Jitter Regulation for Multiple Streams David Hay and

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Jitter Regulation for Multiple Streams David Hay and Gabriel Scalosub Technion, Israel October 5

Jitter Regulation for Multiple Streams David Hay and Gabriel Scalosub Technion, Israel October 5 th, 2005

Motivation l l Today’s applications call for stringent Qo. S • Smooth traffic is

Motivation l l Today’s applications call for stringent Qo. S • Smooth traffic is essential in multimedia applications • l end-to-end delay, loss-ratio, jitter audio/video streaming, interactive communication Moderating traffic throughout the network Delay jitter measures the smoothness of a stream • How far is the stream from being completely periodic? October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 2

Model Description Abstract Source 1 Abstract Source 2 Periodic streams at rate X Network

Model Description Abstract Source 1 Abstract Source 2 Periodic streams at rate X Network Regulator Non-Periodic streams Internal Buffer - B Abstract Source M October 5 th, 2005 Periodic streams at rate X Jitter Regulation for Multiple Streams | Hay and Scalosub 3

Formally… (Single Stream) l Single stream • • • [Mansour, Patt-Shamir, 2001] The regulator

Formally… (Single Stream) l Single stream • • • [Mansour, Patt-Shamir, 2001] The regulator knows the rate X, and a monotonic nondecreasing arrival sequence The regulator produces a release schedule that satisfies • FIFO • Arrival-feasibility: • B-feasibility: at most B cells in the buffer simultaneously. Goal: minimize the delay jitter October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 4

Previous Work Single stream regulation: • Offline optimal algorithm. [Mansour, Patt-Shamir, 2001] • Online:

Previous Work Single stream regulation: • Offline optimal algorithm. [Mansour, Patt-Shamir, 2001] • Online: In order to obtain the minimum B-feasible jitter one needs, and can do with, a buffer of size 2 B. [Mansour, Patt-Shamir, 2001] • Offline and online settings with delay considerations. [Koga, 2001] October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 5

Our Model: Multi Stream Regulation l The input is an interleaving of M streams

Our Model: Multi Stream Regulation l The input is an interleaving of M streams l FIFO should be maintained in every stream l Goal: minimize the maximum delay jitter • Not necessarily between streams. October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 6

Our Results Multi stream jitter regulation: • Offline: • The problem of finding the

Our Results Multi stream jitter regulation: • Offline: • The problem of finding the minimum max-jitter is polynomially solvable. • Online: • In order to obtain the minimum B-feasible jitter one needs (and can do with) a buffer of size Q(MB). Þ Online jitter regulation does not scale well as the number of streams increases. October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 7

Geometric Intuition (Single Stream) 1 2 3 5, 4? Packet Number 9 8 7

Geometric Intuition (Single Stream) 1 2 3 5, 4? Packet Number 9 8 7 6 slope 1/x 5 4 3 2 1 time October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 8

Geometric Intuition (Single Stream) 4 5 3 Packet Number 9 8 7 6 5

Geometric Intuition (Single Stream) 4 5 3 Packet Number 9 8 7 6 5 4 3 2 1 time October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 9

Geometric Intuition (Single Stream) 6 7 8 9? Packet Number 9 8 7 6

Geometric Intuition (Single Stream) 6 7 8 9? Packet Number 9 8 7 6 5 4 3 2 1 time October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 10

Geometric Intuition (Single Stream) 9 7 8 Packet Number 9 8 left margin 7

Geometric Intuition (Single Stream) 9 7 8 Packet Number 9 8 left margin 7 6 5 4 right margin 3 2 1 time The jitter October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 11

Multi Stream Intuition 9 8 7 6 5 4 3 2 1 1 2

Multi Stream Intuition 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 2 Stream 1 Must release 1 or 1 Stream 2 October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 12

Multi Stream Intuition 9 8 7 6 5 4 3 2 1 1 2

Multi Stream Intuition 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 2 Stream 1 Case 1: release 1 max-jitter Stream 2 October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 13

Multi Stream Intuition 9 8 7 6 5 4 3 2 1 1 2

Multi Stream Intuition 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 2 Stream 1 Case 2: release 1 max-jitter Stream 2 October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 14

The Right Margin Property l Lemma 1: The right margin crosses the time axis

The Right Margin Property l Lemma 1: The right margin crosses the time axis in the point l Intuition: Try “moving” the right margin to the left • Why not all the way to the left margin? • We end up ‘’sending’’ some cell before it has arrived. October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 15

The Right Margin Property 9 8 7 6 5 4 3 2 1 time

The Right Margin Property 9 8 7 6 5 4 3 2 1 time October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 16

The Left Margin Property l Given an optimal solution, consider all streams obtaining MJ:

The Left Margin Property l Given an optimal solution, consider all streams obtaining MJ: • There exists one which cannot be improved; • This is due to buffer overflow. October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 17

The Left Margin Property 9 8 7 6 5 4 3 2 1 time

The Left Margin Property 9 8 7 6 5 4 3 2 1 time October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 18

The Left Margin Property l Lemma 2 There exists a stream a cell such

The Left Margin Property l Lemma 2 There exists a stream a cell such that and l that attains MJ, and for some cell Specifically, October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 19

The Offline Algorithm l Enumerate over all pairs of cells • Try • This

The Offline Algorithm l Enumerate over all pairs of cells • Try • This defines a candidate jitter upper bound : • Try and build a feasible schedule assuming the max-jitter is • This is easy, using a greedy scheduling policy. l Take the feasible schedule with minimum October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 20

Online Setting l Upper Bound: Statically partitioning a buffer of size 2 MB among

Online Setting l Upper Bound: Statically partitioning a buffer of size 2 MB among the M streams, one can achieve the optimal B-feasible jitter • l Using [Mansour, Patt-Shamir] online algorithm Lower Bound: To achieve the optimal Bfeasible jitter a buffer of size ≥ M(B-1)+B+1 is required • October 5 th, 2005 Grows linearly with M Jitter Regulation for Multiple Streams | Hay and Scalosub 21

Lower Bound Proof l l Adversarial Traffic: At times X, 2 X, …, BX

Lower Bound Proof l l Adversarial Traffic: At times X, 2 X, …, BX one packet of each stream arrives to the buffer. Two Cases: 1. The online algorithm releases a packet of some stream si at time t 1<(B+1)X. 2. By time (B+1)X, the online algorithm stores all MB packets at its buffer. October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 22

Proof Outline l l Continuation of adversarial traffic after time BX depends on the

Proof Outline l l Continuation of adversarial traffic after time BX depends on the case Case 1: • Online algorithm achieves arbitrarily large jitter, while the offline algorithm achieves zero jitter. l Case 2: • Online algorithm achieves jitter=X, while the offline algorithm achieves zero jitter. October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 23

Summary l l l Extended the model to multi stream Gave a polynomial offline

Summary l l l Extended the model to multi stream Gave a polynomial offline algorithm to find optimal solution Proved that the online setting requires Q(MB) buffer augmentation October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 24

Future Work l Jitter regulation with bounded capacity outgoing links • l Models real-life

Future Work l Jitter regulation with bounded capacity outgoing links • l Models real-life regulators Jitter regulators that can drop a few packets • • May significantly reduce jitter Some applications may tolerate packets’ drops • Video streaming October 5 th, 2005 Jitter Regulation for Multiple Streams | Hay and Scalosub 25

Thank You! October 5 th, 2005

Thank You! October 5 th, 2005