CIPP — a versatile analytical model for VBR traffic
Introduction
Digital video communications (like video phone, video conferencing, television distribution, etc.) form a major class of services provided by broadband networks. Accordingly, the video transport over broadband networks is of significant interest. Most of the video encoding is done using the MPEG standards. The output of the encoder in MPEG systems can be either constant bit rate (CBR) or variable bit rate (VBR). A constant quality video signal is delivered at the receiver by VBR, but at the cost of complex transmission. Broadband network like ATM takes advantage of the bit rate variations of individual sources by statistical multiplexing. In this way, the individual (video) sources share a link of capacity less than the sum of individual peak rates, achieving significant multiplexing gain. This multiplexing gain is restricted by the quality of service (QoS) requirements of the sources. Thus statistical multiplexing could lead to more efficient use of network resources, but may require new kinds of bandwidth management, QoS provisioning and traffic control.
Statistical multiplexing involves N input streams (which are asynchronous and statistical) and N output streams, so that traffic from any of the N input streams can be switched over to any of the N output streams. Now each of the N output streams can be modeled as a single server queue, with the arrival streams forming the superposition of N input streams in general. Accordingly, this single server (with such arrival streams) has been of interest to telecommunication researchers over the years. Hence, understanding the nature of traffic in such heterogeneous multiservice networks is essential for engineering, operations and performance evaluation of these networks. Moreover, to facilitate the mechanization of multiplexing, routing and control, it is imperative to appropriately model and characterize the input traffic and to map the input source parameters (could be mean bit rate, peak bit rate or it could be even Hurst parameter (H) which measures the degree of self-similarity) into network parameters (could be mean cell delay, cell loss rate or delay jitter). In light of the above, an important question often raised by network planners and designers is: “Is there an accurate and useful traffic model in the form of a simple stochastic process with minimal parameters and when fed into the single server queue, gives the same queuing performance as a real traffic stream?” Such a traffic model will be very useful in network design tools or in tools supporting real-time traffic management. We intend here to use the fact that the interarrival correlation plays a major role in imitating the self-similar behavior in increments of the corresponding counting process and to make a contribution towards this key aspect of video traffic modeling.
Two classes of traffic models have been proposed in literature, for modeling the bit rate of a VBR video source, namely, short range dependent (SRD) models [3], [4], [5], [6] and long range dependent (LRD) (or self-similar) models [7], [8]. SRD models addressed in the literature, in turn, broadly fall into two categories: single source models [3], [4], [5], [9] and multiplexed source models [3], [6]. For low motion video telephony and medium-motion video conferencing, there exist the autoregressive (AR) model [3], [5], the discrete autoregressive (DAR(1)) model [4] and the discrete state continuous time Markov model [3], [5]. For full motion MPEG video source, a three class AR model with time-varying coefficients has been developed in [9]. Xu et al. [10] proposed a GAR(1) model for VBR traffic. In [11], a model based on arrival rate histograms of VBR traffic has been proposed and a quasi-static approximation is made for buffer occupancy distributions and cell loss rates. Most of the SRD models proposed for VBR traffic are analytically intractable [4], [6], [9], [11]. Moreover, those SRD models which are analytically tractable [3], [5] predict the queuing performance measures over optimistically. Note that the LRD (or self-similar) models also lack analytical tractability, except that few bounds are obtained for some queuing measures [12], [13].
The above models are intended to capture the correlation in the counts sequence (cells per frame) by a DAR(1) model as in [4] or in the rate process as in ARMA models [3], [4] or by the modulating Markov chain (MC) as in SRD models. In models based on self-similarity (or LRD) or AR models, correlations are in rate process (equivalently cells per unit time). In [1], [2], we proposed a model called correlated interarrival time Poisson process (CIPP) for composite traffic modeling and individual video source modeling. We argued that it is more appropriate to consider a model which captures the correlation in the interarrival sequence rather than the correlation in counts sequence as in the above models. In CIPP, the interarrivals form a first order Markov sequence. In [1], [2], it is shown that the CIPP does exhibit self-similarity over a range of time scales of interest. It is also analytically tractable (see, for instance, [14], [15]). In this paper, after giving a brief account of CIPP, we derive the stationary distributions in a CIPP/M/1 queue and then undertake the performance modeling of a statistical multiplexer with VBR video traffic input using the CIPP/M/1 queue. The rest of the paper is organized as follows. In Section 2, we give a short mathematical account of the CIPP process. Section 3 gives analytical results for the CIPP/M/1 queue. In Section 4, we present the performance modeling of VBR traffic using CIPP/M/1 queue. In Section 5, simulation results corresponding to MPEG-1 real-world VBR traffic traces are given. Section 6 concludes the paper.
