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Transmission Server 0 Retrieval Transmission Server 1 Retrieval ... ...
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Figure 10.3 Service round misalignment between different servers
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A Concurrent Push-Parallel Server Architecture
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Server 0
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Disk Read Transmission
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Server 0
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Server 1 New Request
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Figure 10.4 Transmission jitter depends on both clock jitter and request arrival time
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Theorem 10.1. Assume that new-session requests arrive at all servers at the same time, then the transmission jitter is bounded by TF Proof. Please refer to the Appendix. This bound on transmission jitter will be used to derive the amount of buffer required at the client to prevent buffer under ow and over ow respectively. (10.3)
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10.3.2 Video Block Consumption Model
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Many studies on VoD systems assume that video data are consumed periodically by the video decoder. However, our experience in programming some off-the-shelf hardware and software video decoders reveals that the decoder consumes xed-size data blocks only quasiperiodically. Given the average video data rate, RV , and block size, Q, the average time for a video decoder to consume a single block is Tavg = Q RV (10.4)
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To quantify the randomness of video block consumption time, we rst de ne a few notations. De nition 10.1. (a) Let Ti be the time the video decoder start decoding the ith video block, then the decoding-time deviation of video block i is de ned as TDV (i) = Ti i Tavg T0 and decoding is late if TDV (i) > 0 and early if TDV (i) < 0. (10.5)
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(b) The maximum lag in decoding, T L , and maximum advance in decoding, T E , are de ned as: TL = max{TDV (i)| i 0} TE = min{TDV (i)| i 0} (c) The peak-to-peak decoding-time deviation is de ned as TDV = TL TE (10.8) (10.6) (10.7)
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Assume the bounds TL and TE are known, the time between the consumption of two video blocks i and j ( j > i) will be bounded by max{(( j i)Tavg TDV ), 0} t (( j i)Tavg + TDV ) (10.9)
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We use buffers at the client to absorb these variations to prevent buffer under ow and buffer over ow during playback. Let there be L C = (Y + Z ) buffers (each Q bytes) at the client, organized as a circular buffer. The client starts video playback once the rst Y buffers are completely lled with video data. We pre ll buffers before playback to avoid buffer under ow, and reserve the last Z buffers for incoming data to avoid buffer over ow.
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10.3.3 Buffer Needed to Prevent Under ow
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Since all N S servers transmit data to a client concurrently, the client will be receiving N S video blocks simultaneously. Hence Y must be multiples of N S . We let y = Y /N S and consider groups of N S buffers in the follow derivations (i.e., group zero consists of blocks 0 to N S 1, group one consists of blocks N S to 2N S 1, and so on.). Among the N S servers, let the earliest transmission for the rst round start at time t0 , then the last transmission for the rst round must start at time t0 + . Therefore, the time for video block group i to be completely lled, denoted by F(i), is bounded by ((i + 1)TF + t0 + f ) F(i) ((i + 1)TF + t0 + + f + ) (10.10)
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where f + ( f + 0) and f ( f 0) are used to model the maximum transmission time deviation due to randomness in the system, including transmission rate deviation, CPU scheduling, bus contention, etc. Since the client starts playing the video after lling the rst y groups of buffers, the playback time for video block group 0 is simply F(y 1). From Section 10.3.2, setting T0 = F(y 1) then the playback time for video block group i, denoted by P(i), is bounded by {i Ns Tavg + F(y 1) + TE } P(i) {i Ns Tavg + F(y 1) + TL } (10.11)
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To guarantee video playback continuity, we must ensure that a video block group arrives before playback deadline. In the worst-case scenario, the latest lling time must be smaller than the earliest playback time, i.e. max{F(i)} < min{P(i)} (10.12)