Bounded Delay Scheduling with Packet Dependencies

1. Bounded Delay Scheduling with Packet Dependencies Michael Markovitch Joint work with Gabriel Scalosub Department of Communications Systems Engineering Ben-Gurion University

2. Real Time Video Streaming Sandvine, “Global Internet phenomena report – 1H 2013”

3. Real Time Video Streaming • Video streams are comprised of frames • Bursty traffic • Video frames can be large (>>1500B) • Fragmentation • Interdependency between different packets • Dropping some packets -> drop frame • Packets MUST arrive in a timely manner

4. Current situation & Related work • Best practices: • DiffServ AF queue for video streams • Admission control (average throughput) • Number of streams can be large • Average throughput < channel access rate • Overlapping bursts >> momentary channel rate • Related work • FIFO queuing with dependencies • Deadline scheduling without dependencies [MPR, 2011] [MPR, 2012] [EHMPRR, 2012] [KPS, 2013] [SML, 2013] [EW, 2012] [AMS, 2002]

5. Deadline scheduling • Every packet has a deadline • Focus on scheduling • Queue size assumed unbounded • More information (than FIFO)

6. Buffer and Traffic Model • Single non-FIFO queue of infinite size (one hop) • Discrete time: • Every packet : • One of multiple packets in a frame • Has arrival time, deadline, size and value • Goal: Maximize value of completed frames Arrival substep Delivery substep Cleanup substep Packets arrive • One packet delivered Packets may be dropped

7. Buffer and Traffic Model • Frames of uniform size – k • No redundancy • Packets of uniform size and value – WLG k = 12

8. Buffer and Traffic Model • Uniform slack – d • Packets can be scheduled on arrival Deadline(p) Arrival(p) d Arrival sequence t t schedule d

9. Buffer and Traffic Model • Finite burst size – b b Arrival sequence t

10. Buffer and Traffic Model • Recap: • Frames of uniform size - • Uniform slack – d • Finite burst size – b • No redundancy • Packets of uniform size and value – WLG 1 • Goal: Maximize number of completed frames • NP-hard off-line problem

11. Competitive analysis • Worst case performance of online algorithms • – instance • – problem

12. A proactive greedy algorithm • Ensures completion of at least one frame • Holds packets of only one frame Arrival substep Delivery substep Cleanup substep Packets arrive • One packet delivered Packets may be dropped

13. Proactive greedy - example Arrival sequence Proactive greedy schedule

14. Proactive greedy – competitiveness • Competitive ratio – • Details in the paper • Not far off from the lower bound

15. A better greedy algorithm Why?

16. Greedy algorithm - analysis • Competitive ratio – • Details in the paper • We have a matching lower bound • Reminder: • For proactive greedy –

17. What about the deadlines? • Deadlines not used explicitly • Bad news? • Worst case performance matches lower bound • Good news • There is space for more interesting algorithms • Improve general performance • How can deadlines be utilized? • Several approaches presented in the paper

18. Simulation • Three online algorithms: • “Vanilla” greedy algorithm • Greedy algorithm with slack tie breaker • Opportunistic algorithm • And the best current offline approximation

19. Simulation • Simulation details: • Average throughput = channel access rate • 50 streams at 30FPS • Each stream starts at a random time • Between 0 and 33ms • Random (short) time between successive packets • “jitter” between packets of a single frame

20. Simulation results

21. To sum up • First work considering both deadline scheduling and packet dependencies • Very simplified model • Yet hard • Improvements to the model • Non uniform slack • Randomization • Redundancy

22. Questions? • markomic@post.bgu.ac.il