Section snippets
Correlated interarrival time Poisson process
In this section, we give the axiomatic derivation of CIPP. Few remarks are given to highlight some important features of the CIPP model.
CIPP/M/1 queue
In this section, we obtain analytical expressions for the waiting time distribution and buffer occupancy distribution. Before going into the details of CIPP/M/1 queue, we would like to mention some points about the CIPP/D/1 queue. In [15], the approach of Benes is used to obtain the approximate expression for the buffer occupancy distribution in a CIPP/D/1 queue. Since, this (approximate) analytical expression for the buffer occupancy distribution poses a numerical problem for large values of ρ
Performance modeling of statistical multiplexer with VBR traffic input by CIPP/M/1 queue
Before discussing the performance modeling of statistical multiplexer with real-world VBR video traffic by CIPP queues, we present here the simulation methodology for our performance modeling study.
Simulation results
In this section, we consider the performance modeling of statistical multiplexer with real-world MPEG-1 VBR video traffic using CIPP/M/1 queue. Queuing performance measures4 considered here are mean waiting time, PDV and overflow probability which
Conclusions
In this paper, we have developed the theory for CIPP/M/1 queue and used it to characterize the queuing situation encountered by the VBR video traffic in a statistical multiplexer. We observed that not only the first order statistics of queuing performance corresponding to data namely, the mean waiting time for packets is well modeled by CIPP/M/1 queue but the overflow probability and the higher order statistics namely the PDV as well. In summary, we noted the following:
- 1.
For the VBR video
Acknowledgements
The authors thank the reviewer for many useful suggestions which improved the presentation of this paper.
R. Manivasakan completed his AMIE in 1989. He received his M.E. from the College of Engineering, Anna University, Madras and Ph.D. from IIT, Mumbai in 1993 and 2000, respectively. Currently he is doing his post-doctoral research in Hong Kong University of Science and Technology since July 2000. His research interests include broadband teletraffic modeling, link sharing problems and design of all-optical networks.
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R. Manivasakan completed his AMIE in 1989. He received his M.E. from the College of Engineering, Anna University, Madras and Ph.D. from IIT, Mumbai in 1993 and 2000, respectively. Currently he is doing his post-doctoral research in Hong Kong University of Science and Technology since July 2000. His research interests include broadband teletraffic modeling, link sharing problems and design of all-optical networks.
Abhay Karandikar received his B.E. from Jiwaji University in 1986 and M.Tech. and Ph.D. from IIT Kanpur in 1988 and 1994, respectively. He has worked in Center for Development of Advanced Computing, Pune, India, from 1994 to 1997. Since 1997, he is working as an Assistant Professor in Department of Electrical Engineering in IIT, Mumbai. His research interests include QoS guarantees in Internet.
U.B. Desai received his B.Tech. degree from Indian Institute of Technology, Kanpur, India, in 1974, the M.S. degree from the State University of New York, Buffalo, in 1976, and the Ph.D. degree from The Johns Hopkins University, Baltimore, MD, in 1979, all in Electrical Engineering. From 1979 to 1984, he was an Assistant Professor in the Electrical Engineering Department at Washington State University, Pullman, WA, and an Associate Professor at the same place from 1984 to 1987. Since 1987, he has been a Professor in the Electrical Engineering Department at the Indian Institute of Technology, Mumbai. He has held Visiting Associate Professor’s position at Arizona State University, Tempe, Purdue University, West Lafayette, IN, and Stanford University, Stanford, CA. His research interests are in the areas of multimedia, image and video processing, artificial neural networks, computer vision, adaptive signal processing, space–time signal processing and its application to communication, wavelet analysis, and network traffic modeling. He is also interested in distant education technology. He is the Editor of the book Modeling and Applications of Stochastic Processes (Kluwer Academic Press, Boston, MA, 1986). Dr. Desai is a Senior Member of IEEE and Fellow of IETE. He is an Associate Editor of IEEE Transactions on Image Processing, and he is on the Editorial Board of International Journal of Image and Graphics.