Scheduling techniques for media on demand
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Scheduling Techniques for Media-on-Demand. Amotz Bar-Noy Brooklyn College Richard Ladner Tami Tamir University of Washington. Multimedia-on-Demand Systems. A database of media objects (movies). A limited number of channels. Movies are broadcast based on customer demand.

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Scheduling Techniques for Media-on-Demand

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Scheduling techniques for media on demand

Scheduling Techniques for Media-on-Demand

Amotz Bar-Noy

Brooklyn College

Richard Ladner

Tami Tamir

University of Washington


Scheduling techniques for media on demand

Multimedia-on-Demand Systems

  • A database of media objects (movies).

  • A limited number of channels.

  • Movies are broadcast based on customer demand.

  • The goal: Minimizing clients’ maximal waiting time (delay).

  • Broadcasting schemes: For popular movies, the system does not wait for client requests, but broadcasts these movies continuously.


Broadcasting schemes for media on demand systems

Broadcasting Schemes for Media-on-Demand Systems.

  • A server broadcasting movies of unit-length on h channels. Each channel transmits data at the playback rate.

  • A client that wishes to watch a movie is ‘listening to all the channels’ and is waiting for his movie to start.


Example one movie two channels

Example: One Movie, Two Channels

Staggered broadcasting, [Dan, Sitaram, Shahabuddin, 96]: Transmit the movie repeatedly on each of the channels.

C1:

0 1/2 1 3/2 2 5/2 3

C2:

Guaranteed client delay: at most 1/2 (1/h in general).

Can we do better?

A clue: With today’s advanced technology, clients can buffer data to their local machine.


Using client s buffer

C1:

1

1

1

1

1

1

0 1/3 2/3 1 4/3 5/3 2

C2:

2

3

2

3

2

3

arrive watch & buffer

Using Client’s Buffer

[Viswanathan, Imielinski, 96]: Partition the movie into segments. Early segments are transmitted more frequently.

1

2

3

(3 segments)

Each time-slot has length 1/3.

The client waits for the next slot start, and can then start watching the movie without interruptions.

Maximal client delay: 1/3 (slot size).


Using client s buffer the general case

4

4

4

Using Client’s Buffer, The General Case:

  • The movie is partitioned into s segments, 1,..,s.

  • We schedule these segments such that segment i is transmitted in any window of i slots (i-window).

  • The client has segment i available on time (from his buffer or from the channels).

  • The maximal delay: one slot = 1/s.

  • Therefore, the goal is to maximize s for given h.


Harmonic window scheduling

Examples:h=1, s=1, D=1

1

1

1

C1

1

1

1

1

1

1

h=2, s=3. D=1/3

C1

C2

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C1

C2

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C3

1

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Harmonic Window Scheduling

  • Given h, maximize s such that each i in 1,..,s is scheduled with window at most i.

h=3,

s=9. D=1/9

  • In general, window scheduling is NP-hard [Bay-Noy, Bhatia, Naor, Schieber, 98].

  • Good harmonic schedules can be found greedily [Bar-Noy, Ladner, 02].

Can other techniques do better?

Match a lower bound?


Our results

Our Results

  • Two new segment-scheduling techniques:

    - Shifting.

    - Channel sharing.

  • A lower bound for the guaranteed client’s delay (generalizes the lower bound of [Engebretsen, Sudan, 02] for a single movie).

  • Each of the two techniques produces schedules which

    - Approach the lower bound for any number of channels.

    - Guarantee the minimal known delay for small number of segments.

  • The two techniques can be applied together.


The shifting technique

delay

The Shifting Technique:

  • The movie is partitioned into s segments, 1,..,s.

  • We find a schedule of these segments in h channels such that segment i is transmitted in any window of d+i-1 slots (d is the shifting level).

    • The 1stsegment has window d.

    • The 2nd segment has window d+1, etc.

  • The client waits for the next slot start, buffers data during the next d-1 slots, and then start watching the movie (while continue buffering).

