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
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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.

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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.

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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 todays advanced technology, clients
can buffer data to their local machine.
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Using Clients Buffer
Viswanathan, Imielinski, 96 Partition the
movie into segments. Early segments are
transmitted more frequently.
1
3
2
(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).
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Using Clients 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.

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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.

h3,
s9. D1/9

• 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?
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Our Results

• Two new segment-scheduling techniques
• - Shifting.
• - Channel sharing.

• A lower bound for the guaranteed clients 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.

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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 di-1 slots (d is the shifting
  level).
• The 1st segment has window d.
• The 2nd segment has window d1, 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
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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 i1
window (d2).
C1
C2
The resulting delay is 2/8 1/4.
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Example I One Movie, Two Channels
For a client arriving during the second slot
Clients buffer
Client watches
5
6
7
8
4
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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.
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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.

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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).
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Simulation Results for h1

• We simulate our RRR scheduling algorithm.
• 30 different from the lower bound for s8.
• 13 different from the lower bound for s120
  (one-minute segments in an average movie).

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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 six channels 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.
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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 For h,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.
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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.

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Other Models
and Open Problems

• 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.