This is a tutorial presented in ICPE 2016 (https://icpe2016.spec.org/). In this tutorial, we present the problem of estimating parameters of performance models from measurements of real systems and discuss algorithms that can support researchers and practitioners in this task. The focus lies on performance models based on queueing systems, where the estimation of request arrival rates and service demands is a required input to the model. In the tutorial, we review existing estimation methods for service demands and present models to characterize time-varying arrival processes. The tutorial also demonstrates the use of relevant tools that automate demand estimation, such as LibRede, FG and M3A.
The document discusses parallel processing and matrix multiplication. It introduces parallel processing concepts like dividing a task between multiple processors to complete it faster. As an example, it explains how two people can add 100 numbers in half the time it takes one person. It then discusses using parallel processing to compute the convex hull of a set of points by dividing the set in half and merging the results. The rest of the document focuses on computational models for parallel processing like PRAM and different types of PRAM models including EREW, CREW, CRCW and how they handle read/write conflicts. It also provides an example of using parallel processing to perform matrix multiplication faster by dividing the matrices and merging the results.
- One-to-all broadcast and all-to-one reduction operations can be performed efficiently on networks like rings, meshes, and hypercubes using recursive doubling or similar algorithms.
- All-to-all broadcast, reduction, and personalized communication generalize these operations and can be implemented using similar techniques while accounting for increasing message sizes.
- Operations like all-reduce, prefix-sums, scatter, gather and circular shift can also be implemented efficiently using these basic group communication patterns and algorithms.
This document discusses several graph algorithms:
- Minimum spanning tree algorithms like Prim's and parallel formulations.
- Single-source and all-pairs shortest path algorithms like Dijkstra's and Floyd-Warshall. Parallel formulations are described.
- Other graph algorithms like connected components, transitive closure. Parallel formulations using techniques like merging forests are summarized.
Traffic Class Assignment for Mixed-Criticality Frames in TTEthernetVoica Gavrilut
The document discusses assigning traffic classes to messages in mixed-criticality systems using TTEthernet. It presents:
1) The motivation for integrating systems with applications of different criticality on a shared platform and focuses on mixed time-criticality systems.
2) The architecture and application models considered, including hard real-time, soft real-time, and non-critical messages that must be assigned traffic classes.
3) The problem of determining the optimal traffic class assignment to maximize schedulability of hard real-time messages and total utility of soft real-time messages.
This document summarizes several algorithms for parallel matrix operations, including matrix-vector multiplication, matrix-matrix multiplication, and solving systems of linear equations via Gaussian elimination. For matrix-vector multiplication, it describes row-wise and column-wise partitioning approaches. For matrix-matrix multiplication, it discusses algorithms based on row/column broadcasting, Cannon's algorithm, and a 3D domain decomposition approach. For Gaussian elimination, it analyzes pipelined and 2D mapping implementations. The key aspects of parallelization, communication costs, computation loads, scalability, and cost efficiency are analyzed for each algorithm.
This paper proposes a multiple query optimization (MQO) scheme for change point detection (CPD) that can significantly reduce the number of operators needed. CPD is used to detect anomalies in time series data but requires tuning parameters, which leads to running multiple CPDs with different parameters. The paper identifies four patterns for sharing CPD operators between queries based on whether parameter values are the same. Experiments show the proposed MQO approach reduces the number of operators by up to 80% compared to running each CPD independently, thus improving performance. Integrating MQO with hardware accelerators is suggested as future work.
This document discusses dynamic programming and provides examples of serial and parallel formulations for several problems. It introduces classifications for dynamic programming problems based on whether the formulation is serial/non-serial and monadic/polyadic. Examples of serial monadic problems include the shortest path problem and 0/1 knapsack problem. The longest common subsequence problem is an example of a non-serial monadic problem. Floyd's all-pairs shortest path is a serial polyadic problem, while the optimal matrix parenthesization problem is non-serial polyadic. Parallel formulations are provided for several of these examples.
This document proposes a new algorithmic framework called Cache-Oblivious Wavefront (COW) for parallelizing recursive dynamic programming algorithms. COW aims to improve parallelism without sacrificing cache efficiency. It does so by scheduling tasks for execution as soon as their real dependency constraints are satisfied, while still using the same recursive divide-and-conquer strategy as cache-optimal algorithms to maintain optimal cache performance. The document shows that COW can theoretically reduce the span of several important dynamic programming algorithms like Floyd-Warshall's algorithm and longest common subsequence, while keeping the total work and cache complexity optimal. Experimental results on real machines demonstrate a 3-5x speedup in running time and 10-20x improvement
The document discusses parallel processing and matrix multiplication. It introduces parallel processing concepts like dividing a task between multiple processors to complete it faster. As an example, it explains how two people can add 100 numbers in half the time it takes one person. It then discusses using parallel processing to compute the convex hull of a set of points by dividing the set in half and merging the results. The rest of the document focuses on computational models for parallel processing like PRAM and different types of PRAM models including EREW, CREW, CRCW and how they handle read/write conflicts. It also provides an example of using parallel processing to perform matrix multiplication faster by dividing the matrices and merging the results.
- One-to-all broadcast and all-to-one reduction operations can be performed efficiently on networks like rings, meshes, and hypercubes using recursive doubling or similar algorithms.
- All-to-all broadcast, reduction, and personalized communication generalize these operations and can be implemented using similar techniques while accounting for increasing message sizes.
- Operations like all-reduce, prefix-sums, scatter, gather and circular shift can also be implemented efficiently using these basic group communication patterns and algorithms.
This document discusses several graph algorithms:
- Minimum spanning tree algorithms like Prim's and parallel formulations.
- Single-source and all-pairs shortest path algorithms like Dijkstra's and Floyd-Warshall. Parallel formulations are described.
- Other graph algorithms like connected components, transitive closure. Parallel formulations using techniques like merging forests are summarized.
Traffic Class Assignment for Mixed-Criticality Frames in TTEthernetVoica Gavrilut
The document discusses assigning traffic classes to messages in mixed-criticality systems using TTEthernet. It presents:
1) The motivation for integrating systems with applications of different criticality on a shared platform and focuses on mixed time-criticality systems.
2) The architecture and application models considered, including hard real-time, soft real-time, and non-critical messages that must be assigned traffic classes.
3) The problem of determining the optimal traffic class assignment to maximize schedulability of hard real-time messages and total utility of soft real-time messages.
This document summarizes several algorithms for parallel matrix operations, including matrix-vector multiplication, matrix-matrix multiplication, and solving systems of linear equations via Gaussian elimination. For matrix-vector multiplication, it describes row-wise and column-wise partitioning approaches. For matrix-matrix multiplication, it discusses algorithms based on row/column broadcasting, Cannon's algorithm, and a 3D domain decomposition approach. For Gaussian elimination, it analyzes pipelined and 2D mapping implementations. The key aspects of parallelization, communication costs, computation loads, scalability, and cost efficiency are analyzed for each algorithm.
This paper proposes a multiple query optimization (MQO) scheme for change point detection (CPD) that can significantly reduce the number of operators needed. CPD is used to detect anomalies in time series data but requires tuning parameters, which leads to running multiple CPDs with different parameters. The paper identifies four patterns for sharing CPD operators between queries based on whether parameter values are the same. Experiments show the proposed MQO approach reduces the number of operators by up to 80% compared to running each CPD independently, thus improving performance. Integrating MQO with hardware accelerators is suggested as future work.
This document discusses dynamic programming and provides examples of serial and parallel formulations for several problems. It introduces classifications for dynamic programming problems based on whether the formulation is serial/non-serial and monadic/polyadic. Examples of serial monadic problems include the shortest path problem and 0/1 knapsack problem. The longest common subsequence problem is an example of a non-serial monadic problem. Floyd's all-pairs shortest path is a serial polyadic problem, while the optimal matrix parenthesization problem is non-serial polyadic. Parallel formulations are provided for several of these examples.
