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=10 Mbps, 34 Mbps, when the link multiplexes Internet traffic. The target buffer overflow probability (BOP) is taken to be BOP<=10^-6. The values are computed using the supinf formula for the traces shown below. The dec and lbl traces had duration 58.33 minutes (350000 epochs of 10 msec), whereas the bc trace had duration 116.67 minutes (700000 epochs of 10 msec). See [CSS98] for details regarding experiments with real traffic. Trace Mean(Mbps) Peak (Mbps) Peak/Mean Std.Dev. bc_10msec_a 0.00638 2.34800 368.023 0.05776 bc_20msec_a 0.00638 1.82400 285.892 0.04699 dec-pkt-1_10msec_a 1.01000 10.16320 10.063 1.26416 lbl-tcp-3_10msec_a 0.26781 8.88960 33.193 0.60415 The other variables in the table are the following: B : buffer size in 10^3 Bytes D : buffer size in msec. This is computed using D=B/R, where R is the cell transfer rate. R=10,34,149,600 Mbps for C=10,34,155,622 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(CLP): what it says (log is base 10) eb : effective bandwidth in Mbps Link: C=10 Mbps (Bellcore - bc_10msec_a) D(msec)B(cells)s(kb^-1) t(msec) st(msec/kb) N load log(CLP) eb(Mbps) ------------------------------------------------------------------------- 1 1250 2.056973E-01 10 2.056973 257 0.16397 -6.005 0.016644 2 2500 1.959568E-01 10 1.959568 319 0.20352 -6.010 0.015478 4 5000 1.798951E-01 10 1.798951 456 0.29093 -6.009 0.013836 6 7500 1.105270E-01 20 2.210541 575 0.36685 -6.008 0.011725 8 10000 1.065875E-01 20 2.131749 662 0.42236 -6.007 0.011347 10 12500 8.360660E-02 30 2.508198 750 0.47850 -6.006 0.010426 12 15000 8.185567E-02 30 2.455670 815 0.51997 -6.001 0.010274 14 17500 6.959921E-02 40 2.783968 875 0.55825 -6.005 0.009752 15 18750 5.397238E-02 60 3.238343 893 0.56974 -6.010 0.009213 16 20000 5.383711E-02 60 3.230227 911 0.58122 -6.011 0.009201 18 22500 5.316077E-02 60 3.189646 948 0.60483 -6.003 0.009142 20 25000 4.490935E-02 80 3.592748 979 0.62460 -6.011 0.008833 25 31250 2.909373E-02 160 4.654997 1044 0.66607 -6.001 0.008232 30 37500 2.775609E-02 170 4.718535 1080 0.68904 -6.013 0.008176 40 50000 1.376386E-02 480 6.606655 1122 0.71584 -6.021 0.007785 50 62500 1.066620E-02 660 7.039690 1145 0.73051 -6.010 0.007678 60 75000 7.973812E-03 960 7.654859 1161 0.74072 -6.014 0.007593 70 87500 5.367336E-03 1550 8.319370 1174 0.74902 -6.022 0.007483 80 100000 5.355137E-03 1550 8.300463 1183 0.75476 -6.011 0.007480 Link: C=34 Mbps (Bellcore - bc_10msec_a) D(msec)B(cells)s(kb^-1) t(msec) st(msec/kb) N load log(CLP) eb(Mbps) ------------------------------------------------------------------------- 1 4250 1.098234E-01 10 1.098234 2653 0.49785 -6.001 0.009355 2 8500 1.052465E-01 10 1.052465 3020 0.56672 -6.001 0.009163 4 17000 6.372010E-02 20 1.274402 3539 0.66411 -6.002 0.008464 6 25500 4.912050E-02 30 1.473615 3864 0.72510 -6.004 0.008131 8 34000 3.227963E-02 60 1.936778 4072 0.76413 -6.003 0.007710 10 42500 2.690349E-02 80 2.152279 4209 0.78984 -6.005 0.007561 12 51000 2.658522E-02 80 2.126817 4322 0.81104 -6.002 0.007543 14 59500 1.661849E-02 170 2.825142 4386 0.82305 -6.005 0.007274 15 63750 1.660698E-02 170 2.823186 4414 0.82832 -6.001 0.007274 16 68000 1.316252E-02 240 3.159005 4436 0.83245 -6.001 0.007189 18 76500 7.862862E-03 480 3.774174 4465 0.83790 -6.011 0.007079 