David Lucantoni DLT Consulting, L.L.C.

1. Panel Topic: After Long Range Dependency (LRD) discoveries, what are the lessons learned so far to provide QoS for Internet advanced applications David Lucantoni DLT Consulting, L.L.C.

2. Markovian is not Poisson • Poisson is Markovian • Markovian >> Poisson • MMPP, Markovian Arrival Process (MAP), etc. • Typical quote from recent LRD literature: “Prior to the work by Leland, et.al., the Poisson model was the most commonly used model for network traffic” • This is incorrect and misleading to students coming into the field • Many LRD papers compare their results only to Poisson or at most a 2-state MMPP • Although MAP’s are technically SRD, the exponential tail may not become dominant for some time (medium range dependence?)

3. Approximating LRD Traffic with an MMPP • 2-state on-off processes • Time constants cover several time scales • Superposition of processes is MMPP • Matches correlation lag over 5 orders of magnitude Andersen, A., Nielsen, B., “A Markovian approach for modeling packet traffic with long range dependence”, IEEE Journal on Selected Areas in Communications, vol. 16, no. 5, pp. 719-732, June, 1998.

4. Approximating LRD Traffic with an MMPP (Cont’d) • A novel feature of this approach is that the number of time scales is part of fitting procedure • Bellcore data, p.Oct.tl, has 1 million samples • Fit results in an 88-state MMPP • Matches autocorrelation • Matches simulated packet loss Salvador, P., Valadas, R., Pacheco, A, “Multiscale fitting procedure for Markov modulated Poisson processes”, INFOCOM, 2002

5. Medium Range Dependence Result • Superposition of 60 on-off sources • Exact analysis • Far from Poisson • Exponential tail does not dominate until blocking is 10-40 Choudhury, Lucantoni, Whitt, “Squeezing the most out of ATM”, IEEE Trans. on Comm, 44, No. 2, 203-217, 1996

6. Known Results for the BMAP/G/1 Queue • Stationary distributions • Queue length distribution at arrivals, departures, arbitrary time • Waiting time distributions • Transient distributions (given the appropriate initial conditions) • P(system empty at time t) • Workload at time t • Queue length at time t • Delay of nth arrival • Queue length at nth departure • P(nth departure occurs less than or equal to time x) Lucantoni, D., “The BMAP/G/1 queue: A tutorial”, Models and techniques for Performance Evaluation of Computer and Communications Systems, Editors: L. Donatiello and R. Nelson, Springer Verlag, 330-58, 1993

7. Sample Transient Results -Virtual Delay Distribution • Superposition of four identical two-state MMPP's • Service times are distributed as E16 • Utilization = 0.7 • queue length = 0 at time 0 • queue length = 32 at time 0 Lucantoni, Choudhury, Whitt, “The transient BMAP/G/1 queue”, Stoch. Mod., 10, No. 1, 145-82, 1994

8. Sample Transient Results -Unstable System • Utilization = 2.0 • Queue length = 0 at time 0 Lucantoni, Choudhury, Whitt, “The transient BMAP/G/1 queue”, Stoch. Mod., 10, No. 1, 145-82, 1994

9. State of LRD Performance Models • Several quotes from Park, K., Willinger, W., “Self-similar network traffic: an overview” in Self-Similar Network Traffic and Performance Evaluation, Edited by Kihong Park and Walter Willinger John Wiley & Sons, Inc., 2000

10. State of LRD Performance Models “A major weakness of many of the [LRD] queueing based results is that they are asymptotic, in one form or another.” • MAP/G/1 results are exact

11. State of LRD Performance Models “A further drawback of current performance results is that they concentrate on first-order performance measures that relate to (long-term) packet loss rate but less so on second order measures - for example variance of packet loss or delay, generically referred to as jitter - which are of importance in multimedia communication.” • Moments as well as distributions can be computed for MAP models

12. State of LRD Performance Models “Even less is known about transient performance measures, which are more relevant in practice when convergence to long-term steady-state behavior is too slow to be of much value for engineering purposes.” • As discussed, many transient distributions can be computed exactly for MAP/G/1

13. VBR Video • LRD community agrees that VBR video is modeled accurately by SRD models • Real-time requirements mandate small buffers and large bandwidth • Small busy periods mitigate the effect of LRD • Few arrivals interact in the queue Heyman, D., Lakshman, T., “Long-Range Dependence and Queueing Effects for VBR Video” in Self-Similar Network Traffic and Performance Evaluation, Edited by Kihong Park and Walter Willinger John Wiley & Sons, Inc., 2000

14. Prediction - • As broadband access becomes more ubiquitous (e.g. cable modem, DSL, etc.) customers expectations will demand better real-time behavior for other types of traffic • Consider web browsing. If a user clicks on a link and doesn’t get a response in the expected time the user will click again resulting in wasted requests and bandwidth • It may be necessary to engineer more and more types of traffic with small buffers and higher bandwidth

15. Prediction (Cont’d) • By the time accurate queueing results become available for LRD traffic models, it might be that most of the traffic in the network will be served like VBR video • Hence LRD would not have any effect on the performance of most traffic

16. Conclusion • If networks are operated in regions where LRD might have an effect on performance then existing Markovian models can be used for dimensioning • In the future, the nature of customer requirements might force the network to be operated in regions where LRD has no effect