This document proposes a new algorithmic framework called Cache-Oblivious Wavefront (COW) for parallelizing recursive dynamic programming algorithms. COW aims to improve parallelism without sacrificing cache efficiency. It does so by scheduling tasks for execution as soon as their real dependency constraints are satisfied, while still using the same recursive divide-and-conquer strategy as cache-optimal algorithms to maintain optimal cache performance. The document shows that COW can theoretically reduce the span of several important dynamic programming algorithms like Floyd-Warshall's algorithm and longest common subsequence, while keeping the total work and cache complexity optimal. Experimental results on real machines demonstrate a 3-5x speedup in running time and 10-20x improvement
This document discusses various sorting algorithms that can be used on parallel computers. It begins with an overview of sorting and comparison-based sorting algorithms. It then covers sorting networks like bitonic sort, which can sort in parallel using a network of comparators. It discusses how bitonic sort can be mapped to hypercubes and meshes. It also covers parallel implementations of bubble sort variants, quicksort, and shellsort. For each algorithm, it analyzes the parallel runtime and efficiency. The document provides examples and diagrams to illustrate the sorting networks and parallel algorithms.
From the perspective of Design and Analysis of Algorithm. I made these slide by collecting data from many sites.
I am Danish Javed. Student of BSCS Hons. at ITU Information Technology University Lahore, Punjab, Pakistan.
This document discusses queuing analysis and its applications. Queuing theory models systems with queues and servers that process items. It is useful for analyzing network and system performance when load or design changes are expected. The document outlines different analysis methods and key metrics like arrival rate, service time, waiting time, number of items, and utilization. It also covers important assumptions like Poisson arrivals, service time distributions, Little's Law, and example applications like database servers and multi-processor systems.
Applying Reinforcement Learning for Network Routingbutest
This document discusses the application of reinforcement learning in network routing. It provides an overview of reinforcement learning, including its key elements like the agent, environment, policy, reward function, and value function. It also discusses important reinforcement learning problems like Markov decision processes and elementary methods including dynamic programming, Monte Carlo methods, and temporal-difference learning. Finally, it presents Q-routing and dual reinforcement Q-routing as examples of applying reinforcement learning concepts to optimize network routing.
This document discusses queueing theory and queuing networks. It begins by defining a queue as a model where arrivals come at random times and require random amounts of service from one or more servers. A queuing network can then be modeled as interconnected queues. Key inputs for analyzing a queue include the arrival and service processes, number of servers, and queueing rules. Additional inputs are needed for queueing networks, such as the interconnections between queues and routing strategies. Queues can be open, with arrivals from outside and departures, or closed, with a fixed number of jobs circulating. The document outlines analytical approaches for studying queues and networks through equilibrium analysis, focusing on obtaining mean performance parameters.
Big Graph Analytics Systems (Sigmod16 Tutorial)Yuanyuan Tian
In recent years we have witnessed a surging interest in developing Big Graph processing systems. To date, tens of Big Graph systems have been proposed. This tutorial provides a timely and comprehensive review of existing Big Graph systems, and summarizes their pros and cons from various perspectives. We start from the existing vertex-centric systems, which which a programmer thinks intuitively like a vertex when developing parallel graph algorithms. We then introduce systems that adopt other computation paradigms and execution settings. The topics covered in this tutorial include programming models and algorithm design, computation models, communication mechanisms, out-of-core support, fault tolerance, dynamic graph support, and so on. We also highlight future research opportunities on Big Graph analytics.
The document discusses performance evaluation of parallel computers. It defines key metrics like parallel runtime, speedup and efficiency used to evaluate parallel algorithms. Speedup is the ratio of sequential to parallel runtime and measures how faster a program runs in parallel. Efficiency measures processor utilization. The document also discusses performance measures, benchmarks, sources of parallel overhead, and performance models like Amdahl's law, Gustafson's law and Sun & Ni's law that define relationships between speedup, processors and problem size. It concludes with the scalability metric and isoefficiency function to measure a system's ability to efficiently use more processors by increasing problem size.
This document summarizes search algorithms for discrete optimization problems. It begins with an overview of discrete optimization and definitions. It then discusses sequential search algorithms like depth-first search, best-first search, A*, and iterative deepening search. The document next covers parallel search algorithms including parallel depth-first search using dynamic load balancing. It analyzes different load balancing schemes and evaluates them through experiments on satisfiability problems. Finally, it discusses techniques for termination detection in parallel search algorithms.
The document discusses parallel computing platforms and techniques for hiding memory latency. It covers the following key points:
1) Implicit parallelism in microprocessors has increased through pipelining and superscalar execution, but memory latency remains a bottleneck. Caches help reduce effective latency by exploiting data locality.
2) Multithreading and prefetching are approaches to hide memory latency by keeping the processor occupied while waiting for data, but they increase bandwidth demands and hardware costs.
3) Different applications utilize different types of parallelism, like data-level parallelism for throughput or task-level parallelism for aggregate performance. Understanding performance bottlenecks is important for parallelization.
The document discusses parallel algorithms and their analysis. It introduces a simple parallel algorithm for adding n numbers using log n steps. Parallel algorithms are analyzed based on their time complexity, processor complexity, and work complexity. For adding n numbers in parallel, the time complexity is O(log n), processor complexity is O(n), and work complexity is O(n log n). The document also discusses models of parallel computation like PRAM and designs of parallel architectures like meshes and hypercubes.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
1) The document proposes a mathematical model and optimization service to predict the optimal number of parallel TCP streams needed to maximize data throughput in a distributed computing environment.
2) It develops a novel model that can predict the optimal number using only three data points, and implements this service in the Stork Data Scheduler.
3) Experimental results show the optimized transfer time using this prediction and optimization service is much less than without optimization in most cases.
This document discusses analytical modeling of parallel systems. It begins by outlining topics like sources of overhead in parallel programs, performance metrics, and scalability. It then discusses basics of analytical modeling, noting that parallel runtime depends on input size, number of processors, and machine communication parameters. Several performance measures are introduced, like wall clock time and speedup. Sources of overhead like idling, excess computation, and communication are described. Metrics like parallel time, total overhead, speedup, and efficiency are formally defined. The impact of non-cost optimality and ways to build granularity are discussed. Finally, scaling characteristics and isoefficiency as a metric of scalability are covered.
- The document discusses methods for estimating traffic matrices, which describe the flow of traffic between origin-destination pairs in a network.
- Early methods relied on direct measurements, which are computationally intensive. Recent approaches use inference based on link measurements and routing information.
- Current research looks at techniques like principal component analysis, Kalman filtering, and incorporating additional data like access link measurements to improve estimates while reducing measurement needs. Hybrid methods combining analysis and some direct measurements are also promising.
Queuing theory is the mathematical study of waiting lines and delays. It examines properties like average wait time, number of servers, arrival and service rates. Queues form when demand for a service exceeds capacity. The simplest queuing system has two components - a queue and server - with attributes of inter-arrival and service times. Queuing models use Kendall notation to describe systems, and the M/M/1 model is commonly used to analyze average queue length, wait times, and probability of overflow for single server queues. Queuing theory has applications in fields like telecommunications, healthcare, and computer networking.
This document summarizes basic communication operations for parallel computing including:
- One-to-all broadcast and all-to-one reduction which involve sending a message from one processor to all others or combining messages from all processors to one.
- All-to-all broadcast and reduction where all processors simultaneously broadcast or reduce messages.
- Collective operations like all-reduce and prefix-sum which combine messages from all processors using associative operators.
- Examples of implementing these operations on different network topologies like rings, meshes and hypercubes are presented along with analyzing their communication costs. The document provides an overview of fundamental communication patterns in parallel computing.
The document discusses principles of parallel algorithm design. It introduces parallel algorithms, decomposition techniques, and characteristics of tasks and interactions. Recursive, data, exploratory, and hybrid decomposition techniques are covered. Mapping tasks to processes aims to minimize execution time by balancing load, minimizing interaction between processes, and assigning independent tasks to different processes. Granularity, degree of concurrency, and critical path length are used to analyze decompositions and their performance.
This paper investigates fairness among network sessions that use the Multiplicative Increase Multiplicative Decrease (MIMD) congestion control algorithm. It first studies how two MIMD sessions share bandwidth in the presence of synchronous and asynchronous packet losses. It finds that rate-dependent losses lead to fair sharing, while rate-independent losses cause unfairness. The paper also examines fairness between sessions using MIMD (e.g. Scalable TCP) versus Additive Increase Multiplicative Decrease (AIMD, e.g. standard TCP). Simulations show the AIMD sessions converge to equal throughput, while MIMD sessions' throughput depends on initial conditions. Adding rate-dependent losses can achieve fairness between
Self-adaptive container monitoring with performance-aware Load-Shedding policies, by Rolando Brondolin, PhD student in System Architecture at Politecnico di Milano
El aprendizaje colaborativo es una estrategia educativa en la que los estudiantes trabajan juntos en pequeños grupos para ayudarse mutuamente en el aprendizaje de un tema. Los estudiantes se ayudan entre sí y comparten recursos y conocimientos para mejorar su comprensión. Este método promueve la interacción social y el pensamiento crítico al exigir a los estudiantes que expliquen sus ideas y escuchen las perspectivas de los demás.
