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

2. ZBO@CS.UCCS.EDU 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

3. ZBO@CS.UCCS.EDU 3 What is Differentiated Services  Internet Engineering Task Force (IETF), April 1998 www.ietf.org/html.charters/diffserv-charter.html www.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)

4. 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

5. 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

6. 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

7. 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 q i  i q j  j =, for all i, j, = 1,2,...,n

8. 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

9. ZBO@CS.UCCS.EDU 9 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 Client / Incoming link Server / Outgoing link Queue  Arrival Rate Service Rate E[W/X] =E[W]W[X -1 ]  E[W]/E[X]

10. 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

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

12. 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) x p k Power law w/ exp -  -1

13. ZBO@CS.UCCS.EDU 13 Preliminary of Slowdown  Lemma 1 – Given an M/G P /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,

14. 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 c i be the normalized processing rate of task server i – \sum_{i=1}^{N} c i = 1 0 < c i  1 for 0  i  N – A process, a thread, a processor, a server node  Lemma 2 – Given an M/G P /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[X i ] = 1/c i E[X] E[X 2 i ] = 1/c 2 i E[X 2 ] E[X -1 i ] = c i E[X -1 ]

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

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

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

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

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

20. 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%

21. 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

22. 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

23. 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

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

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

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

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

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

29. 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