b ' 1994 International Symposium on Speech, Image Processing and Neural Networks, 13-16 April 1994, Hong Kong

The Modelling of Variable Bit Rate Video Traffic

P.C.K. Liu, W.L. Cheung and S. W.J. Tam

Hong Kong Polytechnic Hung Hom, Hong Kong

Abstract:

A simple mathematical treatment was derived to predict the probability of frame loss for four different models of Variable Bit Rate (VBR) video coding such that access control into a high speed network could be enforced effectively.

1 Introduction

The advent of high speed digital signal processing parts and the availability of sophisticated algorithms would find applications in low cost videophone, videoteleconfemeces, and video-on-demand. These compressed video signals have a distinct characteristics different from that of the Poisson based data signals and of the synchronous real-time speech signals. The Variable Bit Rate (VBR) video signals have a variable frame size and there is a certain correlation between the consecutive frames. The statistical properties of the VBR bit stream could be exploited by multiplexing several video sources and with other non-video sources.

To maintain a level of Quality-Of-Service (QOS) in Broadband ISDN, access to the network is controlled by an edge node. To do that, the node processor must quickly calculate the effect of the video call establishment. If the QOS can not be guaranteed, the call should be blocked.

This paper presents some results of signal loss due to multiplexing of more than one VBR video signals. Simple simulation techniques were used for the purpose. Modification of the Markov process was done to model several types video signals.

2 LossEstimates

There are various methods to model the VBR video signal sources and the effects on multiplexing the sources. The common analytical approaches use a fluid approximation and a matrix based method [l-31. The other common approaches are based on simulation techniques of various sorts.

0-7803-1865-X/94/$3.00 0 1994 IEEE 284

Much of the theoretical work rely on the empirical data from measurements [4]. Let h(n) represent the bit rate of a single source in the nth frame, a first order auto regressive Markov process h(n) can be generated using the following equation :

h(n) = a h (n-1) + b p (0)

where a and b are suitable constants and p(w) is a random variable of suitable distribution function. The random variable p(o) in the expression (1) is generated by a normal distribution proposed by Maglaris et al. A Gamma function is shown to be a more accurate representation. The results of the Gamma simulation will be shown later.

2.1

Most of the work to date ignored the effect of frame arrival time between different sources. Figure 1 shows the model for the Interarrival calculation.

Interarrival Period of Multiple Sources

Figure 1: Source arrival and departure time model

Let the start of the i* frame video frame be which is also the end of the i-lth frame. The i" frame period is thus T ~ - T ; _ ~ . The index k=1,2, ..., N represents the video source number and the index i=1,2, ... represents the frame number. N is the total number of video sources. The frame size of the k* source in the i-la frame be represented be n: which can be mapped into the number

ISSIPNN'94

- T I

I '

of cells. It is required that all the n: cells be transmitted before the expiration of the frame period at time 7: otherwise part of the frame elements will be lost due to overwriting of the buffer by the next frame. The formulation below assumes that the frame buffer will be emptied one at a time. If the k" source at the i" period is large, it will be continued to be transmitted beyond the start of frame, T? for the (k+l)" source and in the worst case, the transmission will continue beyond the Nth start of frame, T? until its own end of frame z;+, is reached. In this worst case scenario, the (k+l)" source has a maximum of T;:: -T;+' seconds to empty its buffer. The concept of a quasi-bandwidth is introduced to calculate the ratio of cell loss. A source with a smdler quasi-bandwidth will experience a larger cell loss ratio. In general, the time, xr that the buffer for the

Note that by using the min and max functions, the buffer will be reset at the end of the frame period z: even when its content is not yet totally emptied. In this case, the buffer empty time x: coincides with that of the frame period, zk. The content which is not transmitted is said to have experienced signal loss. The signal loss in terms of cell numbers at this frame is given by:

where r x l represents the smallest integer t x. In terms of frame loss, the frame loss counter, I? ,will be incremented by 1 whenever (pk > 0. Thus the ratios of signal loss for source k, in terms of cells and frames are,

The formulations above can be carried out iteratively until the values become steady.

