Vasilios A. Siris December 1997 The tables that follow contain typical values of s,t (computed using the supinf formula [CW96]) for a range of buffer sizes and link capacities C=34 and 155 Mbps, when the link multiplexes MPEG-1 and voice traffic. The target buffer overflow probability (BOP) is taken to be BOP<=10^-7. The multiplexed traffic is a mix of MPEG-1 compressed video and voice traffic. The MPEG-1 sequence containing a segment of the Star Wars movie [Ros95]. In each frame, the cells are assumed to be evenly distributed. No other smoothing is assumed. The sequence contains 40,000 epochs of 40 msec each (total duration approx 30 minutes). The original sequence was segmented into 48 byte payload cells (for simplicity I have not considered other overhead, e.g. AAL). The voice connection contains 30 independent voice channels each modeled using an on-off Markov modulated fluid with peak rate 64 Kbps and average time spent in the ``on'' and ``off'' states 352 msec and 650 msec respectively [Bra69]. See [CSS98] for details regarding experiments with real traffic. Trace Mean (Mbps) Peak(Mbps) Star Wars 0.29 3.46 Voice 0.76 1.48 The other variables in the table are the following: B : buffer size in cells D : buffer size in msec. This is computed using D=B/R, where R is the cell transfer rate. R=34,149,600 Mbps for C=34,155,622 Mbps s : in kb^-1 t : in msec st : product st in msec/kb N : max number of streams multiplexed load : max load (= N*mean/R) log(BOP): what it says (log is base 10) Link: C=34 Mbps, D=4 msec (B=320 cells) Perc voice s(kb^-1) t(msec) st(msec/kb) N load log(CLP) ------------------------------------------------------------------------- .0 3.172954E-02 40 1.269181 62 0.47827 -7.135 .05 3.265026E-02 40 1.306010 59 0.49767 -7.182 .1 3.342933E-02 40 1.337173 57 0.52190 -7.061 .15 3.483676E-02 40 1.393471 54 0.53337 -7.274 .2 3.598271E-02 40 1.439308 52 0.55112 -7.289 .25 3.621190E-02 40 1.448476 51 0.57729 -7.040 .3 3.781622E-02 40 1.512649 49 0.58999 -7.167 .35 3.930595E-02 40 1.572238 47 0.59980 -7.373 .4 4.033731E-02 40 1.613492 46 0.62021 -7.254 .45 4.125406E-02 40 1.650162 45 0.63917 -7.172 .5 4.251460E-02 40 1.700584 44 0.65670 -7.130 .55 4.388974E-02 40 1.755590 43 0.67278 -7.134 .6 4.560866E-02 40 1.824346 42 0.68742 -7.193 .65 4.767136E-02 40 1.906854 41 0.70062 -7.317 .7 5.030704E-02 40 2.012281 40 0.71238 -7.522 .75 5.179677E-02 40 2.071871 40 0.74122 -7.156 .8 5.618047E-02 40 2.247219 39 0.75081 -7.544 .85 5.951792E-02 40 2.380717 39 0.77893 -7.322 .9 6.600742E-02 40 2.640297 39 0.80706 -7.248 .95 8.436341E-02 40 3.374536 39 0.83518 -7.655 1 3.009696E-02 200 6.019392 38 0.84117 -8.136 Link: C=34 Mbps, D=8 msec (B=641 cells) Perc voice s(kb^-1) t(msec) st(msec/kb) N load log(CLP) .0 3.024221E-02 40 1.209689 71 0.54769 -7.082 .04 3.109211E-02 40 1.243684 68 0.56378 -7.144 .1 3.187119E-02 40 1.274847 65 0.59515 -7.004 .14 3.328768E-02 40 1.331507 62 0.60345 -7.222 .2 3.456253E-02 40 1.382501 59 0.62531 -7.273 .24 3.483676E-02 40 1.393471 58 0.64817 -7.064 .3 3.667028E-02 40 1.466811 55 0.66223 -7.286 .34 3.724325E-02 40 1.489730 54 0.68134 -7.152 .4 3.861839E-02 40 1.544735 52 0.70111 -7.191 .44 3.930595E-02 40 1.572238 51 0.71704 -7.131 .5 4.159785E-02 40 1.663914 49 0.73132 -7.323 .54 4.251460E-02 40 1.700584 48 0.74409 -7.358 .6 4.434812E-02 40 1.773925 47 