# A Measurement-Analytic Approach for QoS Estimation (Completed)

**Do Young Eun **(Dept. of ECE, North Carolina State University) **Ness B. Shroff **(Dept. of ECE, Purdue University)

### Publications

- Do Young Eun and Ness B. Shroff, ” A Measurement-Analytic Approach for QoS Estimation in a Network based on the Dominant Time Scale”,
*IEEE/ACM Transactions on Networking*, 11(2), pages 222-235, April. 2003 - Do Young Eun and Ness B. Shroff, “A Measurement-Analytic Framework for QoS Estimation based on the Dominant Time Scale”, in
*Proceedings of IEEE INFOCOM*, 2001

### Research Summary

In this work, we have developed a measurement-analytic framework in which we are able to accurately estimate the *queue-length distribution* (QLD) at any node where a moderate to a large number of flows are aggregated. In the literature, the notion of the *dominant time scale* (DTS) (or critical- or relevant-time scale) has been useful in estimating the QLD. The DTS corresponds to the time-scale relevant for describing the queueing behavior based on particular network configurations, and it is closely related to the concept embodied in the statement “rare event occurs only in the most probable way.” In particular, the QLD depends only on the input statistics up to the DTS. This feature of the DTS led researchers to believe that correlations of input traffic only up to the DTS really matter in estimating the QLD, and it was taken as a way of compromising the dichotomy between the realms of SRD (short-range dependent) and LRD (long-range dependent) models. However, we noted that this in fact could be misleading. Since the DTS is itself defined as a global maximizer of certain statistics of the input traffic over all time, we would still need to know (or estimate by measurements) the statistics over all time to find the DTS, thereby defeating the original feature of the DTS. This in essence results in a *chicken-and-an-egg type of cycle*, which appears to make the problem hopeless. However, we developed a stopping criterion to successfully break this cycle and obtained a bound on the DTS. Thus, our result has significant implications for network measurements in that we only need to measure the statistics of the traffic up to the bound on the DTS, in order to accurately estimate the QLD at any point in the network. We also extended this work to general work-conserving scheduling schemes such as priority queueing and Generalized Processor Sharing (GPS).

### Some Related Papers

- J. Choe and N. B. Shroff, “Use of the supremum distribution of Gaussian processes in queueing analysis with long-range dependence and self-similarity,”
*Stochastic Models,*vol. 16, Issue No. 2, February 2000. - J. Choe and N. B. Shroff, “On the Supremum Distribution of Integrated Stationary Gaussian Processes with Negative Linear Drift, ”
*Advances in Applied Probability,*March 1999, vol. 31, pp. 134-156. - J. Choe and N. B. Shroff, “A Central-Limit-Theorem Based Approach for Analyzing Queue Behavior in ATM Networks,”
*IEEE/ACM Trans. on Networking,*vol. 6, no. 5, October 1998, pp. 659-671. - H. Kim and N. B. Shroff, “Loss Probability Calculations at a Finite Buffer Multiplexer,”
*IEEE/ACM Trans. on Networking,*vol. 9, no. 6, Dec. 2001, pp. 765–768. - M. Grossglauser and J-C. Bolot, “On the Relevance of Long-Range Dependence in Network Traffic,”
*IEEE/ACM Trans. on Networking*, vol 7, no 5, October 1999. - C. Courcoubetis, V.A. Siris, and G. Stamoulis, “Application of the many sources asymptotic and effective bandwidths for traffic engineering,”
*Telecommunications Systems,*12 (1999) 167–191.