Competitive Buffer Management with Packet Dependencies

1. Competitive Buffer Management with Packet Dependencies Alex Kesselman, Google Boaz Patt-Shamir, Tel Aviv University Gabriel Scalosub, University of Toronto

2. Motivation: Video Streaming Smart encoding: Suffices to recover many Every video frame is fragmented into packets Restoration depends on recovering all packets If packets are lost: Affects other packets as well (become redundant) Streaming: retransmission is not an option Competitive Buffer Management with Packet Dependencies

3. Buffering Schematics buffermanagement incoming packets outgoingstream dropped packets finite linkspeed (“drain rate”) Competitive Buffer Management with Packet Dependencies

4. Buffer and Traffic Model Single FIFO queue of size Discrete time: Delivery substep One packet delivered from head of queue Arrival substep Packets arrive Some packets may be dropped Packets accommodated in the buffer Traffic: frames consists of packets Goal: Maximize number of whole frames delivered frame ‘s j-packet Competitive Buffer Management with Packet Dependencies

5. Previous Work Buffer management for QoS Multi-valued packets Constant competitive ratio for finite values Some results for multiple buffers No results about co-dependent packets! [Lapid et al., 2000], [Kesselman et al., 2004], [Englert & Westerman, 2006], and many more Competitive Buffer Management with Packet Dependencies

6. Our Results Frames consisting of k>1 parts Bad news: No finite competitive ratio in general Good news: If frame parts are consistently ordered There exists an algorithm with c.r. All deterministic algorithms have c.r. Competitive Buffer Management with Packet Dependencies

7. Preliminaries Offline Closely related to k-DM (as hard) Simple greedy algorithm is a (k+1)-approximation Online (arbitrary traffic) Not much you can do ALG OPT packets ALG OPT time … … Competitive Buffer Management with Packet Dependencies

8. Restricted Traffic Problem: Selective unbounded delay/burstiness Model requirement (solution): Both ALG and OPT have to deal with same delay/burstiness Order-respecting traffic: Frame order induced by j-packets is the same for every j OK: 2.1 (frame 2, part 1), 3.1, 2.2, 3.2 Not OK: 3.1, 2.1, 2.2, 3.2 Competitive Buffer Management with Packet Dependencies

9. All Is Well if Order-Respecting? Answer: Yes and No No: Any deterministic algorithm has competitive ratio at least Yes: A natural preemptive greedy approach Conservative non-preemptive approaches Competitive Buffer Management with Packet Dependencies

10. Static-Partitioning Algorithm (SPA) Intuition Think ahead: focus on admission control Virtually partition the buffer into k levels of size Buffer is still FIFO!! Level j only holds j-packets Level j accepts j-packets that are “evenly” spaced in time Alternating accept/reject periods Levels synchronize on frame index Ensures delivered packets correspond to the same frame Extra perk: non-preemptive Competitive Buffer Management with Packet Dependencies

11. Example: SPA for k-FTM (k=2) Consider level 1, i.e., 1-packets 1-sync frame indices: Accepts first 1-packets after every 1-sync Specifically, has sufficient buffer space Wait time units Wait time units Accept packets Accept packets is the first 1-packet is the first 1-packet arriving after reject period is the first 1-packet arriving after reject period A R A R time Competitive Buffer Management with Packet Dependencies

12. Example: SPA for k-FTM (k=2) Consider level 2, i.e., 2-packets 2-sync indices 1-sync indices Accepts first 2-packets after every 2-sync Specifically, has sufficient buffer space Wait time units Wait time units Accept packets Accept packets is the first 2-packet is the first 2-packet of a 1-sync arriving after reject period is the first 2-packet of a 1-sync arriving after reject period time A R A R Competitive Buffer Management with Packet Dependencies

13. Summary A new model in buffer management Traffic has inter-packet dependencies Highly applicable to, e.g., video streaming First analytic results (still a lot to discover…) Competitive algorithms (and lower bounds) Complexity Competitive Buffer Management with Packet Dependencies

14. Still Open Gap: vs. Randomization Useful in the packet-weights models How does it work for real traffic? Is greedy still an option? Using forward-error-correction (FEC) Suffices to deliver m-of-k Some preliminary results, but still a lot to discover Competitive Buffer Management with Packet Dependencies

15. Thank You!