investigate the uplink delay of PTT over traditional GPRS/GSM networks and the uplink delay for WiMAX Subscriber Station scheduler under a priority-based fair scheduling. MAC structures capable of supporting dynamically varying traffic are studied for the networks, especially, with the consideration of implementation issues. The model provides useful insights into the dynamic performance behaviours of GPRS/GSM and WiMAX networks with respect to various system parameters and comprehensive traffic conditions. We then evaluate the model under some different practical traffic scenarios. Through modelling of the operation of wireless access systems, under a variety of multimedia traffic, our analytical approaches provide practical analysis guidelines for wireless network dimensioning

Performance analysis and network path characterization for scalable internet streaming

Delivering high-quality of video to end users over the best-effort Internet is a challenging task since quality of streaming video is highly subject to network conditions. A fundamental issue in this area is how real-time applications cope with network dynamics and adapt their operational behavior to offer a favorable streaming environment to end users. As an effort towards providing such streaming environment, the first half of this work focuses on analyzing the performance of video streaming in best-effort networks and developing a new streaming framework that effectively utilizes unequal importance of video packets in rate control and achieves a near-optimal performance for a given network packet loss rate. In addition, we study error concealment methods such as FEC (Forward-Error Correction) that is often used to protect multimedia data over lossy network channels. We investigate the impact of FEC on the quality of video and develop models that can provide insights into understanding how inclusion of FEC affects streaming performance and its optimality and resilience characteristics under dynamically changing network conditions. In the second part of this thesis, we focus on measuring bandwidth of network paths, which plays an important role in characterizing Internet paths and can benefit many applications including multimedia streaming. We conduct a stochastic analysis of an end-to-end path and develop novel bandwidth sampling techniques that can produce asymptotically accurate capacity and available bandwidth of the path under non-trivial cross-traffic conditions. In addition, we conduct comparative performance study of existing bandwidth estimation tools in non-simulated networks where various timing irregularities affect delay measurements. We find that when high-precision packet timing is not available due to hardware interrupt moderation, the majority of existing algorithms are not robust to measure end-to-end paths with high accuracy. We overcome this problem by using signal de-noising techniques in bandwidth measurement. We also develop a new measurement tool called PRC-MT based on theoretical models that simultaneously measures the capacity and available bandwidth of the tight link with asymptotic accuracy

New Perspectives on Modelling and Control for Next Generation Intelligent Transport Systems

This PhD thesis contains 3 major application areas all within an Intelligent Transportation System context. The first problem we discuss considers models that make beneficial use of the large amounts of data generated in the context of traffic systems. We use a Markov chain model to do this, where important data can be taken into account in an aggregate form. The Markovian model is simple and allows for fast computation, even on low end computers, while at the same time allowing meaningful insight into a variety of traffic system related issues. This allows us to both model and enable the control of aggregate, macroscopic features of traffic networks. We then discuss three application areas for this model: the modelling of congestion, emissions, and the dissipation of energy in electric vehicles. The second problem we discuss is the control of pollution emissions in eets of hybrid vehicles. We consider parallel hybrids that have two power units, an internal combustion engine and an electric motor. We propose a scheme in which we can in uence the mix of the two engines in each car based on simple broadcast signals from a central infrastructure. The infrastructure monitors pollution levels and can thus make the vehicles react to its changes. This leads to a context aware system that can be used to avoid pollution peaks, yet does not restrict drivers unnecessarily. In this context we also discuss technical constraints that have to be taken into account in the design of traffic control algorithms that are of a microscopic nature, i.e. they affect the operation of individual vehicles. We also investigate ideas on decentralised trading of emissions. The goal here is to allocate the rights to pollute fairly among the eet's vehicles. Lastly we discuss the usage of decentralised stochastic assignment strategies in traffic applications. Systems are considered in which reservation schemes can not reliably be provided or enforced and there is a signifficant delay between decisions and their effect. In particular, our approach facilitates taking into account the feedback induced into traffic systems by providing forecasts to large groups of users. This feedback can invalidate the predictions if not modelled carefully. At the same time our proposed strategies are simple rules that are easy to follow, easy to accept, and significantly improve the performance of the systems under study. We apply this approach to three application areas, the assignment of electric vehicles to charging stations, the assignment of vehicles to parking facilities, and the assignment of customers to bike sharing stations. All discussed approaches are analysed using mathematical tools and validated through extensive simulations

