Performance models for LAS-based scheduling disciplines in packet switched networks

1. Performance models for LAS-basedscheduling disciplines in packet switched networks Ernst W. Biersack erbi@eurecom.fr Institut Eurecom France In Collaboration with: Idris. A. Rai, Guillaume Urvoy-Keller, Mary Vernon

2. Outline • Motivation • LAS for • Jobs • Flows • Performance Models • FCFS, LAS models • 2-class LAS-based models • Model Validation • Results • Summary • Current work

3. Motivation LAS: Least Attained Service scheduling • At any time, LAS gives service to a job that has received the least amount of service. • A size based policy that favors short jobs without knowing their sizes in advance • Also known as: • Foreground Background (FB) • Shortest Elapsed Service Time (SET) • Question: • Why analyzing LAS today?

4. Motivation • Internet traffic measurements (highly varying flow sizes): • Most of flows are short and a few largest ones contribute a large fraction of the total load • FIFO policy is known to discriminate against short flows • Question: • Can we use LAS to favor short flows without penalizing large flows too much ?

5. Penalty region S(x) S(x)PS x Performance Metrics • T(x) := (T|X=x), Mean conditional response time and • S(x) := T(x)/x, Mean conditional slowdown (normalized response time) • Fairness metric • LAS is always unfair.[Wierman et. al. Sigmetrics 2003] • Some jobs are always penalized under LAS • Fair Sejourn Protocol (FSP) is always fair [Friedman et. al. Sigmetrics03]

6. Mean conditional Slowdown S(x) Mean conditional Slowdown S(x) Job Size Percentile of job size distribution Performance of LAS for Jobs • LAS performance depends on the job size distribution.[Rai et. al., Sigmetrics 2003] For CoV ≥ 6, less than 0.5% of largest jobs see a penalty

7. first window = S/R RTT second window = 2S/R third window = 4S/R fourth window = 8S/R transmission delivered TCP during Slow Start Client Server initiate TCP connection request object object complete time at client time at server

8. Priority queue Lowest Priority Pkt Highest Priority Pkt LAS for Flows First packet from a new flow coming to a full queue First packet from a new flow • LAS reduces queuing delay of first packets of a flow •  Reduces RTT (for short TCP flows) LAS Reduces loss rate of short flow  Avoids Timeouts and the use of RTO to recover losses Reduces transmission time of short flows

9. Web Traffic: Mean Transmission TimePareto flow size distr., load = 0.7 Factor of 2.5

10. Intermediate Conclusion for Plain LAS • LAS based on observation that not all packets are equally important • First packets in a flow are more important • Smaller RTT to allow • Faster completion of Three-way handshake • Faster ramp-up during slow start • Avoid loss, since not enough packets in the pipe to result in triple duplicate ACKs • When applied to flows, LAS • Significantly improves response time performance for Web traffic • Hardly at all affects long lived FTP session • Yet, some long-lived flows may find un-acceptable the performance degradation under LAS

11. Motivation for 2-class LAS-based models • Why new LAS-based models? • User request better service for some long flows (e.g. video streaming) • Achieving service differentiation without hurting much the performance of short flows

12. Priority value Packet number 2-class LAS-based models • Obtained by altering the speed of priority decrease of some flows in LAS • Flow classes and priority decrease orders • Class 1, Regular flows : Same as under plain LAS • Class 2, Priority flows : Use a different priority function P(x) • Models and Priority Functions: • LAS-fixed(k) : fixed priority function, P(x) = k • LAS-linear(k) : linear priority function, P(x) = x/k • LAS-log(k) : logarithmic function, P(x) = log2(x)1/k • Motivation of priority functions • Reducing the number of regular flows (resp. their packets) that a priority flow has to compete against

13. Analysis of LAS in Packet Networks • Job • Workload that arrives in the system at once • In packet networks: flow • Sequence of packets arriving in bursts • Not obvious if the results obtained for jobs apply to flows • How to evaluate? • Simulation using network simulator (ns2) • Analysis

14. Performance Models in Packet Networks • FCFS • Multiplex of packets from different flows Processor Sharing • LAS Model • The same as the model for jobs • A flow has always at least one packet in the bottleneck queue

15. 2-class LAS-based models • Expressions for T(x) • Derived different for different classes of flows and different priority functions • Obtained by considering the flow sizes that interfere the service of a given flow (determined by its size and priority) Let the truncated n-th moment for the flows of size x and class i be defined as:

16. 2-class LAS based models If q is the fraction of priority flows, and subscriptsp and r denote priority and ordinary flows, the n-th moments ( ) for the models are:

17. 2-class LAS based models • Expression of T(x) for LAS-log: • Priority flows • Ordinary flows where

18. Model validation: FCFS • Good agreement • Analytical model slightly underestimates (sizes < 100) and slightly overestimates (flows >1000)

19. Model validation: LAS Simulation fits the analytical model well

20. Model Validation • 2-class LAS-based models • 10% Priority class flows, 90% ordinary flows • offered load = 0.7

21. Model validation Ordinary Flows Priority Flows • LAS-linear k = 5

22. Ordinary Flows Priority Flows Model validation • LAS-log k = 0.5

23. Model validation • LAS-log k = 2 Ordinary Flows Priority Flows

24. Policy Comparison: T(x)P/T(x)FIFO Priority Flows Ordinary Flows fixed LAS linear log LAS log fixed

25. q Mean transfer time for ordinary flows of size less than 100 FCFS log linear fixed Percentage of priority flows

26. Loss Rate of TCP Flows Ordinary Flows Priority Flows linear(k=25) linear(k=125) log (k=0.5) log (k=2.5) Loss rate quite insensitive to choice of k

27. Conclusion • We proposed new LAS-based models, which, compared to plain LAS • Improve the response time of certain long flows while • Maintain the good performance of plain LAS for short flows • The performance of priority flows in terms of mean response time, packet loss rates, and jitter is significantly improved.

28. Current work Discrepancy due to losses of packets from long flows • Modeling the impact of packet losses in the analytic models LAS at loss rate = 3.6%

29. Fairness Classification • Classes; always fair, sometimes fair, never fair[Wierman et. al. Sigmetrics 2003] • For 2-class LAS-based models policies • What are the fairness properties for the priority class