We propose and analyze several strategies for performing timestamping of an MPEG-2 Transport Stream transmitted over a packet-switched network using the PCR-unaware encapsulation scheme, and analyze their effect on the quality of the recovered clock at the MPEG-2 Systems decoder. When the timestamping scheme is based on a timer with a fixed period, the PCR values in the packet stream may switch polarity deterministically, at a frequency determined by the timer period and the transport rate of the MPEG signal. This, in turn, can degrade the quality of the recovered clock at the receiver beyond acceptable limits. We consider three timestamping schemes for solving this problem: 1) selecting a deterministic timer period to avoid the phase difference in PCR values altogether, 2) fine-tuning the deterministic timer period to maximize the frequency of PCR polarity changes, and 3) selecting the timer period randomly to eliminate the deterministic PCR polarity changes. For the case of deterministic timer period, we derive the frequency of the PCR polarity changes as a function of the timer period and the transport rate, and use it to find ranges of the timer period for acceptable quality of the recovered clock. We also analyze a random timestamping procedure based on a random telegraph process and obtain lower bounds on the rate of PCR polarity changes such that the recovered clock does not violate the PAL/NTSC clock specifications. The analytical results are verified by simulations with both synthetic and actual MPEG-2 Transport Streams sent to a simulation model of an MPEG-2 Systems decoder.
We examine the problem of accepting a new request for a pre-stored VBR video stream that has been smoothed using any of the smoothing algorithms found in the literature. The output of these algorithms is a piecewise constant-rate schedule for a Variable Bit-Rate (VBR) stream. The schedule guarantees that the decoder buffer does not overflow or underflow. The problem addressed in this paper is the determination of the minimal time displacement of each new requested VBR stream so that it can be accommodated by the network and/or the video server without overbooking the committed traffic. We prove that this call-admission control problem for multiple requested VBR streams is NP-complete and inapproximable within a constant factor, by reducing it from the VERTEX COLOR problem. We also present a deterministic morphology-sensitive algorithm that calculates the minimal time displacement of a VBR stream request. The complexity of the proposed algorithm along with the experimental results we provide indicate that the proposed algorithm is suitable for real-time determination of the time displacement parameter during the call admission phase.
The burstiness of a video source can be characterized by its burstiness curve. The burstiness curve is useful in the optimal allocation of resources to satisfy a desired quality of service for the video stream in a packet network. In this paper, we present deterministic algorithms for exact computation of the burstiness curve of a video source, for both elementary video streams and MPEG-2 Transport Streams. The algorithms exploit the piecewise linearity of the burstiness curve and compute only the points at which the slope of the burstiness curve changes. We also present approximate versions of these algorithms, which save computational effort by considering only a small number of candidate points at which the slope of the burstiness curve may change. The approximate algorithm was able to compute the burstiness curve of a 2-h long elementary video stream in approximately 10 s, as compared to over 6 h for the exact algorithm, with virtually no loss of accuracy in the computation. The efficiency of the proposed algorithms makes them suitable for quality-of-service (QoS) provisioning not only in off-line environments such as in video-on-demand (VoD) servers, but also in real-time applications such as in live TV distribution systems.
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