bounded delay scheduling with packet dependencies

Michael MarkovitchJoint work with Gabriel Scalosub

Department of Communications Systems Engineering Ben-Gurion University

Bounded Delay Scheduling with Packet Dependencies

Real Time Video Streaming

2 Sandvine, “Global Internet phenomena report – 1H 2013”

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

3

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]

4

Deadline scheduling

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

5

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

6

Buffer and Traffic Model

• Frames of uniform size – k• No redundancy• Packets of uniform size and value – WLG

7

k = 12

Buffer and Traffic Model

• Uniform slack – d• Packets can be scheduled on arrival

8

Arrival sequence

schedule

t

t

Arrival(p) Deadline(p)d

d

Buffer and Traffic Model

• Finite burst size – b

9

Arrival sequencet

b

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

10

Competitive analysis

• Worst case performance of online algorithms

• – instance• – problem

11

A proactive greedy algorithm

• Ensures completion of at least one frame– Holds packets of only one frame

12

Arrival substep

Delivery substep

Cleanup substep

Packets arrive One packet delivered Packets may be dropped

Proactive greedy - example

Arrival sequence

Proactive greedy schedule

13

Proactive greedy – competitiveness

• Competitive ratio – Details in the paper

• Not far off from the lower bound

14

A better greedy algorithm

15

Why?

Greedy algorithm - analysis

• Competitive ratio – Details in the paper

• We have a matching lower bound

• Reminder: For proactive greedy –

16

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

17

Simulation

• Three online algorithms:– “Vanilla” greedy algorithm– Greedy algorithm with slack tie breaker– Opportunistic algorithm

• And the best current offline approximation

18

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

19

Simulation results

20

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

21

Questions?

• markomic@post.bgu.ac.il

22