Scheduling Techniques for Broadcasting Popular Media.

1. Scheduling Techniques for Broadcasting Popular Media. Amotz Bar-Noy Brooklyn College Richard Ladner Tami Tamir University of Washington

2. 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.

3. Minimizing Clients’ Maximal Delay. • We measure the quality of service by the maximal possible delay (different from ‘average delay’). • Our goal is to guarantee that no client will wait more than some ‘D’. Short delay = happy customers

4. 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.

5. Broadcasting Schemes for Media-on-Demand Systems. This means that the client can read data at a rate which is h times the rate needed for playback. With new technologies, this is possible!

6. 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.

7. 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 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).

8. C1: 1 1 1 1 1 1 … C2: 2 3 2 3 2 3 … Using Client’s Buffer Why does it work? The first segment is transmitted in any window of one slot. The second segment is transmitted in any window of two slots. The third segment is transmitted in any window of three slots.

9. 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. …

10. 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 2 3 2 3 2 3 … 4 4 4 C1 … C2 … 5 5 5 … C3 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 6 7 3 8 3 6 7 3 8 9 9 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 Can other techniques do better? Match a lower bound?

11. Example: Input: W={2,4,5} Output: one channel … 4 2 5 2 4 2 5 2 4 2 5 2 There is at least one transmission of in any window of 5 time-slots There is at least one transmission of in any window of 4 time-slots 5 4 The Windows Scheduling Problem • Input: A set W={w1,w2,…,wn} of requests for periodic broadcast. A request with window wi needs to be tranmitted at least once in any window of wi time-slots. • Output: A feasible windows scheduling of W. • Goal: minimize number of channels used.

12. w = 3 w = 4 w = 5 The Windows Scheduling Problem • Windows Scheduling has applications in media delivery systems, and in machine maintenance. • Client-server-provider. • QoS in push system. • - MoD systems. • Periodic job-scheduling Transmit the weather at least once in any 3 time units. Replace batteries at least once a week

13. Our Results - Better Techniques • Two new segment-scheduling techniques: • Shifting. • Channel sharing. • A lower bound for the minimum client’s delay (generalizes the lower bound of [Engebretsen, Sudan, 02] for a single movie). • Each of these techniques produces schedules that - 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.

14. 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 slots (d is the shifting level). • The 1stsegment has window d+1. • The 2nd segment has window d+2, etc. • The client waits for the next slot start, buffers data during the next d slots, and then starts watching the movie (while continue buffering). The total delay is at most d+1 slots arrive buffer watch & buffer d slots s slots

15. … 1 1 1 1 1 1 … 2 3 2 3 2 3 3 3 3 4 4 4 1 1 1 1 1 1 2 5 6 2 7 2 5 6 2 7 8 8 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=1). C1: C2: The resulting delay is (d+1)/s =2/8 = 1/4.

16. t t t t t t t t t t C1: 1 3 1 4 1 3 1 4 1 3 1 4 … C2: 2 5 6 2 7 8 2 5 6 2 7 8 … 1 6 8 2 4 7 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

17. 1 1 1 C1 … Example II: One Movie, One Channel Without shifting, even if the client can buffer data, a maximal 1-delay is inevitable. If you are taking a short nap, and you miss the beginning of the movie, you must wait for the next broadcast - even if you have your very own screen.

18. With shifting (d=3): 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 4 5 3 4 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 … The resulting delay: at most 4 slots = 4/5.

19. (DLB(1)= 0.58). Asymptotic Results • How far can we go with this technique? • What happens when d is very large? • Answer: Asymptotically, this is an optimal scheme. • Lower bound [Engebretsen, Sudan, 02]: The 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 delay at most

20. Simulation Results for h=1 delay Lower bound=0.58 Number of segments • 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).

21. 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 guarantees max delay 1/9. 1 2 3 4 5 9 6 7 8 Bandwidth is lost since the actual windows of 5,7,8,9 are smaller than required. Can we do better with sixchannels and two movies?

22. 3 3 6 6 2 2 4 4 7 7 5 5 8 8 9 9 Only these segments have an actual small window 10 10 Channel Sharing - continue For sixchannels and two movies, we have a double-harmonic schedule of ten segments (delay =1/10). Ch4 Ch3 1 1 Ch1 Ch2 Ch5 Ch6

23. 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.

24. 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.

25. Algorithm RR1 Algorithm RR2 Greedy Algorithm 0.55 0.55 0.55 0.5 0.5 0.5 0.45 0.45 0.45 m=1 0.4 0.4 0.4 m=2 m=3 0.35 0.35 0.35 m=5 delay m=10 0.3 0.3 0.3 m=20 0.25 0.25 0.25 m=50 m=80 0.2 0.2 0.2 0.15 0.15 0.15 0.1 0.1 0.1 1 5 15 25 40 1 5 15 25 40 1 5 15 25 40 # of segments # of segments # of segments Combining Techniques – Simulation Results Case study 1: h=2m D  0.158

26. m=1 1.05 m=2 m=3 1 m=5 0.95 m=10 m=20 0.9 m=50 0.85 m=80 0.8 0.75 0.7 0.65 0.6 1 5 15 25 40 0.55 Combining Techniques – Simulation Results Algorithm RR1 Algorithm RR2 Greedy Algorithm delay 1 5 15 25 40 1 5 15 25 40 # of segments # of segments # of segments Case study 2: m=h. D  0.582

27. 2.1 2.1 2.1 2 2 2 m=2 1.9 1.9 m=4 1.9 m=6 m=10 1.8 1.8 m=20 1.8 m=50 m=80 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1 5 15 25 40 1 5 15 25 40 1 5 15 25 40 Combining Techniques – Simulation Results Algorithm RR1 Algorithm RR2 Greedy Algorithm delay # of segments # of segments # of segments Case study 3: h=½m D  1.552

28. 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.

29. More Open Problems • Product delivery systems: Any popular digital data can be broadcast - games, software (originals and updates), educational material. • Delivering multimedia vs. flexible data (that can be received in any order). • Delivering dependent data (e-learning) • Integrated error recovery. • Combining broadcasting and unicast. • Better broadcasting techniques, better disk utilization.