Optimization and Regulation of Performance for Computing Systems

The current demands of computing applications, the advent of technological advances related to hardware and software, the contractual relationship between users and cloud service providers and current ecological demands, require the re\ufb01nement of performance regulation on computing systems. Powerful mathematical tools such as control systems theory, discrete event systems (DES) and randomized algorithms (RAs) have o\ufb00ered improvements in e\ufb03ciency and performance in computer scenarios where the traditional approach has been the application of well founded common sense and heuristics. The comprehensive concept of computing systems is equally related to a microprocessor unit, a set of microprocessor units in a server, a set of servers interconnected in a data center or even a network of data centers forming a cloud of virtual resources. In this dissertation, we explore theoretical approaches in order to optimize and regulate performance measures in di\ufb00erent computing systems. In several cases, such as cloud services, this optimization would allow the fair negotiation of service level agreements (SLAs) between a user and a cloud service provider, that may be objectively measured for the bene\ufb01t of both negotiators. Although DES are known to be suitable for modeling computing systems, we still \ufb01nd that traditional control theory approaches, such as passivity analysis, may o\ufb00er solutions that are worth being explored. Moreover, as the size of the problem increases, so does its complexity. RAs o\ufb00er good alternatives to make decisions on the design of the solutions of such complex problems based on given values of con\ufb01dence and accuracy. In this dissertation, we propose the development of: a) a methodology to optimize performance on a many-core processor system, b) a methodology to optimize and regulate performance on a multitier server, c) some corrections to a previously proposed passivity analysis of a market-oriented cloud model, and d) a decentralized methodology to optimize cloud performance. In all the aforementioned systems, we are interested in developing optimization methods strongly supported on DES theory, speci\ufb01cally In\ufb01nitesimal Perturbation Analysis (IPA) and RAs based on sample complexity to guarantee that these computing systems will satisfy the required optimal performance on the average

Topics in perturbation analysis for stochastic hybrid systems

Control and optimization of Stochastic Hybrid Systems (SHS) constitute increasingly active fields of research. However, the size and complexity of SHS frequently render the use of exhaustive verification techniques prohibitive. In this context, Perturbation Analysis techniques, and in particular Infinitesimal Perturbation Analysis (IPA), have proven to be particularly useful for this class of systems. This work focuses on applying IPA to two different problems: Traffic Light Control (TLC) and control of cancer progression, both of which are viewed as dynamic optimization problems in an SHS environment. The first part of this thesis addresses the TLC problem for a single intersection modeled as a SHS. A quasi-dynamic control policy is proposed based on partial state information defined by detecting whether vehicle backlogs are above or below certain controllable threshold values. At first, the threshold parameters are controlled while assuming fixed cycle lengths and online gradient estimates of a cost metric with respect to these controllable parameters are derived using IPA techniques. These estimators are subsequently used to iteratively adjust the threshold values so as to improve overall system performance. This quasi-dynamic analysis of the TLC\ problem is subsequently extended to parameterize the control policy by green and red cycle lengths as well as queue content thresholds. IPA estimators necessary to simultaneously control the light cycles and thresholds are rederived and thereafter incorporated into a standard gradient based scheme in order to further ameliorate system performance. In the second part of this thesis, the problem of controlling cancer progression is formulated within a Stochastic Hybrid Automaton (SHA) framework. Leveraging the fact that cell-biologic changes necessary for cancer development may be schematized as a series of discrete steps, an integrative closed-loop framework is proposed for describing the progressive development of cancer and determining optimal personalized therapies. First, the problem of cancer heterogeneity is addressed through a novel Mixed Integer Linear Programming (MILP) formulation that integrates somatic mutation and gene expression data to infer the temporal sequence of events from cross-sectional data. This formulation is tested using both simulated data and real breast cancer data with matched somatic mutation and gene expression measurements from The Cancer Genome Atlas (TCGA). Second, the use of basic IPA techniques for optimal personalized cancer therapy design is introduced and a methodology applicable to stochastic models of cancer progression is developed. A case study of optimal therapy design for advanced prostate cancer is performed. Given the importance of accurate modeling in conjunction with optimal therapy design, an ensuing analysis is performed in which sensitivity estimates with respect to several model parameters are evaluated and critical parameters are identified. Finally, the tradeoff between system optimality and robustness (or, equivalently, fragility) is explored so as to generate valuable insights on modeling and control of cancer progression

