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Xiaobo Zhou Department of Computer Science University of Colorado at Colorado Springs

Robust Processing Rate Allocation with Feedback Control for Proportional Slowdown Differentiation. Xiaobo Zhou Department of Computer Science University of Colorado at Colorado Springs. Outline. Proportional Slowdown Differentiation (PSD) State-of-the-Art An Integrated Approach to PSD

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Xiaobo Zhou Department of Computer Science University of Colorado at Colorado Springs

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  1. Robust Processing Rate Allocationwith Feedback Control for Proportional Slowdown Differentiation Xiaobo Zhou Department of Computer Science University of Colorado at Colorado Springs

  2. Outline • Proportional Slowdown Differentiation (PSD) • State-of-the-Art • An Integrated Approach to PSD • Queueing-theoretical processing rate allocation • control-theoretical feedback control • Performance Evaluation • Research Plan ZBO@CS.UCCS.EDU

  3. What is Differentiated Services • Internet Engineering Task Force (IETF), April 1998www.ietf.org/html.charters/diffserv-charter.html • The Goal • To define configurable types of packet forwarding (called Per-Hop Behaviors, PHBs), which can provide local (per-hop) service differentiation for large aggregates of network traffic, as opposed to end-to-end performance guarantees for individual flows Best-effort services (Same-service-to-all) Integrated Services Differentiated Services (Reservations-based) (relative vs. absolute) ZBO@CS.UCCS.EDU

  4. Why Differentiated Services • Network Service Providers want to: • Offer a scalable service differentiation (defined in SLA’s) on core routers in stead of current best-effort service • Improve revenues through premium pricing and competitive differentiation • Applications seek better than best effort: • Bandwidth • Packet Delay characteristics • Packet loss characteristics • Jitter characteristics ZBO@CS.UCCS.EDU

  5. End-to-End Differentiation • Why Service Differentiation on Servers? • To provide predictable and controllable differentiation QoS levels to different request classes of clients • Diverse service expectations and constraints from Internet applications and users, making the current same-service-to-all model inadequate and limiting • End-to-end DiffServ • Network core: • Per-hop differentiated queueing delay and loss rate • Network edge: • Service differentiation on Servers and Proxies ZBO@CS.UCCS.EDU

  6. Models and Properties • Models: • Absolute differentiated services: clients receive an absolute share of resource usages; possible low resource utilization • For hard real-time applications • Relative differentiated services: higher classes will receive relatively better (or no worse) QoS than lower classes • For soft real-time applications • Properties: • Predictability: differentiation schedules must be consistent, independent of variations of the class workloads • Controllability: a number of controllable parameters adjustable for quality differentiation between classes • Fairness: lower classes not be over-compromised, especially when workload is low ZBO@CS.UCCS.EDU

  7. A Proportional DiffServ Model • A proportional differentiation model assigns quality factors to the traffic classes in proportion to their pre-specified differentiation weights, independent of class workloads • It is popular • differentiation predictability • proportional fairness qi i qj j = , for all i, j, = 1,2,...,n ZBO@CS.UCCS.EDU

  8. QoS Metrics on Servers • Multimedia Applications • Mutli-dimensional QoS metric • Responsiveness • Image size, resolution, formats • Streaming bandwidth • Audio sample rate and sample size • Video frame rate, frame size, and color depth • Web Applications • Responsiveness • Throughput ZBO@CS.UCCS.EDU

  9.  Arrival Rate Service Rate Queue Client / Incoming link Server / Outgoing link Response Time vs. Slowdown • Response time • Queueing delay + service time • Favors requests that need more service time • Slowdown • queueing delay / service time • gives equal weights to requests regardless of service time • A high slowdown also means a server is heavily loaded * Clients expect long delay for “large” requests, and anticipate short delay for “small” requests E[W/X] =E[W]W[X-1]  E[W]/E[X] ZBO@CS.UCCS.EDU

  10. State-of-the-Art • Queueing-delay differentiation • Strict priority based packet/request scheduling • Time-dependent priority based request packet/scheduling • Response time differentiation • Strict priority based request scheduling • Adaptive process allocation for proportional differentiation • Slowdown differentiation • queueing-theoretical Processing rate allocation • M/M/1 PS queue for stretch factor differentiation • M/G_P/1 FCFS queue ZBO@CS.UCCS.EDU

  11. Challenges and Contributions • A closed form of slowdown for M/GP/1 FCFS Q • Average slowdown on Task servers • Processing rate allocation scheme for PSD • Control-theoretical approach for robust PSD ZBO@CS.UCCS.EDU

