2. Packet Scheduling: SCFQ, STFQ, WF2Q Yongho Seok

3. Contents Review: GPS, PGPS SCFQ( Self-clocked fair queuing ) STFQ( Start time fair queuing ) WF2Q( Worst-case fair weighted fair queuing ) Conclusion

4. GPS An idealized policy that can split bandwidth among multiple sessions simultaneously –Each session I has a queue and a weight –At time t, GPS serves all non-empty queues simultaneously in proportion to –Property

5. GPS(Cont ’ ) Observation : –Guaranteed service rate for session j whenever it becomes backlogged Another View –Weighted round robin with infinitely small service amount

6. PGPS Intuition –Compute the time a packet would complete service had we been serving packets with a GPS server, then serve packets in order of these finishing times –emulates GPS “ on the side ” and uses the results of this simulation to determine service order Three virtual times –Not real time, but time for representing the amount of service –Virtual Star time, Virtual Finish time : each flow –Virtual System time : system-wide time

7. PGPS(Cont ’ ) Virtual Start Time Virtual Finish Time Virtual Time Implementation of WFQ

8. PGPS(Cont ’ )

9. WFQ : Scheduling Example Situation –Three sessions : A, B, and C –Time 0 : packets of size 1(A), 2(B), and 2(C) arrives –Time 4 : a packet of size 2(A) arrives Assumption –Weight are all same –Link Capacity C = 1

10. Result comparison(GPS, WFQ) 03 4 5.567 01357 GPS WFQ

11. 12345678 0 0.5 1 1.5 2 2.5 3 3.5 A B,C V(t) Slope = C / weighted sum of backlogged flows = 1/3 Real Time(At time 0) Virtual Time F(0) = Max(0,0) + 2 = 2 F(0) = Max(0,0) + 1 = 1

12. 12345678 0 0.5 1 1.5 2 2.5 3 3.5 A B,C V(t) Flow A is unbacklogged in GPS at time 3 Flow A is unbacklogged in WFQ at time 1 Virtual Time Real Time(AT time 3)

13. 12345678 0 0.5 1 1.5 2 2.5 3 3.5 A B,C V(t) Slope = 1/2 2 nd packet of size 2 arrives F(4) = Max(1.5,1) + 2 = 3.5 Virtual Time Real Time(At time 4)

14. 12345678 0 0.5 1 1.5 2 2.5 3 3.5 A B,C V(t) Slope = 1/3 Flow B or C is unbacklogged in GPS at time 5.5 Virtual Time Real Time(At time 5.5)

15. 12345678 0 0.5 1 1.5 2 2.5 3 3.5 A B,C V(t) Slope = 1 Virtual Time Real Time(At time 7)

16. Fairness of WFQ The difference between GPS and WFQ Cannot fall behind GPS by one packet One Packet difference means Problem –Cannot fall behind GPS by one packet, however, can fall ahead GPS by infinite amount –Motivation of WF2Q

17. Self-Clocked Fair Queuing (SCFQ) Same as WFQ except CF : the virtual finish time of the packet currently in service Easier to implement than WFQ

18. Relative Fairness & Absolute Fairness The service rate allocated to connection I at the kth switch on its path from source to its destination Relative Fairness Absolute Fairness

19. Fairness of SCFQ The author has shown that the relative fairness bound for SCFQ is But, the absolute fairness bounded for SCFQ is currently unknown Although the SCFQ round number update rule is easy to implement, it can be unfair over short term scales

20. Fairness of SCFQ(Cont ’ ) Worst-case latency for SCFQ is compared to for WFQ STFQ improve a large worst case delay and short- term unfairness

21. Start-time Fair Queuing (STFQ) Same as WFQ except SF : the virtual start time of the packet currently in service Serves the packet having smallest virtual start time Easier to implement than WFQ Note

22. Worst-case Fair Weighted Fair Queuing (WF2Q) Conceptually, –S(t) : the total amount of service received by flow I –V(t) : the total amount of service, which would be received in GPS WF 2 Q algorithm –WFQ scheduling + eligibility test –eligible test Among packets that have started service under GPS, pick the packet having the smallest virtual finish time

23. WF2Q : Scheduling Example

27. Fairness of WF2Q Cannot fall behind GPS by one packet, however, can not fall ahead GPS by one packet This means

28. Conclusion WFQ provides fairness and end-to-end delay bound, but has a heavy implementation complexity SCFQ, STFQ, WF2Q are easy to implement Issues –Delay & bandwidth requirement is coupled