Scheduling Techniques for Media-on-Demand 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 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.

4 Example: One Movie, Two Channels Staggered broadcasting, [ Dan, Sitaram, Shahabuddin, 96 ]: Transmit the movie repeatedly on each of the channels. Guaranteed client delay: at most 1/2 (1/h in general). A clue: With today’s advanced technology, clients can buffer data to their local machine. 0 1/2 1 3/2 2 5/2 3 C1:C1: C2:C2: Can we do better? … …

5 Using Client’s Buffer [ Viswanathan, Imielinski, 96 ]: Partition the movie into segments. Early segments are transmitted more frequently. The client waits for the next slot start, and can then start watching the movie without interruptions. Maximal client delay: 1/3 (slot size). 132 (3 segments) Each time-slot has length 1/3. arrive watch & buffer 0 1/3 2/3 1 4/3 5/3 2 C1:C1: C2:C2: … …

6 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. 444 …

7 Harmonic Window Scheduling Given h, maximize s such that each i in 1,..,s is scheduled with window at most i. Can other techniques do better? Match a lower bound? In general, window scheduling is NP-hard [ Bay-Noy, Bhatia, Naor, Schieber, 98 ]. Good harmonic schedules can be found greedily [ Bar-Noy, Ladner, 02 ] … … … C1C1 C2C2 C3C3 111 … C1C1 Examples: h=1, s=1, D=1 C1C C2C2 … … h=2, s=3. D=1/3 h=3, s=9. D=1/9

8 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 produce 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.

9 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 1 st segment has window d.  The 2 nd 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). arrive buffer watch & buffer d-1 slots s slots The total delay is at most d slots

10 Example I: One Movie, Two Channels Without shifting, the best schedule has delay 1/ C1:C1: C2:C2: C1:C1: C2:C2: With shifting, we can schedule 8 segments 1..8, such that segment i is transmitted in any i+1 window (d=2). … … … … The resulting delay is 2/8 = 1/4.

11 Example I: One Movie, Two Channels For a client arriving during the second slot: C1:C1: C2:C2: arrive buffer watch & buffer tttttttttt Client’s buffer Client watches … …

12 Example II: One Movie, One Channel Without shifting, even if the client can buffer data, a maximal 1-delay is inevitable The first segment is transmitted every 4 th slotThe second segment is transmitted every 4 th slot The third, fourth, and fifth segments are transmitted every 6 th slot. We broadcast segment i in any i+3 (or smaller) window With shifting (d=4): We partition the movie into 5 segments. The resulting delay: at most 4 slots = 4/5. arrive buffer watch & buffer …

13 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.

14 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 c h, 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. (D LB (1)= 0.58).

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

16 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. 2a2b4a 9a8a4b 8b9b With two movies: …… With one movie: …

17 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 Proof: An algorithm that produces an RRR schedule. Theorem: For h,m  1, there is a constant c h,m, such that there exists a schedule with guaranteed delay at most

18 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.

19 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. and Open Problems