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

Spatial stochastic models for network analysis

This thesis proposes new stochastic interacting particle models for networks, and studies some fundamental properties of these models. This thesis considers two application areas of networking - engineering design questions in future wireless systems and algorithmic tasks in large scale graph structured data. The key innovation introduced in this thesis is to bring tools and ideas from stochastic geometry to bear on the problems in both these application domains. We identify certain fundamental questions in design and engineering both wireless systems and large scale graph structured data processing systems. Subsequently, we identify novel stochastic geometric models, that captures the fundamental properties of these networks, which forms the first research contribution. We then rigorously study these models, by bringing to bear new tools from stochastic geometry, random graphs, percolation and Markov processes to establish structural results and fundamental phase transitions in these models. Using our developed mathematical methodology, we then identify design insights and develop algorithms, which we demonstrate are instructive in many practical settings. In the setting of wireless systems, this thesis studies both ad-hoc and cellular networks. In the ad-hoc network setting, we aim to understand fundamental limits of the simplest possible protocol to access the spectrum, namely a link transmits whenever it has data to send by treating all interference as noise. Surprisingly this basic question itself was not understood, as the system dynamics is coupled spatially due to the interference links cause one another and temporally due to randomness in traffic arrivals. We propose a novel interacting particle model called the spatial birth-death wireless network model to understand the stability properties of the simple spectrum access protocol. Using tools from Palm calculus and fluid limit theory, we establish a tight characterization of when this model is stable. Furthermore, we show that whenever stable, the links in steady-state exhibit a form of clustering. Leveraging these structural results, we propose two mean field heuristics to obtain formulas for key performance metrics such as average delay experienced by a link. We empirically find that the proposed formulas for delay predicts accurately the system behavior. We subsequently study scalability properties of this model by introducing an appropriate infinite dimensional version of the model we call the Interference Queueing Networks model. The model consists of a queue located at each grid point of an infinite regular integer lattice, with the queues interacting with each other in a translation invariant fashion. We then prove several structural properties of the model namely, tight conditions for existence of stationary solutions and some sufficient conditions for uniqueness of stationary solutions. Remarkably, we obtain exact formula for mean delay in this model, unlike the continuum model where we relied on mean-field type heuristics to obtain insights. In the setting of cellular networks, we study optimal association schemes by mobile phones in the case when there are several possible base station technologies operating on orthogonal bands. We show that this choice leads to a performance gain we term technology diversity. Interestingly, we show that the performance gain relies on the amount of instantaneous information a user has on the various base station technologies that it can leverage to make the association decision. We outline optimal association schemes under various information settings that a user may have on the network. Moreover, we propose simple heuristics for association that relies on a user obtaining minimal instantaneous information and are thus practical to implement. We prove that in certain natural asymptotic regime of parameters, our proposed heuristic policy is also optimal, and thus quantifying the value of having fine grained information at a user for association. We empirically observe that the asymptotic result is valid even at finite parameter regimes that are typical in todays networks. In the application of analyzing large scale graph structured data, we consider the graph clustering problem with side information. Graph clustering is a standard and widely used task which consists in partitioning the set of nodes of a graph into underlying clusters where nodes in the same cluster are similar to each other and nodes across different clusters are different. Motivated by applications in social and biological networks, we consider the task of clustering nodes of a graph, when there is side information on the nodes, other than that contained in the graph. For instance in social networks, one has access to meta data about a person (node in a social graph) such as age, location, income etc, along with the combinatorial data of who are his friends on the social graph. Similarly, in biological networks, there is often meta-data about an experiment that provides additional contextual data about a node, in addition to the combinatorial data. In this thesis, we propose a generative model for such graph structured data with side information, which is inspired by random graph models in stochastic geometry such as the random connection model and the generative models for networks with clusters without contexts, such as the stochastic block model or the planted partition model. We propose a novel graph model called the planted partition random connection model. Roughly speaking, in this model, each node has two labels - an observable R [superscript d] valued (for some fixed d) feature label and an unobservable binary valued community label. Conditional on the node labels, edges are drawn at random in this graph depending on both the feature and community labels of the two end points. The clustering task consists in recovering the underlying partition of nodes corresponding to the respective community labels better than a random assignment, when given an observation of the graph generated and the features of all nodes. We show that if the 'density of nodes', i.e., average number of nodes having features in an unit volume of space of R [superscript d] is small, then no algorithm can cluster the graph that can asymptotically beat a random assignment of community labels. On the contrary, if the density of nodes is sufficiently high, we give a simple algorithm that recovers the true underlying partition strictly better a random assignment. We then apply the proposed algorithm to a problem in computational biology called Haplotype Phasing and observe empirically, that it obtains state of art results. This demonstrates, both the validity of our generative model, as well as our new algorithm.Electrical and Computer Engineerin

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Формирование профессиональных компетенций юриста

В статье рассматривается проблема формирования профессиональных компетенций юриста в рамках дисциплины «Профессиональные навыки юриста» в условиях игрового состязательного судебного процесса, различные формы организации учебной деятельности студентов, которые способствуют приобретению студентами новых знаний, закреплению коммуникативных умений и навыков публичных выступлений