This document discusses various sorting algorithms that can be used on parallel computers. It begins with an overview of sorting and comparison-based sorting algorithms. It then covers sorting networks like bitonic sort, which can sort in parallel using a network of comparators. It discusses how bitonic sort can be mapped to hypercubes and meshes. It also covers parallel implementations of bubble sort variants, quicksort, and shellsort. For each algorithm, it analyzes the parallel runtime and efficiency. The document provides examples and diagrams to illustrate the sorting networks and parallel algorithms.
From the perspective of Design and Analysis of Algorithm. I made these slide by collecting data from many sites.
I am Danish Javed. Student of BSCS Hons. at ITU Information Technology University Lahore, Punjab, Pakistan.
This document discusses queuing analysis and its applications. Queuing theory models systems with queues and servers that process items. It is useful for analyzing network and system performance when load or design changes are expected. The document outlines different analysis methods and key metrics like arrival rate, service time, waiting time, number of items, and utilization. It also covers important assumptions like Poisson arrivals, service time distributions, Little's Law, and example applications like database servers and multi-processor systems.
Applying Reinforcement Learning for Network Routingbutest
This document discusses the application of reinforcement learning in network routing. It provides an overview of reinforcement learning, including its key elements like the agent, environment, policy, reward function, and value function. It also discusses important reinforcement learning problems like Markov decision processes and elementary methods including dynamic programming, Monte Carlo methods, and temporal-difference learning. Finally, it presents Q-routing and dual reinforcement Q-routing as examples of applying reinforcement learning concepts to optimize network routing.
This document discusses queueing theory and queuing networks. It begins by defining a queue as a model where arrivals come at random times and require random amounts of service from one or more servers. A queuing network can then be modeled as interconnected queues. Key inputs for analyzing a queue include the arrival and service processes, number of servers, and queueing rules. Additional inputs are needed for queueing networks, such as the interconnections between queues and routing strategies. Queues can be open, with arrivals from outside and departures, or closed, with a fixed number of jobs circulating. The document outlines analytical approaches for studying queues and networks through equilibrium analysis, focusing on obtaining mean performance parameters.
Big Graph Analytics Systems (Sigmod16 Tutorial)Yuanyuan Tian
In recent years we have witnessed a surging interest in developing Big Graph processing systems. To date, tens of Big Graph systems have been proposed. This tutorial provides a timely and comprehensive review of existing Big Graph systems, and summarizes their pros and cons from various perspectives. We start from the existing vertex-centric systems, which which a programmer thinks intuitively like a vertex when developing parallel graph algorithms. We then introduce systems that adopt other computation paradigms and execution settings. The topics covered in this tutorial include programming models and algorithm design, computation models, communication mechanisms, out-of-core support, fault tolerance, dynamic graph support, and so on. We also highlight future research opportunities on Big Graph analytics.
The document discusses performance evaluation of parallel computers. It defines key metrics like parallel runtime, speedup and efficiency used to evaluate parallel algorithms. Speedup is the ratio of sequential to parallel runtime and measures how faster a program runs in parallel. Efficiency measures processor utilization. The document also discusses performance measures, benchmarks, sources of parallel overhead, and performance models like Amdahl's law, Gustafson's law and Sun & Ni's law that define relationships between speedup, processors and problem size. It concludes with the scalability metric and isoefficiency function to measure a system's ability to efficiently use more processors by increasing problem size.
This document summarizes search algorithms for discrete optimization problems. It begins with an overview of discrete optimization and definitions. It then discusses sequential search algorithms like depth-first search, best-first search, A*, and iterative deepening search. The document next covers parallel search algorithms including parallel depth-first search using dynamic load balancing. It analyzes different load balancing schemes and evaluates them through experiments on satisfiability problems. Finally, it discusses techniques for termination detection in parallel search algorithms.
The document discusses parallel computing platforms and techniques for hiding memory latency. It covers the following key points:
1) Implicit parallelism in microprocessors has increased through pipelining and superscalar execution, but memory latency remains a bottleneck. Caches help reduce effective latency by exploiting data locality.
2) Multithreading and prefetching are approaches to hide memory latency by keeping the processor occupied while waiting for data, but they increase bandwidth demands and hardware costs.
3) Different applications utilize different types of parallelism, like data-level parallelism for throughput or task-level parallelism for aggregate performance. Understanding performance bottlenecks is important for parallelization.
The document discusses parallel algorithms and their analysis. It introduces a simple parallel algorithm for adding n numbers using log n steps. Parallel algorithms are analyzed based on their time complexity, processor complexity, and work complexity. For adding n numbers in parallel, the time complexity is O(log n), processor complexity is O(n), and work complexity is O(n log n). The document also discusses models of parallel computation like PRAM and designs of parallel architectures like meshes and hypercubes.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
1) The document proposes a mathematical model and optimization service to predict the optimal number of parallel TCP streams needed to maximize data throughput in a distributed computing environment.
2) It develops a novel model that can predict the optimal number using only three data points, and implements this service in the Stork Data Scheduler.
3) Experimental results show the optimized transfer time using this prediction and optimization service is much less than without optimization in most cases.
This document discusses analytical modeling of parallel systems. It begins by outlining topics like sources of overhead in parallel programs, performance metrics, and scalability. It then discusses basics of analytical modeling, noting that parallel runtime depends on input size, number of processors, and machine communication parameters. Several performance measures are introduced, like wall clock time and speedup. Sources of overhead like idling, excess computation, and communication are described. Metrics like parallel time, total overhead, speedup, and efficiency are formally defined. The impact of non-cost optimality and ways to build granularity are discussed. Finally, scaling characteristics and isoefficiency as a metric of scalability are covered.
- The document discusses methods for estimating traffic matrices, which describe the flow of traffic between origin-destination pairs in a network.
- Early methods relied on direct measurements, which are computationally intensive. Recent approaches use inference based on link measurements and routing information.
- Current research looks at techniques like principal component analysis, Kalman filtering, and incorporating additional data like access link measurements to improve estimates while reducing measurement needs. Hybrid methods combining analysis and some direct measurements are also promising.
Queuing theory is the mathematical study of waiting lines and delays. It examines properties like average wait time, number of servers, arrival and service rates. Queues form when demand for a service exceeds capacity. The simplest queuing system has two components - a queue and server - with attributes of inter-arrival and service times. Queuing models use Kendall notation to describe systems, and the M/M/1 model is commonly used to analyze average queue length, wait times, and probability of overflow for single server queues. Queuing theory has applications in fields like telecommunications, healthcare, and computer networking.
This document summarizes basic communication operations for parallel computing including:
- One-to-all broadcast and all-to-one reduction which involve sending a message from one processor to all others or combining messages from all processors to one.
- All-to-all broadcast and reduction where all processors simultaneously broadcast or reduce messages.
- Collective operations like all-reduce and prefix-sum which combine messages from all processors using associative operators.
- Examples of implementing these operations on different network topologies like rings, meshes and hypercubes are presented along with analyzing their communication costs. The document provides an overview of fundamental communication patterns in parallel computing.
The document discusses principles of parallel algorithm design. It introduces parallel algorithms, decomposition techniques, and characteristics of tasks and interactions. Recursive, data, exploratory, and hybrid decomposition techniques are covered. Mapping tasks to processes aims to minimize execution time by balancing load, minimizing interaction between processes, and assigning independent tasks to different processes. Granularity, degree of concurrency, and critical path length are used to analyze decompositions and their performance.
