1. 2002/04/18Chin-Kai Wu, CS, NTHU1 Jitter Control in QoS Network Yishay Mansour and Boaz Patt-Shamir IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 9, NO. 4, AUGUST 2001

2. 2002/04/18Chin-Kai Wu, CS, NTHU2 Outline Introduction Model Delay-Jitter Control Off-Line Delay-Jitter Control On-Line Delay-Jitter Control Distributed Delay-Jitter Control Rate-Jitter Control On-Line Rate-Jitter Control Multiplicative Rate Jitter

3. 2002/04/18Chin-Kai Wu, CS, NTHU3 Introduction Delay jitter Bounds the maximum difference in the total delay of different packets The maximum buffer needed at the destination Rate jitter Bounds the difference between minimal and maximum inter-arrival time

4. 2002/04/18Chin-Kai Wu, CS, NTHU4 Buffer Consumption Off-line (Optimal) On-line Delay jitter B2B Rate jitter B2B+h Introduction (Cont’d)

5. 2002/04/18Chin-Kai Wu, CS, NTHU5 Model B-feasible

6. 2002/04/18Chin-Kai Wu, CS, NTHU6 Rate jitter Delay jitter Maximum inter-arrival time Minimum inter-arrival time Average inter-arrival time Model (notation)

7. 2002/04/18Chin-Kai Wu, CS, NTHU7 Model (Cont’d) The delay jitter of σ equals iff the rate jitter of σ equals 0 If the delay jitter of σ is J, then the rate jitter of σ is at most 2J For all ε > 0 and M, there exists a sequence σ ε, M with rate jitter at most ε and delay jitter at least M

8. 2002/04/18Chin-Kai Wu, CS, NTHU8 Off-Line Delay-Jitter Control For each, define the interval Find an interval M of minimal length which intersects all intervals E k For each packet k, let, and define

9. 2002/04/18Chin-Kai Wu, CS, NTHU9 Off-Line Delay-Jitter Control (Cont’d) min(E k ) ≤ min(M) M min(M) ≤ min(E k ) M

10. 2002/04/18Chin-Kai Wu, CS, NTHU10 On-Line Delay-Jitter Control (Algorithm) Definefor all, the release sequence is defined by

11. 2002/04/18Chin-Kai Wu, CS, NTHU11 On-Line Delay-Jitter Control (Theorem) If an off-line algorithm can attain delay jitter J with buffer space B, then the algorithm has delay jitter at most J using no more than 2B buffer space Slope =

12. 2002/04/18Chin-Kai Wu, CS, NTHU12 On-Line Delay-Jitter Control (Lemma) Let be any B -feasible sequence for a given arrival sequence. Then for all 0 ≤ k ≤ n, we have Let J be the minimal delay jitter for a given arrival sequence suing space B, and let 0 ≤ i ≤ j ≤ n be packets such that j ≤ i + B. There exists a B -feasible sequence with delay jitter J such that

13. 2002/04/18Chin-Kai Wu, CS, NTHU13 A Lower Bound for On-Line Delay- Jitter Control Algorithm Let. There exist arrival sequences for which an off-line algorithm using space B gets jitter 0, and any on-line algorithm using buffer space gets delay jitter at least There exist arrival sequences for which an off-line algorithm using space B gets 0-jitter, no on-line algorithm using less than B buffer space can guarantee any finite delay jitter

14. 2002/04/18Chin-Kai Wu, CS, NTHU14 Distributed Delay-Jitter Control (Algorithm) For each 1 ≤ j ≤ m, node v j employs on-line delay jitter control algorithm with buffer space 2B/m Node j sets, and it releases packet k as close as possible to subject to 2B/m -feasibility

15. 2002/04/18Chin-Kai Wu, CS, NTHU15 Distributed Delay-Jitter Control (Theorem) Suppose that for a given arrival sequence, there exists a centralized off-line algorithm attaining jitter J using space B, with packet 0 released before time a(B/m) Then if σ is released at v 0, the sequence released at v m has delay jitter at most J

16. 2002/04/18Chin-Kai Wu, CS, NTHU16 Distributed Delay-Jitter Control (Lemma) For all nodes 1 ≤ j ≤ m and all packets k, If, then

17. 2002/04/18Chin-Kai Wu, CS, NTHU17 Distributed Delay-Jitter Control (Lemma, Cont’d) Let be any B -feasible sequence for a given arrival sequence such that. Then for all 0 ≤ k ≤ m, we have

18. 2002/04/18Chin-Kai Wu, CS, NTHU18 On-Line Rate Jitter Control (Algorithm) Use

19. 2002/04/18Chin-Kai Wu, CS, NTHU19 On-Line Rate Jitter Control (Theorem) The maximal rate jitter in the release sequence is at most and never more than I max – I min

20. 2002/04/18Chin-Kai Wu, CS, NTHU20 Multiplicative Rate Jitter Use