0.76926 -7.230 .64 4.583785E-02 40 1.833514 46 0.77943 -7.362 .7 4.835893E-02 40 1.934357 45 0.80142 -7.371 .74 4.950487E-02 40 1.980195 45 0.82738 -7.016 .8 5.525340E-02 40 2.210136 43 0.82782 -7.899 .84 2.854242E-02 160 4.566787 42 0.83280 -8.088 .9 1.947684E-02 280 5.453514 41 0.84845 -7.711 .94 2.068086E-02 280 5.790640 40 0.85083 -7.972 1 2.165309E-02 280 6.062866 39 0.86330 -7.558 Link: C=155 Mbps, D=4 msec (B=1405 cells) Perc voice s(kb^-1) t(msec) st(msec/kb) N load log(CLP) ------------------------------------------------------------------------- 0 1.519105E-02 40 0.607642 443 0.77979 -7.006 .04 1.590165E-02 40 0.636066 418 0.79080 -7.076 .1 1.670760E-02 40 0.668304 387 0.80857 -7.048 .14 1.719900E-02 40 0.687960 369 0.81954 -7.029 .2 1.808100E-02 40 0.723240 345 0.83436 -7.030 .24 1.877517E-02 40 0.751007 331 0.84407 -7.008 .3 1.966922E-02 40 0.786769 312 0.85723 -7.012 .34 2.056328E-02 40 0.822531 300 0.86375 -7.125 .4 2.161060E-02 40 0.864424 285 0.87683 -7.070 .44 2.207040E-02 40 0.882816 276 0.88548 -7.020 .5 2.340800E-02 40 0.936320 263 0.89570 -7.100 .54 2.434432E-02 40 0.973773 255 0.90202 -7.181 .6 1.134586E-02 160 1.815337 244 0.91129 -7.046 .64 1.196388E-02 160 1.914221 236 0.91248 -7.288 .7 1.228006E-02 160 1.964810 226 0.91844 -7.100 .74 1.281280E-02 160 2.050048 219 0.91882 -7.451 .8 1.373867E-02 160 2.198187 210 0.92253 -7.551 .84 8.813846E-03 280 2.467877 205 0.92755 -7.162 .9 9.216105E-03 280 2.580509 197 0.93025 -7.196 .94 9.537297E-03 280 2.670443 192 0.93191 -7.239 1 9.992733E-03 280 2.797965 185 0.93447 -7.288 Link: C=155 Mbps, D=8 msec (B=2811 cells) Perc voice s(kb^-1) t(msec) st(msec/kb) N load log(CLP) ------------------------------------------------------------------------- .0 1.466909E-02 40 0.586764 491 0.86428 -7.022 .05 7.425731E-03 160 1.188117 454 0.87385 -7.129 .1 7.715918E-03 160 1.234547 422 0.88170 -7.123 .15 8.124434E-03 160 1.299909 394 0.88803 -7.191 .2 8.463747E-03 160 1.354199 370 0.89482 -7.164 .25 8.717585E-03 160 1.394814 349 0.90146 -7.103 .3 2.693926E-03 720 1.939627 330 0.90668 -7.026 .35 2.826440E-03 720 2.035037 312 0.90856 -7.297 .4 2.879769E-03 720 2.073434 297 0.91375 -7.081 .45 3.341100E-03 640 2.138304 283 0.91725 -7.069 .5 3.491606E-03 640 2.234628 270 0.91954 -7.212 .55 3.714537E-03 640 2.377304 258 0.92112 -7.457 .6 3.556437E-03 680 2.418377 248 0.92623 -7.114 .65 3.719591E-03 680 2.529322 238 0.92804 -7.290 .85 6.148519E-03 440 2.705348 206 0.93885 -7.171 .9 6.509759E-03 440 2.864294 199 0.93969 -7.439 .95 6.535206E-03 440 2.875490 193 0.94312 -7.209 1 6.972166E-03 440 3.067753 187 0.94457 -7.365 References [Bra69] P.T. Brady. A model for generating ON-OFF speech patterns in two-way conversations. Bell Syst. Tech. J., 48, September 1969. [CSS98] C. Courcoubetis, V.A. Siris, G.D. Stamouli. Application and evaluation of large deviation techniques for traffic engineering in broadband networks. In Proc. of ACM SIGMETRICS'98/ PERFORMANCE'98, Madison, Wisconsin, June 1998. [CW96] C. Courcoubetis and R. Weber. Buffer overflow asymptotics for a switch handling many traffic sources. Journal of Applied Probability, 33, 1996. [Ros95] O. Rose. Statistical properties of MPEG video traffic and their impact on traffic modeling in ATM systems. University of Wuerzburg. Institute of Computer Science Research Report Series. Report No. 101.