This paper investigates fairness among network sessions that use the Multiplicative Increase Multiplicative Decrease (MIMD) congestion control algorithm. It first studies how two MIMD sessions share bandwidth in the presence of synchronous and asynchronous packet losses. It finds that rate-dependent losses lead to fair sharing, while rate-independent losses cause unfairness. The paper also examines fairness between sessions using MIMD (e.g. Scalable TCP) versus Additive Increase Multiplicative Decrease (AIMD, e.g. standard TCP). Simulations show the AIMD sessions converge to equal throughput, while MIMD sessions' throughput depends on initial conditions. Adding rate-dependent losses can achieve fairness between
Self-adaptive container monitoring with performance-aware Load-Shedding policies, by Rolando Brondolin, PhD student in System Architecture at Politecnico di Milano
El aprendizaje colaborativo es una estrategia educativa en la que los estudiantes trabajan juntos en pequeños grupos para ayudarse mutuamente en el aprendizaje de un tema. Los estudiantes se ayudan entre sí y comparten recursos y conocimientos para mejorar su comprensión. Este método promueve la interacción social y el pensamiento crítico al exigir a los estudiantes que expliquen sus ideas y escuchen las perspectivas de los demás.
El documento habla sobre los efectos del calentamiento climático, incluyendo el aumento de la contaminación, la destrucción continua de la capa de ozono, y el incremento del efecto invernadero.
This document summarizes the activities of Rosehub, a small group of creative and tech-skilled individuals, in 2015. Some key points:
- They ran educational content on their YouTube channel rosehubTV, gaining over 1,250 subscribers and 130,000 views by December 2015. Content covered cultural sites across India.
- They conducted workshops on learning skills, math, animation, and filmmaking for schools, reaching over 150 students. Evaluations found the workshops improved students' math skills and engagement.
- As Rosehub Studio, they provided design, video, and photography services for business and personal clients, creating websites, videos, and other marketing materials.
- Plans for 2016 included documenting 51
The document discusses the changing consumer behavior landscape and rise of social and data-driven marketing. It notes that consumers are more savvy and demanding than ever, controlling when and where they buy. Brands must have multi-platform sales strategies and take a "phygital" approach, integrating social and digital into their retail strategies. It emphasizes that understanding consumer passions and influences through psychographic profiling is key to deeper engagement and repeat business in today's changing environment.
Melanie Chudyk has experience working for Elections Manitoba and as a foster provider. She previously worked for DASCH Inc. from 2002-2015 in roles such as case management, foster care coordination, and staff supervision. She has certifications in first aid, non-violent crisis intervention, applied physical techniques, and suicide prevention. Her work history also includes positions as a program coordinator, manager, substitute teacher, and child care coordinator dating back to 1998. She holds a Bachelor of Education degree from the University of Winnipeg.
The document summarizes research on using blogs as electronic portfolios for student teachers. It finds that student teachers were generally satisfied with using an online website builder to create blog-based portfolios, finding it user-friendly. Student teachers also felt more knowledgeable about applying blog portfolios for learning and teaching after receiving information technology training. Elements like discussion forums, blog posts, polls and embedded videos were seen as enhancing communication between teachers and students.
The document describes updates to Recruiting Solutions' project and clipboard functionality. The updates include:
1) Making the "Add to project" and "Add to clipboard" buttons more prominent in the profile view.
2) Allowing users to easily see which projects a profile is already added to and add/edit status values.
3) Allowing users to remove a profile from a project or clipboard directly from the profile view with an "undo" option.
Up north apparel company report new new newElizabeth Bahr
This document provides an overview of the Up North Apparel company started by students at West Fargo High School as part of a Junior Achievement program. Up North Apparel sells long sleeve pocket tees that embrace northern styles. The company has generated over $2000 in sales since March 2016. It has a website and social media presence and is working to expand distribution to local retailers. The students have learned valuable business lessons through starting this company and plan to continue operating Up North Apparel beyond the Junior Achievement program.
Ankush Sharma is seeking a job as an electrical engineer where he can upgrade his skills working with experienced professionals. He has a Bachelor's degree in Electrical Engineering with over 70% marks. His experience includes roles in sales engineering, design engineering, and estimation engineering where he was responsible for tasks like cable sizing, cost estimating, and developing new products. He has strong organizational, technical, and communication skills and is proficient in software like MS Office and MS Project.
John J. Cederstrom is seeking a position that utilizes his strong communication, problem-solving, and customer service skills. He has over 20 years of experience in customer service roles including as a corrections officer, assistant general manager, and driver for Papa John's Pizza. Cederstrom has multiple degrees including an Associate's in General Studies, Bachelor's in Criminal Justice, and some coursework completed towards a Master's in Criminal Justice/Homeland Security. He is skilled in areas such as corrections, leadership, research, and maintaining calm under pressure.
This document is a resume for Zachary Taylor Eich. It outlines his education at Saint John's University where he is majoring in computer science and anticipates graduating in May 2015. It also lists his related coursework and programming knowledge. For related experience, it describes his internship with the US Army in Africa, leadership roles in military training programs, and experience shadowing an Army Lieutenant. It concludes with additional experience as a firefighter and interests including commissioning as an Army 2nd Lieutenant and running marathons.
London Exponential Technologies Meetup Peter Morgan
This document summarizes an inaugural meetup on exponential technologies hosted by the London Exponential Technologies Meetup group. It provides an overview of several major exponential technologies that will be covered by future meetups, including artificial intelligence, longevity, bioengineering, and quantum computing. It also lists recommended reading materials on these topics and announces upcoming meetup themes on robotics, high-performance computing, quantum computing, and other emerging technologies. The meetup is sponsored by organizations like the Data Science Partnership, Innovation Warehouse, O'Reilly, and Nvidia.
O documento conta a história de dois amigos que decidiram escalar uma montanha na Suíça sem guia. Ignoraram os avisos de um pastor e acabaram presos na montanha durante a noite em uma tempestade. Sobreviveram por pouco à hipotermia. A história serve como lição sobre a importância de contar com a ajuda de um guia experiente, assim como Jesus é o guia espiritual para alcançarmos nossas metas no novo ano.
Topics covered in this presentation:
1. What is drive testing?
2. Need for drive testing?
3. Types of drive testing
4. Key Performance Indicators and Parameters
5. Test Methods
Dokumen tersebut membahas tentang sinergitas pembentukan gugus paud sebagai layanan pendidikan anak usia dini yang terdiri dari satu paud inti dan beberapa paud imbas. Gugus paud dibentuk untuk meningkatkan kualitas layanan pendidikan anak usia dini melalui pembinaan kompetensi pendidik dan pengelola paud serta memanfaatkan sumber belajar setempat.
Este documento describe el diagnóstico y tratamiento del edentulismo total. Explica las consecuencias anatómicas, estéticas y psicológicas de la pérdida de todos los dientes, así como los mecanismos de soporte, retención y estabilidad de las prótesis totales. También clasifica a los pacientes edéntulos según la altura y localización ósea residual para determinar el tipo de prótesis apropiado.
Georgia Tech: Performance Engineering - Queuing Theory and Predictive ModelingBrian Wilson
This is one lecture in a semester long course \'CS4803EPR\' I put together and taught at Georgia Tech, entitled "Enterprise Computing Performance Engineering"
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Performance Engineering Overview - Part 2…
Queuing Theory Overview
Early life-cycle performance modeling
Simple Distributed System Model
Sequence Diagrams
Maximum Likelihood Estimation of Closed Queueing Network Demands from Queue L...Weikun Wang
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Nafems15 Technical meeting on system modelingSDTools
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C:\Documents And Settings\User\桌面\Sciece Talk投影片\Science Talk 100111 陸行guestf4730f1
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Automated Parameterization of Performance Models from Measurements
1. Automated Parameterization of
Performance Models from
Measurements
Giuliano Casale
Imperial College London, UK
Simon Spinner
University of Würzburg, Germany
Weikun Wang
Imperial College London, UK
Tutorial @ ICPE 2016, Delft, the Netherlands, March 13, 2016
2. 2
Workload Characterization
Common parameters in performance models:
Service demand of a request
CPU time, bandwidth consumed, …
Arrival rate of requests
Applications
Automated performance modelling
Resource cost splitting
Performance anomaly detection
…
4. 4
Example: Cost Splitting
Carico Workload 1
Transazioni/ora
Lun Mar Mer Gio Ven Sab Dom
0100200300400
Carico Workload 2
Transazioni/ora
050150250
Lun Mar Mer Gio Ven Sab Dom
Ripartizione dei Costi
UtilizzoCPU-%
020406080100
Lun Mar Mer Gio Ven Sab Dom
Carico Workload 3
Transazioni/ora
050100150200
Lun Mar Mer Gio Ven Sab Dom
Workload 1
Workload 2
Workload 3
#Transactions#Transactions#Transactions
Mo Tu We Th Fr Sa Su
Mo Tu We Th Fr Sa Su
Mo Tu We Th Fr Sa Su
Mo Tu We Th Fr Sa Su
How to recover weight of individual
contributions to utilization?