The total delay is at most d slots

arrive buffer watch & buffer

d-1 slots s slots


Example i one movie two channels

1

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Example I: One Movie, Two Channels

Without shifting, the best schedule has delay 1/3

C1:

C2:

With shifting, we can schedule 8 segments 1..8, such that segment i is transmitted in any i+1 window (d=2).

C1:

C2:

The resulting delay is 2/8 = 1/4.


Example i one movie two channels1

t

t

t

t

t

t

t

t

t

t

C1:

1

3

1

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1

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C2:

2

5

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2

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1

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2

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3

arrive buffer watch & buffer

1

2

Example I: One Movie, Two Channels

For a client arriving during the second slot:

Client’s buffer

Client watches

4

5

6

7

8


Example ii one movie one channel

With shifting (d=4): We partition the movie into 5 segments.

1

2

3

4

5

We broadcast segment iin any i+3 (or smaller) window

1

1

1

1

arrive buffer watch & buffer

3

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3

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5

3

2

2

2

2

The first segment is transmitted every 4th slot

The third, fourth, and fifth segments are transmitted every 6th slot.

The second segment is transmitted every 4th slot

Example II: One Movie, One Channel

Without shifting, even if the client can buffer data, a maximal 1-delay is inevitable.

The resulting delay: at most 4 slots = 4/5.


Asymptotic results

Asymptotic Results

  • How far can we go with this technique?

  • What happens when d is very large?

  • Answer: Asymptotically, this is an optimal scheme.

  • Proof: Based on Recursive Round Robin (RRR) schedules.


Asymptotic results cont

Asymptotic Results (cont’)

Lower bound [Engebretsen, Sudan, 02]: The guarantied delay for one movie and h channels is at least

Theorem: For h  1, there is a constant ch, such that shifting produces a schedule with maximal delay at most

Proof : Given h,d, we find an RRR schedule on h channels of segments 1,..,s with shift level d, such that s is large enough to satisfy the theorem.

(DLB(1)= 0.58).


Simulation results for h 1

delay

Lower bound=0.58

Number of segments

Simulation Results for h=1

  • We simulate our RRR scheduling algorithm.

  • 30% different from the lower bound for s=8.

  • 13% different from the lower bound for s=120 (one-minute segments in an average movie).


The channel sharing technique for multiple movies

With one movie:

2

4

2

5

2

4

2

5

2a

2b

4a

4b

8a

9a

4a

4b

8b

9b

With two movies:

The Channel Sharing Technique for Multiple Movies

The idea: We can gain from transmitting segments of different movies on the same channel.

Example: For three channels and one movie the best harmonic schedule is of nine segments (delay = 1/9).

For sixchannels and two movies, we have a double-harmonic schedule of ten segments (delay =1/10).

Why does it work? more segments can be transmitted with window close to their requirement.


Asymptotic results1

Asymptotic Results

  • How far can we go with this technique? What happens when the number of movies, m, is very large?

  • Answer: Asymptotically, this is an optimal scheme.

Lower bound: The guaranteed delay for m movies and h channels is at least

Theorem: Forh,m  1, there is a constant ch,m, such that there exists a schedule with guaranteed delay at most

Proof: An algorithm that produces an RRR schedule.


Combining techniques

Combining Techniques

  • The shifting and the channel sharing techniques can be applied together.

  • For small values of h,s, and m, we present schedules that achieve the smallest known delay.

  • Asymptotically, we are getting closer to the lower bound much faster – to show this we analyze and simulate two simple RRR-schedules.


Other models

and Open Problems

Other Models

  • Our shifting and channel sharing techniques can be used also:

  • To reduce average client delay.

  • In the receive-r model - where clients have limited number of readers.

  • For movies with different lengths.

  • For movies with different popularity/priority (where the desired maximal delay varies).

For all these models we have examples of the efficiency of shifting and/or sharing. We have no general algorithm or asymptotic analysis.


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