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included

Stochastic Estimation and Control of Queues within a Computer Network

An extended Kalman filter is used to estimate size and packet arrival rate of network queues. These estimates are used by a LQG steady state linear perturbation PI controller to regulate queue size within a computer network. This paper presents the derivation of the transient queue behavior for a system with Poisson traffic and exponential service times. This result is then validated for ideal traffic using a network simulated in OPNET. A more complex OPNET model is then used to test the adequacy of the transient queue size model when non-Poisson traffic is combined. The extended Kalman filter theory is presented and a network state estimator is designed using the transient queue behavior model. The equations needed for the LQG synthesis of a steady state linear perturbation PI controller are presented. These equations are used to develop a network queue controller based on the transient queue model. The performance of the network state estimator and network queue controller was investigated and shown to provide improved control when compared to other simplistic control algorithms

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

Analytical modeling of spatial dependencies and calibration techniques for stochastic traffic simulators

Thesis (S.M. in Transportation)--Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (pages 79-82).Exact numerical evaluation of the stationary joint queue-length distribution of a Markovian finite capacity network with arbitrary size and topology can be obtained numerically. Nonetheless, the main challenge to such an approach remains the dimensionality of the joint distribution, which is exponential in the number of queues. This thesis proposes an analytical approximation of the joint distribution with a dimension that is linear in the number of queues. The method decomposes the network into overlapping subnetworks. The state of each subnetwork is described aggregately, i.e. in terms of a reduced state space, while ensuring consistency with the disaggregate, i.e., full state space, distribution. This aggregation-disaggregation technique is proposed for the analysis of Markovian tandem finite capacity queueing networks. The model is validated. We present its use to address an urban traffic control problem, and show the added value of accounting for higher-order spatial between-queue dependency information in the control of congested networks. A second, distinct goal of this thesis is to examine the calibration of route choice parameters in microscopic traffic simulators. Automatically calibrating simulators using traffic counts requires describing the relationship between route choice and traffic flows. This thesis proposes an analytical finite capacity queueing model that accounts for the relationship between route choice and traffic flows. The method is embedded in a simulation-based optimization framework and applied to a calibration problem.by Carter Wang.S.M.in Transportatio

Maximizing Patient Satisfaction in Systems with Time-Varying Arrival Rates

Time-Varying Little’s Law (TVLL) can be regarded as part of the theory of Infinite Servers (IS) models, for the abstract system can be considered as a general IS model if waiting time is considered as service time. Moreover, the time-varying arrival rate does not affect the waiting time distribution, when there are adequate time-varying servers in the system. In this study, we estimate the average number of entities in the system over a sub-interval and the arrival rate function, and apply TVLL combined with time-varying staffing to estimate the unknown mean wait times. When the arrival rate function is approximated by a linear (quadratic) function, the average waiting time satisfies a quadratic (cubic) equation. The estimation of average waiting time based on TVLL is a positive real root of the average waiting time equation. If, the arrival rate function is neither approximately linear nor approximately quadratic, it must be approximated by a polynomial function of higher degree. In this study, we investigate systems with arrival rate function of degree 3, and find the estimation of average waiting time which is the root of a polynomial of degree 4. Also, we study queues with time-varying arrival rate to obtain optimal visit time leading to maximum satisfaction of patients in walk-in clinics. If there is adequate time-varying staffing, then customers receive service upon arrival and waiting times tend to be approximately as equal as the service times though the arrival rates are time-varying. However, in the systems with limited servers, some customers must wait in the waiting room and when there is no room in the area, the new arriving customers are refused. Rejection of customers may lead to their dissatisfaction. If we decrease the average service time, less customers will be refused, but shorter service time decreases happiness of admitted customers. Another issue is the revenue of walk-in clinics. Walk-in clinics work on a fee-for-service model, so they benefit from the number of patients they serve. As the number of patients increases, more revenue is gained. Hence, it may be in interest of some walk-in clinics to reduce visit times to increase profit. As mentioned, short visit time sacrifices the quality of service and leads to the dissatisfaction of patients. Patients want to be heard carefully and be asked directly why they have come to the clinic. The problem gets worse in rush hours when the number of arrivals increases but the number of servers could not be increased due to limitation in the number of doctors. We obtain optimal value for visit time considering satisfaction of customers and revenue of walk-in clinics simultaneously