Algorithms for Deterministic Call Admission Control of Pre-stored VBR Video Streams Christos Tryfonas ∗ Kazeon Systems, Inc., 1161 San Antonio Road , Mountain View, CA 94043, USA Email: tryfonas@kazeon.com Dimitris Papamichail ∗ Computer Science Department, University of Miami, Coral Gables, FL 33146, USA Email: dimitris@cs.miami.edu Andrew Mehler, Steven S. Skiena Computer Science Department, SUNY at Stony Brook, Stony Brook, NY 11794, USA Email: {mehler, skiena}@cs.sunysb.edu Abstract— 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 dis- placement 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. Index Terms— Variable Bit-Rate Stream, Call-Admission Control, Time Displacement, 3SUM hard, Constant Factor Inapproximable. I. I NTRODUCTION A significant portion of the forecasted network traffic is expected to be multimedia (e.g. voice and video) traffic. New services such as video-on-demand (VoD) and TV broadcasting are currently under massive deployment. One of the salient characteristics of video traffic is that it usually exhibits high variability in its bandwidth demands in different time scales. The need to better understand the bandwidth demands of video streams is essential for * Authors contributed equally to this work. proper resource provisioning of both the network re- sources and the resources of the video servers when stored video is transported. Proper resource dimensioning has direct correlation with the quality of the recovered video on the decoder and, therefore, a variety of techniques have been proposed in the past. Significant work has been done in the literature in the area of statistical modeling of video traffic for resource provisioning purposes, so that it can be effectively trans- ported over packet-switched networks [1]–[5]. In most cases, the objective of these efforts is to build a general model that can be used for resource dimensioning for all the video traffic transported over the network. In some cases, the long-range dependence (LRD) characteristic of video traffic is exploited to create a model of the traffic source [1], [6], [7]. These methods, in general, characterize the traffic source based on its statistical properties, and provide value when the video stream is not known a-priori. However, when dealing with pre-stored video, the resource dimensioning process can be made deterministic and any statistical technique is of limited value, since it does not capture the exact dynamics of the video stream in the time domain. In video applications that transport stored video over a packet-switched network, the resource provisioning pro- cess can take advantage of the fact that video streams can be pre-processed off-line. During the pre-processing of a video stream, a transmission schedule is typically computed to minimize its rate variability and, therefore, facilitate the resource provisioning and the call admission control process. The reduction in rate variability is done by work-ahead smoothing, i.e. sending more data to the receiver with respect to its playback time. Significant JOURNAL OF MULTIMEDIA, VOL. 4, NO. 4, AUGUST 2009 169 © 2009 ACADEMY PUBLISHER