2.2 Effect of Inter-Source-Departure Time

The time intervals between the different source departure time have a strong effect on the value of the signal losses. The following table illustrates the differences in signal loss if the inter-source departure times are arranged differently.

Table 1 Relations between signal loss and inter-source departure time

ITdl.01 IT=O.Ol IT=O.Ol Ldg=120% L0.072 M.072 k0.086 EO.230 Ldg=l10% L0.049 M.045 L0.057 x.=0.151 Ldg=100% k0.025 M.024 L0.030 M.079

ITdl.02 IT=.0067 IT=.0067 Ldg=120% M.009 M.074 L0.150 50.232 Ldg=llO% M.004 L0.043 L0.059 50.153 Ldg=100% M.001 L0.021 M.059 EO.081

ITdl.01 IT=.0067 ITz.0167 Ldg=120% M.058 M . 1 3 8 M.035 Cdl.231 Ldg=110% M.036 M.095 L0.021 m.152 Ldg=100% M.017 M.053 LA.010 1.=0.080

Here inter-source departure time, I T = z ~ + ' - Z; ; loading, Ldg is defined as the average signal rate to the assigned virtual circuit capacity; signal loss L is the average portion of the signal over-written by the next video frame to the average signal rate for each individual signal and the total signal loss after multiplexing is denoted by the symbol E.

2.3 Quantisalion Effect due to Transmission Block Size

Depending on the multiplexing scheme, a block of signal is transmitted. The entire block is considered to be lost when part of it is lost. These blocks are assumed to be of uniform size for ease of implementation. The smallest unit of a block is an ATM cell. The coarse size of a block will increase loss rate. Table 2 depicts the relationship between block size and signal loss rate. For relative small block size or for large bandwidth, the block size effect is small. However, if the relative signal bit rate and its required channel capacity is small, the coarse block size will increase the loss rate.

hading

120% 110%

100% 90%

3 Other Serving Disciplines

The results presented are based on a serving discipline where the video signal frames are stored in separate buffers and the buffers are emptied one at a time. The advantage of this scheme is that priorities and relative loss can be controlled by arranging the inter-source departure time between the different sources. Another approach is to buffer the incoming video signals in a common buffer on a first come fust serve bases. The frames are therefore stored in an interleaving fashion. Table 3 shows the result of simulation. The block size is assumed to be infmitely small for simplicity. It could be observed that this approach is a fair approach and that the total loss over the multiplexed signal is smaller to that of the f is t approach. However, the smallest loss rate for a single channel can be arranged to be much smaller in the f i s t approach.

Block size: blocks per frame period 300 150 I 75 38 : 19 10

,276 ,278 ,281 I ,285 / ,294 / ,310 ,204 I 205 ,207 ,210 / ,217 / ,230

,140 I ,141 I ,143 I ,145 ,152 ,162

,085 I ,081 I ,087 ,089 I ,094 I ,103

........................................................................ ~ .............._.

Table 3 Relations between signal loss and inter- source departure time, second approach

lTa.01 lT=O.Ol lT=O.Ol

Ldg=120% L0.066 L0.079 L0.042 L0.187 Ldg=llO% L0.043 L0.056 L0.027 1=0.125 Ldg=100% M.023 M.035 M.073 m . 0 7 3

lTS.02 lT=.0067 IT=.0067 Ldg=120% k0.072 M.058 IA.184 1=0.213 Ldg=llO% L0.047 LO.040 L.=O.060 Xd.147 Ldg=lOO% L0.028 L0.024 L0.039 1=0.090

A third approach would be an optimal approach in theory but difficult to implement when high speed transmission is required. In this approach, the size of each frame for the individual signal is assumed to be obtainable and that a packing scheme be employed to reduce the idle period of the inter-source department time. A scheme is currently under investigation.