  12. A Heavy-tailed Distribution • The Pareto distribution is a typical heavy-tailed • In practice, there is some upper bound on the maximum size of a job (p) -- Bounded Pareto distribution f(x) Power law w/ exp - -1 x p k ZBO@CS.UCCS.EDU

  13. Preliminary of Slowdown • Lemma 1 • Given an M/GP/1 FCFS queue on a server, where the arrival process has rate  and X denotes the Bounded Pareto service time density distribution. Let W be a job’s queueing delay (W is indepenent to X from a FCFS queue), and S be its slowdown. According to Pollaczek-Khinchin Formula, ZBO@CS.UCCS.EDU

  14. Slowdown on a Task Server • What is a task server? • A processing unit, handling a request class in FCFS manner • Let ci be the normalized processing rate of task server i • \sum_{i=1}^{N} ci = 1 0 < ci  1 for 0  i N • A process, a thread, a processor, a server node • Lemma 2 • Given an M/GP/1 FCFS queue on a task server i with processing rate. Xi denotes the Bounded Pareto service time density distribution on the task server: • E[Xi] = 1/ci E[X] • E[X2i] = 1/c2i E[X2] • E[X-1i] = ci E[X-1] ZBO@CS.UCCS.EDU

  15. Processing Rate Allocation • PSD model • A Proportional Processing Rate Allocation E[Si ] i E[Si ] j = , for all i, j, = 1,2,...,N ZBO@CS.UCCS.EDU

  16. Simulation Model • Processing procedure is partitioned into sampling periods • Request generator • Load estimator • Rate allocator • GNU Scientific library (GSL) ZBO@CS.UCCS.EDU

  17. Effectiveness of Rate Allocation • Simulated and expected slowdowns of 2 classes (1: 2= 1:2/1:4) ZBO@CS.UCCS.EDU

  18. Effectiveness of Rate Allocation • Simulated and expected slowdowns of 3 classes (1: 2: 2= 1:2:3) ZBO@CS.UCCS.EDU

  19. Predictability vs. Variance • Percentiles of simulated slowdown ratios for 2 and 3 classes ZBO@CS.UCCS.EDU

  20. Microscopic Views • Queueing-theoretical allocation is based on the average, a macro-behavior of class load instead of micro-behaviors, such as experienced slowdowns of individual requests. 50% vs. 90% ZBO@CS.UCCS.EDU

  21. Drawbacks of Q-based Approach • Queueing theory can be applied to calculate a request class’s average slowdown based on the allocated processing rate. However, we cannot control the variance of slowdown simultaneously • Processing rate allocation is based on the average load conditions of classes, instead of per-request experienced slowdown: macro-behavior vs. micro-behavior • Load condition is stochastic, it is difficult to accurately estimate a class’s load based on its history; estimation errors may cause inaccurate rate allocation in the short time scales and slowdown deviation between achieved slowdown ratio and predicted slowdown ratio. • So, how to improve micro-behavior so more robust? • Integrating control theory and queueing theory ZBO@CS.UCCS.EDU

  22. Queueing & Control Integration • Queueing theoretical rate predictor • A control loop is used for each pair of adjacent classes • Sensor/monitor measures the achieved slowdown ratio • Deviation controller adjusts the rate allocation • Actuator translate the abstract controller output to physical action ZBO@CS.UCCS.EDU

  23. PID Control • PID (proportional integral derivative) controller • Simplicity: adjust the rate allocations in proportion to the difference between the achieved slowdown ratio and desired one • A linear feedback control function • f(e i (k)) = g  e i (k) //g is the control gain parameter • Rate allocation adjustment • At the end of sampling period k, the adjustment for k+1 period • Rate allocation for k+1 period is ZBO@CS.UCCS.EDU

  24. A New Simulation Model • Integration of queueing and control theory • Feedback controller • Comparator (sensor/monitor) ZBO@CS.UCCS.EDU

  25. Performance Evaulation • Integrated approach vs. queueing-theoretical approach ZBO@CS.UCCS.EDU

  26. Performance Evaulation • System load is 0.8 and 3: (2 : 1) = 4: (2 : 1) ZBO@CS.UCCS.EDU

  27. Performance Evaulation • Sensitivity analyses of the integrated approach Load:0.4->0.2->0.4 ZBO@CS.UCCS.EDU

  28. Future Work • Evaluate different control techniques • Integration of process allocation and admission control with feedback for robust responsiveness differentiation ZBO@CS.UCCS.EDU

  29. P&P for IDF Applications • Multi-dimensional Input & Requirements • Distributed data sources • Different data formats • Different data priority levels • Different decision requirements • Different workload characteristics • Multi-dimensional Platform and Performance Metric • Cluster node partitioning • Performance measurement • Performance differentiation ZBO@CS.UCCS.EDU

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