Approximate Analysis of an ATM Multiplexer with MPEG Video Input

Variable bit rate VBR video is expected to be a major source of tra c for the Broadband Integrated Services Digital Network B ISDN The MPEG coding scheme is one of the possibilities considered for the compression of video data In this paper a simple model for an MPEG coded video stream is developed which is used for the approximation of the cell loss rate at an ATM multiplexer bu er with MPEG video input Results showing the approximation quality of the tra c model for several load and cross correlation scenarios are presented Introduction Variable bit rate VBR video is expected to be a major source of tra c for the Broad band Integrated Services Digital Network B ISDN Due to the high bandwidth needs of uncompressed video streams several coding algorithms for the compression of such data streams are in discussion The MPEG ISO Moving Picture Expert Group coding scheme is one of the possibilities considered for the compression of video data One of the major problems analizing multiplexers with compressed video input is the considerable impact of the high level of autocorrelation of the the frame size process of a single stream and the cross correlation e ects of several input streams during multiplexing A large number of models have been proposed to describe the frame size process of a single video tra c source but almost all of them are designed only for the purpose of describing a given video data set as accurately as possible cf for a detailed overview Few of them are used for analysis e g estimating the losses and delays at an ATM multiplexer bu er In this paper a simple model for an MPEG coded video stream is presented which is used for the estimation of the cell loss rate at an ATM multiplexer bu er The analysis is approximate due to the coarse nature of the video tra c model which is substantially di erent from the nature of the models mentioned above The paper is organized as follows In Section the MPEG video tra c model is presented after an outline of some properties of MPEG coded video streams In Section the approximate analysis of the cell loss rate is described and in Section the numerical results are presented A discussion section concludes the paper MPEG video tra c model A video sequence consists of a series of frames each containing a two dimensional array of pixels The number of frames per second and the number of lines per frame and pixels per line depend on national standards For each pixel both luminance and chrominance information is stored A compression algorithm is used to reduce the data rate before transmitting the video stream over communication networks In MPEG coded streams there are three types of frames each using a slightly di erent coding scheme I frames use only intra frame coding based on the discrete cosine transform and entropy coding P frames use a similar coding algorithm to I frames but with the addition of motion compensation with respect to the previous I or P frame B frames are similar to P frames except that the motion compensation can be with respect to the previous I or P frame the next I or P frame or an interpolation between them Typically I frames require more bits than P frames B frames have the lowest bandwidth requirement The di erences in coding result in di erent tra c characteristics for the di erent frame types After coding the frames are arranged in a deterministic periodic sequence e g IBBPBB or IBBPBBPBBPBB which is called frame pattern throughout the rest of the paper These frames are packetized into ATM cells In this paper a payload of Bytes per cell is assumed All frame sizes mentioned in this paper are measured in cells The experimental video data we use is the canyon mpg video which is available via anonymous ftp from several ftp sites The video shows the view from a helicopter ying through Grand Canyon The sequence is about one minute long and the frame pattern of this video is IBBPBB The size of the decoded video frames is Pixels x Pixels Frame type Number Mean Min Max CoV all I P B Table Statistical data of canyon mpg IBBPBB Tab shows some statistical data of the video stream and Fig shows the histograms of the number of cells per frame of the di erent frame types 0. 0 0. 05 0. 10 0. 15 0. 20 0. 25 0. 30 0. 0 0. 05 0. 10 0. 15 0. 20 0. 25 0. 30 0. 0 0. 05 0. 10 0. 15 0. 20 0. 25 0. 30 0 10 20 30 40 50 60 70 80 I Frames P Frames B Frames No. of cells R el at iv e fr eq ue nc y Figure Distributions of the I B and P frame sizes of canyon mpg In addition to the distributions of the frame sizes there are the following correlation properties of MPEG coded video streams which can be used for modeling Dependences introduced by the coding algorithm due to the use of a certain frame pattern short term correlations Long term correlations within the frame process of a single stream The frame pattern plays the most important role concerning autocorrelation e ects of an MPEG video stream coded with di erent types of frames because it xes the periodic nature of the stream Fig shows the coe cients of autocorrelation for several lags of the example stream canyon mpg used for this paper 0 6 12 18 Lag [frames] -1.0 -0.5 0.0 0.5 1.0 C oe ffi ci en t o f a ut oc or re la tio n I B B P B B I B B P B B I B B P B B I Figure Coe cients of autocorrelation of canyon mpg The long term dependences within the stream e g the correlations introduced by similar pictures of one movie scene seem to be less important for the MPEG case whereas they are of great importance for video streams coded only with I frames To check this assumption there is a need for MPEG videos which last longer than some tens of seconds like those available to the author In this paper the frame pattern is the only correlation information which is used for the model The complexity of the analysis taking into account the distributions of all types of frames led to the idea to use only the mean frame sizes FI FP and FB to describe the statistical properties of the three frame types To complete the description of a single MPEG video source the maximum number of cells per frame i e the maximum bandwidth available for a single video stream has to be set This number should be at least as large as the maximum frame size Fmax e g cells for the canyon mpg video Since it is assumed that the video coder transmits an ATM cell as soon as possible we get a model video stream as shown in Fig For the sake of clarity the frame pattern is IP