Vasilios A. Siris
July 1997 

These are some typical values of s,t (computed using the supinf
formula [CW96]) for C=34, 155, and 622 Mbps links and a range of
buffer sizes. The buffer overflow probability is approx. 10^-7. 

The source is an 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). 

Other MPEG files, for the same values of C,B, and CLP, give
approximately the same product s*t. See [CSS98] for details regarding
experiments with real traffic.

Trace      Mean (Mbps)       Peak(Mbps)
Star Wars  0.29              3.46

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


Link: C=34 Mbps 
D(msec) B(cells)s(kb^-1)	t(msec)
--------------------------------------
1 	80 	3.27 E-02 	40
2 	160 	3.23 E-02 	40
4 	320 	3.16 E-02 	40
6 	481 	3.06 E-02 	40
8 	641 	3.01 E-02 	40
10 	801 	2.98 E-02 	40
15 	1202 	2.82 E-02 	40
20 	1603 	1.42 E-02 	160
25 	2004 	2.08 E-03 	1560
30 	2405 	1.99 E-03 	1560
40	3207	1.57 E-03	2080
50	4009	1.13 E-03	2880


Link: C=155 Mbps (ATM cell transfer rate approx. 149 Mbps)
D(msec) B(cells)s(kb^-1)	t(msec)
--------------------------------------
1	351	1.56 E-02	40
2	702	1.55 E-02	40
4	1405	1.52 E-02	40
6	2108	1.51 E-02	40
8	2811	1.47 E-02	40
10	3514	6.97 E-03	160
15	5271	1.03 E-03	1560
20	7028	7.75 E-04	2080
25	8785	6.85 E-04	2400
30	10542	4.76 E-04	3520
40	14056	3.03 E-04	5800
50	17570	2.98 E-04	5800


Link: C=622 Mbps (ATM cell transfer rate approx. 600 Mbps)
D(msec) B(cells)s(kb^-1)	t(msec)
--------------------------------------
1 	1415 	8.06 E-03  	40 
2 	2830 	7.94 E-03  	40 
4 	5660 	3.59 E-03  	160
6 	8490 	5.25 E-04  	1560 
8 	11320 	5.21 E-04  	1560 
10 	14150 	4.04 E-04  	2080 
15 	21226 	2.47 E-04  	3520 
20 	28301 	1.55 E-04  	5800 
25 	35377 	1.56 E-04  	5800 
30 	42452 	1.54 E-04  	5800 
40	56603	9.53 E-05	9880
50	70754	9.59 E-05	9880




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.

[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.