4 Traffic Modelling

Simulation of four different video scenes were performed using the first order auto-regressive model described earlier. Probabilities of signal loss of the VBR bit streams were obtained using a normal distribution. However, actual data show that a normal distribution is acceptable but a different distribution function could fit the measured data better. Several Gamma distribution models were used to represent four different cases: namely, the videophone, the videoteleconference, the cable TV and the studio TV, respectively. Thus simple models could be used to predict signal loss due to high level of video signal loading which may be useful for network access and control purpose. Two examples on Video conferences and video phones are shown in Figure 2 and Figure 3, respectively.

Video conference

14 l6 T I I

14 l 6 I

Figure 2 Simulated Video conference signals

Video phone

I I

Figure 3 Simulated Video Phone signals

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To facilitate fast computation, the frame size distribution could be modelled by simple Gamma distribution functions as shown in Figure 4. The parameters a and p of the gamma distribution are obtained with standard techniques.

Bit rate distribution of video sources

pdwConference

0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

,Cable TV

+

Bit rate in Mbits

Table 6: CATV Signal Loss Probabilities

CATV Loss Probabilities

70% loading 80% loading 90% loading 95% loading Sim. Cal. Sim. Cal. Sim. Cal. Sim. Cal.

1 0.054 0.056 0.150 0.230 0.306 0.305 0.376 0.386 3 0.002 0.005 0.038 0.062 0.220 0.254 0.350 0.393

5 0.OOO 0.OOO 0.014 0.019 0.160 0.164 0.314 0.311

Table 7: Studio TV Loss Probabilities

Studio TV Loss probabilities 70% loading 80% loading 90% loading 95% loading Sim. Cal. Sim. Cal. Sim. Cal. Sim. Cal.

1 0.OOO 0.OOO 0.022 0.024 0.168 0.179 0.338 0.318 3 0.OOO 0.OOO 0.OOO O.OO0 0.074 0.066 0.234 0.229

5 0.OOO 0.OOO 0.OOO 0.OOO 0.038 0.027 0.172 0.174

It is evident that due to the peakness of the video conference and video phone distributions that a relatively higher signal loss even at low loading values as compared to that of the TV signals.

5.0 Conclusions Figure 4: Bit rate distribution of video sources

The tables below show the results of simulation and from calculation. The two methods track quite well. A switching node could simply calculate the probability of signal loss due to multiplexing a number of video signals.

Table 4 Video Phone Loss Probabilities ~~

Video Phones Loss Probabilities 70% loading 80% loading 90% loading 95% loading Sim. Cal. Sim.. Cal. Sim. Cal. Sim. Cal.

1 0.214 0.214 0.280 0.287 0.358 0.353 0.394 0.388

3 0.150 0.131 0.246 0.252 0.360 0.343 0.408 0.397

5 0.076 0.081 0.194 0.187 0.310 0.321 0.386 0.392

Table 5: Video Conference Loss Probabilities

Video Conference Loss Probabilities 70% loading 80% loading 90% loading 95% loading Sim. Cal. Sim. Cal. Sim. Cal. Sim. Cal.

1 0.180 0.170 0.278 0.260 0.348 0.350 0.402 0.395 3 0.118 0.112 0.210 0.215 0.336 0.335 0.392 0.396

5 0 . i ~ 0.102 0.202 0.206 0.326 0.325 0.394 0.394

The method presented shows potential for further study of the approach to estimate the loss of multiplexing various signals with limited channel capacities. An efficient estimate of the loss probability could facilitate the decision of access control of high speed networks.

References

[l] B. Maglaris et al., "Performance models of statistical multiplexing in a packet video communications," IEEE Trans. Coin". , vol. COM-36, pp.834-844,1988.

D.P. Heyman et al., "Statistical analysis and simulation study of video teleconference traffic in ATM networks," IEEE Trans. Circuits and Sys tem for Video Technology, vol. 2, pp, 49-59, March 1992.

L. Pmcco et al., "A variable bit rate video codec for Asynchronous Transfer Mode networks," IEEE Journal on SelectedAreas in Communications, Vol. 7, No. 5, pp. 761-770, June 1989.

D.L. McLaren and D. Thong Nguyen, "Variable bit rate source modelling of ATM-based video services," Image Communication Vol. 4, pp.233-244, 1992.

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