Utilization[0-100%]
We know from theory that the weight is
exactly the service demand!
5. 5
A Typical Challenge
5
HTTP Requests
in the WS
(Web Server)
Observation period T
1 request in WS
3 requests in WS
0 requests in WS
Time
6. 6
A Typical Challenge
OS schedules jobs in round robin
If n requests run simultaneously, each will
approximately receive 1/n of the CPU time
Process Sharing is a round robin where the
quantum of time assigned to each request is
infinitesimal
6
X X
Service time S
of the yellow request
Time
CPU
33% CPU
time each
50%
each
100%
for blue
X
Quantum
Requests
Arrive
Simultaneously
3 requests
running
10. 3
Response Time Approximation
Trivial approximation: 𝐷𝐷𝑖𝑖,𝑐𝑐 ≈ 𝑅𝑅𝑐𝑐
Assumptions
resource dominates system response time
waiting time in queue ≪ 𝐷𝐷𝑖𝑖,𝑐𝑐
Only applicable at low resource utilization
11. 4
Service Demand Law
Basic operational law:
𝐷𝐷𝑖𝑖,𝑐𝑐 =
𝑈𝑈𝑖𝑖,𝑐𝑐
𝑋𝑋0,𝑐𝑐
Partial utilization 𝑈𝑈𝑖𝑖,𝑐𝑐 is hard to derive
Operating system: per-process statistics
Profilers: high-overheads
2 alternative solutions:
Controlled experiment
Partitioning
12. 5
Controlled Experiment
Measurement
Interval
CPU Utilization
Requests executed in separate experiments
Resource
Demand
Problems:
Not applicable at runtime
Mutual interference
40%
Request1
30%
Request2
13. 6
Partitioning
Measurement
Interval
CPU Utilization
Mixed Workload
How to partition
processing time?
Response times
Additional performance counters
60%
Request2
Request1
?
14. 7
Estimation Approaches
Data Collection Data Collection
Demand Estimation
Demand Estimation
Modeling Assumptions
(scheduling, service distribution)
Modeling Assumptions
(scheduling, service distribution)
Model Solution Model Solution
Utilization Approach Response Time Approach
18. 11
Other Approaches
Robust regression
Least Absolute Differences: Zhang et al. (2007)
Least Trimmed Squares: Casale et al. (2008)
Machine-learning
Clusterwise linear regression: Cremonesi et al. (2010)
Pattern matching: Cremonesi et al. (2014)
19. 12
Utilization Approaches
Utilization-based approaches
Advantages
Only utilization and throughput data required
Minimal assumptions:
– Any scheduling strategy
– Any interarrival distribution
– (Any service time distribution)
Disadvantages
Robustness
Amount of data
20. 13
Response Time Approaches
Assumptions
Single queue: closed-form solution exists
Queueing network: product-form
Response time equations depend on
Scheduling strategy
Service distribution
Interarrival time distribution
If M/G/1 with PS or LCFS
or M/M/1 with FCFS and class-independent service
times, then 𝑅𝑅 =
𝐷𝐷
1−𝑈𝑈
21. 14
General Optimization
Assumptions:
Variables 𝑫𝑫 = (𝐷𝐷1,1, … , 𝐷𝐷1,𝑛𝑛, … , 𝐷𝐷𝑖𝑖,1, … , 𝐷𝐷𝑖𝑖,𝑛𝑛)
Queueing Network QN 𝒛𝒛 = 𝑓𝑓(𝑫𝑫)
Observation data 𝒛𝒛�
Optimization Problem:
min
𝑫𝑫
𝒛𝒛 − 𝒛𝒛�
𝑫𝑫 may be subject to certain constraints
arbitrary norm
22. 15
Examples
Menascé (2008):
Liu et al. (2006):
Squared response time error Product-form solution (non-linear!)
Constrained to valid solutions
23. 16
Kalman Filter
Dynamical system
State model:
𝑿𝑿𝑘𝑘=𝑭𝑭𝑘𝑘−1 𝑿𝑿𝑘𝑘−1+𝑩𝑩𝑘𝑘−1 𝒖𝒖𝑘𝑘−1 + 𝒘𝒘𝑘𝑘−1
Observation model:
𝒁𝒁𝑘𝑘 = 𝑯𝑯𝑘𝑘 𝑿𝑿𝑘𝑘+𝒗𝒗𝑘𝑘
Filter
𝒛𝒛𝑘𝑘, 𝒛𝒛𝑘𝑘−1, 𝒛𝒛𝑘𝑘−2, … , 𝒛𝒛1 𝑿𝑿� 𝑘𝑘~𝑁𝑁(𝒙𝒙�𝑘𝑘, 𝑷𝑷� 𝑘𝑘)
observations
previous state controlled input uncorrelated noisenext state
estimated mean value
estimated covariance
time-series of observations
observation noise
24. 17
Applied to Demand Estimation
State vector 𝑿𝑿𝑘𝑘 = 𝑫𝑫
Constant state model 𝑿𝑿𝑘𝑘=𝑿𝑿𝑘𝑘−1 + 𝒘𝒘𝑘𝑘−1
Observation model (e.g., Kumar et al. 2009)
𝑅𝑅1
⋮
𝑈𝑈
=
𝐷𝐷1
1 − 𝑈𝑈
⋮
𝑋𝑋1 ∙ 𝐷𝐷1 + ⋯ + 𝑋𝑋𝐶𝐶 ∙ 𝐷𝐷𝑐𝑐
Other observation models are possible (e.g.,
Zheng et al. 2008, Wang et al. 2012)
28. 2
Paradigm Shift
Demand Estimation
Modeling Assumptions
(Scheduling, Service Distribution)
Model Generation and Solution
Data Collection
Demand Estimation
Modeling Assumptions
(Scheduling, Service Distribution)
Model Generation and Solution
Data Collection
Utilization Approach Response Time Approach
29. 3
Estimate demand D from response time R
We investigate the likelihood function in
First-Come First-Served (FCFS) queues
– e.g., admission control, disk drive buffers, …
Processor Sharing (PS) queues
– e.g., CPUs, bandwidth sharing, …
Observation
R
D4
D3
D1
D2D0
1. For each observed R sample
2. Draw D from parameter space
3. Compute likelihood P[R|D]
4. Move in parameter space to
maximize P[R|D]
Parameter Space
Maximum Likelihood Estimator
30. 4
Model response time using absorbing CTMCs
Under FCFS, future arrivals do not affect
response time distribution of the tagged job
RT Likelihood in FCFS queues
D1D2 D2 D1D1
nK, jobs of class k in queue
D1D1
1
2
3
45
1
Absorbingtransition
Model
State Space of
Markov Chain
2
1
D1D2 D2 D1 D1
3
D1D2 D2
4
D2 D2
5
D2
1
31. 5
RT Likelihood in FCFS queues
Probability of being absorbed by time t
into a give CTMC state
Well-understood: PH-type distributed
FCFS Example:
Backlog
seen
upon
arrival
Class 1 arrival
ML Problem (K classes)
32. 6
Monitoring dataset
Active mix: (1 ,2 ,1 ,1 , 0 )
Admission state (mix) and response times
Assumptions
V CPUs
R Classes +
Class switching
W Workers
…
Admission
Response time
Multi-core server
33. 7
PI: Trajectory Inference
Class switching probabilities
Users submit requests cyclically
Requests issued change class over time
Closed class-switching queueing model
V CPUs, R classes O(V2R) states
Inference of trajectory too complex
?