20 85000 7.836684E-03 480 3.761608 4485 0.84168 -6.011 0.007076 25 106250 6.092244E-03 660 4.020881 4528 0.84967 -6.006 0.007034 30 127500 4.511435E-03 960 4.330978 4559 0.85557 -6.010 0.006990 40 170000 3.040121E-03 1550 4.712187 4605 0.86416 -6.004 0.006937 50 212500 2.590403E-03 1880 4.869957 4636 0.87006 -6.003 0.006917 60 255000 2.056522E-03 2470 5.079610 4661 0.87486 -6.002 0.006888 70 297500 1.475055E-03 3650 5.383951 4677 0.87789 -6.009 0.006860 80 340000 1.473062E-03 3650 5.376677 4691 0.88052 -6.002 0.006859 Link: C=34 Mbps (dec-pkt-1_10msec_a) D(msec)B(cells)s(kb^-1) t(msec) st(msec/kb) N load log(CLP) eb(Mbps) ------------------------------------------------------------------------- 1 4250 8.084054E-02 10 0.808405 7 0.20794 -6.654 2.635346 2 8500 7.082818E-02 10 0.708282 9 0.26735 -6.166 2.306180 4 17000 3.804541E-02 20 0.760908 12 0.35647 -6.085 1.865527 6 25500 3.609730E-02 20 0.721946 14 0.41588 -6.002 1.789764 8 34000 3.609730E-02 20 0.721946 15 0.44559 -6.507 1.789764 10 42500 2.273478E-02 40 0.909391 17 0.50500 -6.204 1.576008 12 51000 1.497040E-02 70 1.047928 18 0.53471 -6.127 1.464742 14 59500 1.527681E-02 70 1.069377 18 0.53471 -6.573 1.480345 15 63750 9.144193E-03 130 1.188745 19 0.56441 -6.008 1.383427 16 68000 7.022624E-03 180 1.264072 19 0.56441 -6.141 1.359788 18 76500 7.056065E-03 180 1.270092 19 0.56441 -6.349 1.362632 20 85000 4.236971E-03 330 1.398200 19 0.56441 -6.553 1.329915 25 106250 4.071626E-03 330 1.343637 20 0.59412 -6.074 1.308354 30 127500 4.154298E-03 330 1.370918 20 0.59412 -6.377 1.318977 40 170000 3.234334E-03 440 1.423107 21 0.62383 -6.172 1.290694 50 212500 2.540724E-03 610 1.549842 21 0.62383 -6.552 1.288194 60 255000 2.452463E-03 610 1.496002 22 0.65353 -6.075 1.272429 70 297500 1.501527E-03 1140 1.711741 22 0.65353 -6.434 1.246933 80 340000 1.520474E-03 1140 1.733340 22 0.65353 -6.658 1.251883 Link: C=34 Mbps (lbl-tcp-3_10msec_a) D(msec)B(cells)s(kb^-1) t(msec) st(msec/kb) N load log(CLP) eb(Mbps) ------------------------------------------------------------------------- 1 4250 7.175525E-02 10 0.717553 32 0.25206 -6.144 0.552679 2 8500 6.786156E-02 10 0.678616 39 0.30720 -6.033 0.521251 4 17000 3.919136E-02 20 0.783827 51 0.40172 -6.095 0.448946 6 25500 1.921639E-02 50 0.960819 57 0.44898 -6.106 0.411351 8 34000 9.739377E-03 110 1.071331 59 0.46473 -6.165 0.393585 10 42500 5.187706E-03 220 1.141295 60 0.47261 -6.179 0.384657 12 51000 5.167038E-03 220 1.136748 61 0.48049 -6.142 0.383840 14 59500 5.125701E-03 220 1.127654 62 0.48836 -6.105 0.382220 15 63750 5.167038E-03 220 1.136748 62 0.48836 -6.181 0.383840 16 68000 5.105033E-03 220 1.123107 63 0.49624 -6.069 0.381418 18 76500 2.542004E-03 480 1.220162 63 0.49624 -6.145 0.375860 20 85000 2.516456E-03 480 1.207899 64 0.50412 -6.022 0.374022 25 106250 2.510069E-03 480 1.204833 65 0.51199 -6.012 0.373567 30 127500 2.005500E-03 620 1.243410 65 0.51199 -6.180 0.372326 40 170000 1.000276E-03 1310 1.310362 66 0.51987 -6.205 0.365684 50 212500 9.905174E-04 1310 1.297578 67 0.52775 -6.145 0.364086 60 255000 9.856380E-04 1310 1.291186 68 0.53562 -6.086 0.363295 70 297500 9.758792E-04 1310 1.278402 69 0.54350 -6.028 0.361727 80 340000 9.856380E-04 1310 1.291186 69 0.54350 -6.173 0.363295 References [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.