Variance of Aggregated Web Traffic Robert Morris MIT Laboratory for Computer Science IEEE INFOCOM 2000’

Agenda Introduction Preliminaries Aggregating bandwidth Correlation ON/OFF Comment

Introduction Internet Traffic Model : Poisson In aggregation of multiple sources Poisson : Size of variations in bandwidth increases with the square root of the total bandwidth

Introduction Against Poisson : Strong 24-hour cycle Shared bottleneck problem Global TCP window synchronization

Preliminaries Port 80 Data from Two 24 hour traces of Internet Traffic (Nearly half) 1. Link between Harvard ’ s main campus and its Internet connection – Point-to-point 100Mb Ethernet between two routers – Internet link is 45Mb T3 line – 3pm 16/4/1998

Preliminaries Port 80 Data from Two 24 hour traces of Internet Traffic (Nearly half) 2.Ethernet which have two Lucent ’ s T1 Internet connections – Serves 900 Lucent Bell labs employees – 7am EST 10/12/1998

Preliminaries Treat localhosts as users Count the number of active users by distinct local IP address that appear in the source or destination IP header in that interval Use 0.1s intervals Because router buffering ~ 0.1s Variations in bandwidth at smaller time scales can be smoothed out using buffering

Preliminaries 1. Smooth = s.d. increases with square root of the average 2. Perfectly bursty = s.d. increases linearly with the average

Aggregating bandwidth Average bandwidth for each minute s.d. each minute, taken from 0.1 second samples Both cases : s.d. rises along with the bandwidth at all times

Aggregate bandwidth Each point ( x ) : minute’s average bandwidth ( y ) : variance measured in 0.1-second interval Variance almost linearly with the bandwidth 1. Smooth = s.d. increases with square root of the average 2. Perfectly bursty = s.d. increases linearly with the average

Changes in number of users Correlation Coefficient : ~0.88 (Harward) ~0.84 (Lucent)

Correlation X i : random variables describe the amount of bandwidth produced by ith user in each 0.1 interval X : total amount of bandwidth from all N users in each 0.1 interval Synthetic : 500 sources, on/off on time 4.5s, off time 360s inter-packet spacing 0.06s during on time

Correlation Samples interval over 0.1s 1s 10s are nearly normal distributed

Correlations Because the bandwidths from individual users are not significantly correlated

Per-user Variance

variation in user bandwidth mainly caused by the different OFF period average ON period and transfer size have less effect on the bandwidth for most user. 80% of OFF periods are at least 10 times bigger than ON periods. similar results in both traces

ON/OFF B : user ’ s average bandwidth in a cycle T on : ON period T off : OFF period X : transfer size N : number of samples in cycle B = f(X, T on, T off )

ON/OFF Assume ON period fixed ON value = c for all users Transfer size is fixed. (cc..cc ) K “ c ” s N

Comment Use ~ Normal distribution confirmed But ~ In link at router level Over thousands of connections Our ~ Estimation : make use of normal distribution End-to-end user level. Latest Internet result! (2004->1998~) Corporate ? Because our estimation is poor in determine variance. If linearly relationship forms between variance and the aggregate bandwidth, we can make use to increase the estimation accuracy.