34. 8
Dataset characteristics
CI: Complete information (baseline)
V=1 CPU: full state trajectory
V>1 CPUs: no individual CPU states
We split demand proportionally, taking into
account the active workers
PI: Partial information
Sample admission state and response time
Mean throughput is assumed known
35. 9
CI: Demand estimation
V=1 CPU
Full demand distribution Request
Runtime
Active workers
Demand
Request j
Class r
Scale by Active CPUs V>1 CPU
37. 11
CI requires very detailed measurements
Closed queueing network model
Assume a fixed mix as seen upon job arrival
No class switching ( tractable)
Model can estimate response time of arriving job
PI: Approximation
CPU-0
CPU-1
Admission
Inter
Admission
Time
CPU 0+1
(PS queue)
38. 12
V=1 CPU
Model assumed in equilibrium
RPS: Regression Approach
Queue seen
at admission
(incl. arriving job)
Response
Time
Class r
V>1 CPU
Individual CPU state estimated
Demand
Class r
Average queue per CPU
40. 14
MLPS: Maximum Likelihood
Maximum Likelihood Estimation (MLPS)
Search over mean demand guesses
Maximize likelihood of observed dataset
Response time likelihood
Tagged customer method (absorbing CTMC)
Initialized with state seen upon admission
Mean demand guess CTMC rates
41. 15
Job of class 3 arrives at system with V=1 CPU
Mix seen upon arrival: 1 job of class 1, 3 jobs of class 2
We study the transient of this CTMC to obtain the
response time distribution of the class-3 job
MLPS: Absorbing CTMC
0,0,1
1,0,1
0,1,1
0,2,1
0,2,1
1,1,1
0,3,1
1,2,1
1,3,1
1/E[D3]
1/(2E[D3])
1/(3E[D3])
1/(4E[D3])
1/(5E[D3])
1/(4E[D3])
1/(3E[D3])
1/(2E[D3])
1/(3E[D3])
Initial state
Transitions depend
on E[D1] and E[D2]
42. 16
MLPS: Absorbing CTMC
V=1 CPU
Dataset:
Likelihood function for each sample:
V>1 CPUs
Load-dependent rates
init with state at
admission
trajectory
in ri sec
completion rates
CTMC generator1/demand
46. 20
MinPS: Sensitivity Analysis
Magnitude of class demands
3 orders of difference: CI gap ~insensitive
Class switch probability
High / Rare: CI gap ~insensitive
Non-exponential service
low CV: CI gap weakly sensitive
high CV: CI gap ~insensitive for CV<2
47. 21
Case Study: SAP ERP
3-tier commercial application
Modified MLPS with setup times
Transactions grouped in R=2 classes
Response Time
User 1
Worker Database
SAP ERP Application Server
Workload
Generator
Dispatcher
SAP ERP Database
48. 22
0
0.05
0.1
0.15
0.2
0.25
N 5N 7N 10N 15N
MEAS
SIM
SAP ERP Queueing Model
Measured vs Simulation with Estimated Demands
Population - Baseline N = [6 jobs class 1, 4 jobs class 2]
ResponseTime
49. 23
Fluid MLPS (FMLPS)
Limit behaviour of the CTMC for growing rates
and requests increasingly deterministic
V=scale factor. Request mix is unchanged.
Limit behaviour can be modelled via ODEs
State
occupancy
measure
at time t=100
53. 27
Monitor occupancy at all resources
Observations:
Ill-posed, unless think times known
Probabilistic model of distributed system
Gibbs: iteratively sample posterior
Gibbs Sampling (GQL)
prior
58. 32
GQL vs Other MCMC Methods
Far better convergence properties than
Metropolis-Hastings and Slice sampling
About 13-15% error in estimating demands
against cloud ERP data (Apache OFBiz)
59. 33
QMLE Approximation
Based on Maximum Likelihood Estimation
Works with mean queue length
A simple approximation of the MLE:
Consider the demand vector where
More details at tomorrow’s talk!
61. 35
Tool support
FG - “Filling-the-Gap”
Batch offline analysis, support for Condor
Open Source Software
MCR executables (BSD-3)
Main repo:
https://github.com/Imperial-AESOP/Filling-the-Gap
Manual available in the repo
62. 36
FG: Initial design
Outputs
Model parameters
Visualization
Forecasting
–Requires analysis, but not decision-making
User control knobs
Analysis frequency
Horizon of analysis
Monitoring intensity
Maximum collection window
68. 2
Monitor occupancy at all resources
Observations:
Ill-posed, unless think times known
Probabilistic model of distributed system
Markov-Chain Monte-Carlo (MCMC)
draw samples from target distribution
averaging samples provides estimate
Gibbs Sampling (GQL)
75. 9
GQL vs Other MCMC Methods
Far better convergence properties than
Metropolis-Hastings and Slice sampling
About 13-15% error in estimating demands
against cloud ERP data (Apache OFBiz)
76. 10
QMLE Approximation
Based on Maximum Likelihood Estimation
Works with mean queue length
A simple approximation of the MLE:
Consider the demand vector where
Approach generalizes to load-dependent QNs
More details at tomorrow’s talk!
78. 12
Tool support
FG - “Filling-the-Gap”
Batch offline analysis, support for Condor
Open Source Software
MCR executables (BSD-3)
Main repo:
https://github.com/Imperial-AESOP/Filling-the-Gap
Manual available in the repo
79. 13
FG: Initial design
Outputs
Model parameters
Visualization
User control knobs
Analysis frequency
Horizon of analysis
Algorithm selection
87. 4
Compared Approaches
Based on Service Demand Law (Brosig et al.
2009)
Utilization Regression (Rolia and Vetland 1995)
Kalman Filter (Kumar et al. 2009)
Opitimization 1 (Menascé 2008)
Optimization 2 (Liu et al. 2006)
Response time regression (Kraft et al. 2009)
Gibbs Sampling (Wang et al. 20133)
89. 6
Number of Samples
0
1
2
3
4
5
6
7
8
SDL Util.
Regression
Kalman Filter Optim. 1 Optim. 2 Rt. Regression Gibbs
RelativeError(in%)
600 samples 3600 samples
Dataset D1
Number of samples has only limited impact.
90. 7
Number of Workload Classes
0
20
40
60
80
100
120
140
160
180
SDL Util.
Regression
Kalman Filter Optim. 1 Optim. 2 Rt.
Regression
Gibbs
RelativeError(in%)
1 class 2 classes 5 classes
Dataset D1
Number of classes has strong impact on D1.
91. 8
Number of workload classes
0
5
10
15
20
25
30
SDL Util.
Regression
Kalman Filter Optim. 1 Optim. 2 Rt. Regression Gibbs
RelativeError(in%)
1 class 2 classes 3 classes
Dataset D2
Number of classes has a much smaller impact on D2.
102. 19
Case Study: SAP HANA
Admission control
Multi-tenant application (extended TPC-W)
SAP HANA cloud platform
Supports Performance isolation between tenants
IEEE/ACM CCGrid 2014.
106. 23
Case Study: Zimbra
Goal: Automatic vertical CPU scaling of VMs
Zimbra is a collaboration server
Transactional workload
SLA: Mails need to be delivered within 2 minutes
Mails may be queued
IEEE SASO 2014.
108. 25
Layered Performance Model
Application
layer
Virtual resource
layer
Physical resource
layer
VM1 VM2vApp
vCPU vCPU
Physical CPU
Service rate depends
on physical hardware
+ Hypervisor Scheduling
Delays
+ OS scheduling delays
+ Wait times for other
resources
Hierarchical modeling approach (Method of Layers [1]):
Service time at layer 𝑖𝑖 is equal to response time of an underlying closed queueing network
at layer 𝑖𝑖 − 1
Load-dependent
Service Demands
109. 26
Influence of Layers
Zimbra MTA with linearly increasing workload:
Demands(inseconds)
Estimated demands reflect contention at hypervisor and
application level
110. 27
Reconfigurations
Controller Mean
latency [s]
Reconfigurations Mean
vCPUs
Max
vCPUs
Model-based 20.48 13 1.4 2
Trigger-based
(1 min)
10.82 273 1.83 3
Trigger-based
(5 min)
25.97 72 1.46 3
Static allocation 1385 0 1 1
Zimbra MTA VM:
Model-based controller needs less reconfigurations and
resources
111. 28
Bibliography
Menascé, D. A. (2008). “Computing missing service demand
parameters for performance models”. In: CMG Conference
Proceedings, pp. 241–248
Liu, Z., L. Wynter, C. H. Xia, and F. Zhang (2006). “Parameter
inference of queueing models for IT systems using end-to-end
measurements”. In: Perform. Eval. 63.1, pp. 36–60
Kumar, D., A. N. Tantawi, and L. Zhang (2009a). “Real-time
performance modeling for adaptive software systems with multi-
class workload”. In: Proceedings of the 17th Annual Meeting of the
IEEE/ACM International Symposium on Modelling, Analysis and
Simulation of Computer and Telecommunication Systems,
MASCOTS, pp. 1–4
Zheng, T., C. M. Woodside, and M. Litoiu (2008). “Performance
Model Estimation and Tracking Using Optimal Filters”. In: IEEE
Trans. Software Eng. 34.3, pp. 391–406
112. 29
Bibliography
Wang, W., X. Huang, X. Qin, W. Zhang, J. Wei, and H. Zhong
(2012). “Application-Level CPU Consumption Estimation: Towards
Performance Isolation of Multi-tenancy Web Applications”. In:
Proceedings of the 2012 IEEE Fifth International Conference on
Cloud Computing, CLOUD, pp. 439–446
Brosig, F., S. Kounev, and K. Krogmann (2009). “Automated
extraction of palladio component models from running enterprise
Java applications”. In: Proceedings of the 4th International
Conference on Performance Evaluation Methodologies and Tools,
VALUETOOLS, p. 10
Rolia, J. and V. Vetland (1995). “Parameter estimation for
performance models of distributed application systems”. In:
Proceedings of the 1995 Conference of the Centre for Advanced
Studies on Collaborative Research, CASCON, p. 54
113. 30
Bibliography
Kraft, S., S. Pacheco-Sanchez, G. Casale, and S. Dawson (2009).
“Estimating service resource consumption from response time
measurements”. In: Proceedings of the 4th International
Conference on Performance Evaluation Methodologies and Tools,
VALUETOOLS, p. 48
Wang, W. and G. Casale (2013). “Bayesian Service Demand
Estimation Using Gibbs Sampling”. In: Proceedings of the 2013
IEEE 21st International Symposium on Modelling, Analysis and
Simulation of Computer and Telecommunication Systems,
MASCOTS, pp. 567–576
G. Casale, P. Cremonesi, R. Turrin, Robust Workload Estimation in
Queueing Network Performance Models, in: 16th Euromicro
Conference on Parallel, Distributed and Network-Based Processing
(PDP), 2008, pp. 183-187.
114. 31
Bibliography
P. Cremonesi, K. Dhyani, A. Sansottera, Service Time
Estimation with a Refinement Enhanced Hybrid Clustering
Algorithm, in: Analytical and Stochastic Modeling Techniques
and Applications, Vol. 6148 of Lecture Notes in Computer
Science, Springer Berlin / Heidelberg, 2010, pp. 291--305
P. Cremonesi, A. Sansottera, Indirect estimation of service
demands in the presence of structural changes, Performance
Evaluation 73 (0) (2014) 18--40, special Issue on the 9th
International Conference on Quantitative Evaluation of Systems
116. 2
Outline
Introduction
Moments and probabilities in Marked MAPs
Fitting of second-order acyclic Marked MAPs
Results
Conclusions
117. 3
Requests Traffic
Time-Varying Peaks of User Activity
High
Performance
Will the system
sustain the load?
Sun Mon Tue Wed Thu
request number
Inter-arrival times
[µs]
FAST
RATE
SLOW
RATE
SLOW
RATE
FAST
RATE
SLOW
RATE
118. 4
Stochastic models
Generate statistically similar request arrival patterns
Analytical models accelerate search for optimal decisions
Markovian Traffic Model
request number
Inter-arrival times
[µs]Arrival Process Modelling
Stochastic analysis
SLOW
RATE
FAST
RATE
FAST
RATE
SLOW
RATE
30%
70%
50%
50%
Request number
Interarrivaltime[ms]
119. 5
Stochastic models
Generate statistically similar request arrival patterns
Analytical models accelerate search for optimal decisions
Arrival Process Modelling
SLOW
RATE
FAST
RATE
FAST
RATE
SLOW
RATE
Markovian Traffic Model Automated fitting methods
30%
70%
50%
50%
Models evaluated: ~350Initial Guess
120. 6
Network of queues
mathematical abstraction for prediction, what-if scenarios, …
describes billions of possible states for the resources
efficient output analysis techniques [Smirni, QEST’09]
Incoming
Requests
Traffic Decomposition for QN
FAST
RATE
SLOW
RATE
Completed
Requests
Web Server
Storage
Database
CPU
Disks
CPUs
Cloud
Resources
121. 7
Network of queues
mathematical abstraction for prediction, what-if scenarios, …
describes billions of possible states for the resources
developed efficient analysis techniques
Output Flow
Traffic Decomposition for QN
Completed
Requests
Storage
Database
Disks
CPUs
FAST
RATE
SLOW
RATE
SLOW
RATE
Cloud
Resources
122. 8
Network of queues
mathematical abstraction for prediction, what-if scenarios, …
describes billions of possible states for the resources
developed efficient analysis techniques
Output Flow
Traffic Decomposition for QN
Completed
Requests
Storage
Database
Disks
CPUs
FAST
RATE
SLOW
RATE
SLOW
RATE
Cloud
Resources
123. 9
Network of queues
mathematical abstraction for prediction, what-if scenarios, …
describes billions of possible states for the resources
developed efficient analysis techniques
Output Flow
Traffic Decomposition for QN
Completed
Requests
SLOW
RATE
FAST
RATE
SLOW
RATE
FAST
RATE
Cloud
Resources
125. 11
PH-type Distribution
N transient states
Exit vector
No-mass at 0 assumption
CTMC
Representation PH(D0, α)
1 absorbing state
Phase-type Distribution: distribution of the time to absorption
126. 12
PH-type Renewal Process
Renewal Process with Phase-type distribution
Inter-arrival times: i.i.d. with PH(D0, α) distribution
Counting process N(t) is a CTMC
Blocks of N states
Block k: N(t) = k
After absorption, go to block k+1
Initial state in block k+1: probability α
Rate of exit from state i and restart from state j = si αj
⋅
⋅
⋅
=
α
α
α
sD
sD
sD
Q
0
0
0
00
00
00
Transitions in block k
N(t) = 2
N(t) = 3
Event: exit from block k, restart from block k+1
N(t) = 1
127. 13
Some Tools for PH Fitting
EMpht (1996)
http://home.imf.au.dk/asmus/pspapers.html
EM algorithm for ML fitting, based on Runge-Kutta
methods
Local optimization technique
jPhase (2006)
http://copa.uniandes.edu.co/software/jmarkov/index.html
Java library
ML and canonical form fitting algorithms
128. 14
Some Tools for PH Fitting
PhFit (2002)
http://webspn.hit.bme.hu/∼telek/tools.htm
Separate fit of distribution body and tail
Both continuous and discrete ML distributions
G-FIT (2007)
http://ls4-www.cs.uni-dortmund.de/home/thummler/gfit.tgz
Hyper-Erlang PHs used as building block
Automatic aggregation of large traces, dramatic
speed-up of computational times compared to EMpht
129. 15
Correlated Arrivals
Microsoft Live Maps Back End Trace
Disk read/write inter-issue time
Phase-type Renewal Processes Markovian Arrival Processes
130. 16
Markovian Arrival Process
Phase-type Renewal Process
Rate of exit from state i and restart from state j = si αj
Markovian Arrival Process (MAP)
Rate of exit from state i and restart from state j = sij
Generalization of PH-Renewal: allows to model correlation
=
10
10
10
00
00
00
DD
DD
DD
Q
−
−
−
=
nnn rr
rr
rr
D
λ
λ
λ
21
23221
13121
0
−
=
nnnn sss
sss
sss
D
21
232221
131211
1
Representation: MAP(D0,D1)
Interval-stationary initialization
131. 17
Tools for MAP fitting
KPC-Toolbox (2008)
http://www.cs.wm.edu/MAPQN/kpctoolbox.html
Moment-matching method
Composition of large MAPs by two-state MAPs
Property of KPC Process (similar relations for
higher-order moments, ACF, …)
KPC Process
!/][][][ kXEXEXE k
b
k
a
k
=
132. 18
Motivation and Goals
Marked Markovian Arrival Processes (MMAPs)
Generalization of MAPs to model multi-class arrivals
Allow to model non-Poisson cross-correlated arrivals
Allow efficient solution of the models with matrix-
analytic methods
Modeling the arrival process at a queuing
system (MMAP[K]/PH[k]/1-FCFS queue)
FCFS queues can be analyzed analytically using age process
Q-MAM: https://bitbucket.org/qmam/qmam/src
BU-Tools: http://webspn.hit.bme.hu/~telek/tools/butools/
133. 19
Multi-class Arrivals
Microsoft Live Maps Back End Trace
Disk read/write inter-issue time
Markovian Arrival Processes Marked Markovian Arrival Processes
134. 20
Marked MAPs
(D0,D1) is a representation of
the MAP underlying the MMAP
(D0,D11,D12) is a representation of a
MMAP[2] process (2 classes)
135. 21
Fitting
Fitting problem
Marked trace from a real system: (Xi, Ci) MMAP
Queues with arrivals that follow MMAP can be solved
analytically
Two families of methods
Maximum-likelihood
Matching moments (or other characteristics)
We focus on moment matching
More computationally efficient
In real systems, easier to save moments than the whole
trace
136. 22
Issues of moment matching
Representation of MMAPs is not minimal
Number of parameters >> Degrees of freedom
Hard to obtain analytical fitting formulas for
the parameters
Easy: Parameters -> Moments
Hard: Moments -> Parameters
Requires solving a non-linear system of equations in the
general case
Non-linear least squares for MMAP fitting [Buchholz, 2010]
137. 23
Issues of moment matching
Feasibility: given a number of states n for the
MMAP, which values of the moments can be fitted
exactly?
Related issue: how to perform approximate fitting?
Which characteristics best capture the queueing
behavior?
Caveat 1: not all characteristics have known analytical
formulas
Caveat 2: inverting the analytical formulas might be harder
for some characteristics
139. 25
Definitions
Ordinary moment of order j:
Backward moment of order j for class c (green):
Forward moment of order j for class c (green):
Cross moments of order j for class c followed by class k:
Probability of a class c arrival:
“Transition” probability of a class c arrival followed by class k
140. 26
Moment Dependencies
Ordinary moments can be expressed as linear
combination of
the forward moments, weighted by the class probabilities
the backward moments, weighted by the class probabilities
the cross moments, weighted by the class-transition probabilities
For 2 classes and j = 1
Linear system for M1ck
4 unknowns, rank 3
A cross-moment might
be needed to uniquely
determine a second-
order MMAP[2]
142. 28
AMMAP[2] Fitting
7 degrees of
freedom
4 for the
underlying
AMAP
3 for the
marginal
Phase-type
1 for the
auto-
correlation
decay
3 for
multi-class
characteristics
D0 D1
143. 29
AMMAP[2] Fitting
Any MAP(2) has geometric autocorrelation decay with rate γ
• Canonical form for the underlying MAP(2) [Bodrog et al., 2010]
Acyclic: two forms for γ > 0 and γ < 0
For γ = 0, acyclic phase-type renewal
γ > 0 γ < 0
144. 30
AMMAP[2] Fitting
Any MAP(2) has geometric autocorrelation decay with rate γ
• Canonical form for the underlying MAP(2) [Bodrog et al., 2010]
Acyclic: two forms for γ > 0 and γ < 0
For γ = 0, acyclic phase-type renewal
γ > 0 γ < 0
145. 31
AMMAP[2] Fitting
Any MAP(2) has geometric autocorrelation decay with rate γ
• Canonical form for the underlying MAP(2) [Bodrog et al., 2010]
Acyclic: two forms for γ > 0 and γ < 0
For γ = 0, acyclic phase-type renewal
γ > 0 γ < 0
3 degrees of freedom 3 degrees of freedom
146. 32
AMMAP[2] Fitting
How to spend the 3 available degrees of
freedom?
We have found closed, analytical formulas for the
three parameters q11, q21, q22, for both canonical
forms
Three different sets of characteristics considered
Class probabilities and…
1) Forward moments and backward moments
2) Forward moments and class transition probabilities
3) Backward moments and class transition probabilities
147. 33
AMMAP[m] Fitting
How to handle more than 2 classes?
p1 = 0.29
F11 = 0.08
B11 = 0.08
p2 = 0.43
F12 = 0.13
B12 = 0.12
p3 = 0.29
F13 = 0.08
B13 = 0.09
148. 34
M3A Toolbox
Latest version:
https://github.com/Imperial-AESOP/M3A
A set of Matlab functions designed for computing
the statistical descriptors of MMAPs and fitting
marked traces with MMAPs
Syntax compatibility with KPC-Toolbox
– M3A’s MMAPs are treated by KPC-Toolbox as MAPs
151. 37
Bibliography
Menascé, D. A. (2008). “Computing missing service demand
parameters for performance models”. In: CMG Conference
Proceedings, pp. 241–248
Liu, Z., L. Wynter, C. H. Xia, and F. Zhang (2006). “Parameter
inference of queueing models for IT systems using end-to-end
measurements”. In: Perform. Eval. 63.1, pp. 36–60
Kumar, D., A. N. Tantawi, and L. Zhang (2009a). “Real-time
performance modeling for adaptive software systems with multi-
class workload”. In: Proceedings of the 17th Annual Meeting of the
IEEE/ACM International Symposium on Modelling, Analysis and
Simulation of Computer and Telecommunication Systems,
MASCOTS, pp. 1–4
Zheng, T., C. M. Woodside, and M. Litoiu (2008). “Performance
Model Estimation and Tracking Using Optimal Filters”. In: IEEE
Trans. Software Eng. 34.3, pp. 391–406
152. 38
Bibliography
Wang, W., X. Huang, X. Qin, W. Zhang, J. Wei, and H. Zhong
(2012). “Application-Level CPU Consumption Estimation: Towards
Performance Isolation of Multi-tenancy Web Applications”. In:
Proceedings of the 2012 IEEE Fifth International Conference on
Cloud Computing, CLOUD, pp. 439–446
Brosig, F., S. Kounev, and K. Krogmann (2009). “Automated
extraction of palladio component models from running enterprise
Java applications”. In: Proceedings of the 4th International
Conference on Performance Evaluation Methodologies and Tools,
VALUETOOLS, p. 10
Rolia, J. and V. Vetland (1995). “Parameter estimation for
performance models of distributed application systems”. In:
Proceedings of the 1995 Conference of the Centre for Advanced
Studies on Collaborative Research, CASCON, p. 54
153. 39
Bibliography
Kraft, S., S. Pacheco-Sanchez, G. Casale, and S. Dawson (2009).
“Estimating service resource consumption from response time
measurements”. In: Proceedings of the 4th International
Conference on Performance Evaluation Methodologies and Tools,
VALUETOOLS, p. 48
Wang, W. and G. Casale (2013). “Bayesian Service Demand
Estimation Using Gibbs Sampling”. In: Proceedings of the 2013
IEEE 21st International Symposium on Modelling, Analysis and
Simulation of Computer and Telecommunication Systems,
MASCOTS, pp. 567–576
G. Casale, P. Cremonesi, R. Turrin, Robust Workload Estimation in
Queueing Network Performance Models, in: 16th Euromicro
Conference on Parallel, Distributed and Network-Based Processing
(PDP), 2008, pp. 183-187.
154. 40
Bibliography
P. Cremonesi, K. Dhyani, A. Sansottera, Service Time
Estimation with a Refinement Enhanced Hybrid Clustering
Algorithm, in: Analytical and Stochastic Modeling Techniques
and Applications, Vol. 6148 of Lecture Notes in Computer
Science, Springer Berlin / Heidelberg, 2010, pp. 291--305
P. Cremonesi, A. Sansottera, Indirect estimation of service
demands in the presence of structural changes, Performance
Evaluation 73 (0) (2014) 18--40, special Issue on the 9th
International Conference on Quantitative Evaluation of Systems
Giuliano Casale, Evgenia Smirni: KPC-toolbox: fitting Markovian
arrival processes and phase-type distributions with MATLAB.
SIGMETRICS Performance Evaluation Review 39(4): 47 (2012)
Andrea Sansottera, Giuliano Casale, Paolo Cremonesi: Fitting
second-order acyclic Marked Markovian Arrival Processes. DSN
2013: 1-12
Work supported by the EU projects DICE (644869) and MODAClouds (318484) and the EPSRC project
OptiMAM (EP/M009211/1).