Ming Li & Wei Zhao on Traffic Models Utilized in Computer Science
Fast Breaking Papers Commentary, June 2011
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Article: Representation of a Stochastic Traffic BounD
Authors: Li, M;Zhao, W |
Ming Li & Wei Zhao talk with ScienceWatch.com and answer a few questions about this month's Fast Breaking Paper paper in the field of Computer Science.
Why do you think your paper is highly
cited?
Teletraffic is a class of fractal time series. It is paid attention to by not only computer scientists but also statisticians and researchers who are interested in fractal signals as well.
Two categories of traffic models are utilized in computer science. One is in deterministic modeling, such as the (sigma, ru) model of Cruz. The other is in stochastic models with long-range dependence (LRD), such as the generalized Cauchy (GC) process. Usually, people are interested in traffic models that exhibit traffic behaviors at both large and small time scales. On the one hand, there are two parameters in the (sigma, ru) model of Cruz to characterize the traffic behaviors at large and small time scales, respectively. On the other hand, there are two parameters, namely, the fractal dimension and the Hurst parameter, in the traffic model of the GC process to respectively describe the small and large scale properties of traffic.
We combine the deterministic traffic model of Cruz with the stochastic traffic model of the GC process to reveal a stochastic bound of traffic. Therefore, the present results in our article may be helpful for researchers who are interested in random fractal traffic, deterministic bound of traffic, or scale analysis of traffic. All results in this article may be a help in fractal time series in general, though the article focused on the topic of traffic time series.
Does it describe a new discovery, methodology, or
synthesis of knowledge?
Figure 1:
Coauthor Wei Zhao.
We discovered a novel bound of traffic. In addition, we established a relationship between the deterministic traffic model of Cruz and the stochastic traffic model of the GC process.
Would you summarize the significance of your paper
in layman's terms?
The traffic model of Cruz has the advantage to deterministically model a traffic time series at the cost of using inequality to characterize the traffic bound. The present representation of traffic bound has the advantage to bound the traffic tighter than that of Cruz. One thing implied in this article is that the potential application of the present bound may considerably improve the computations regarding end-to-end delay of packets based on the network calculus in communication networks.
How did you become involved in this research, and
how would you describe the particular challenges, setbacks, and
successes that you've encountered along the way?
We started this research in 1998. However, we suffered from a lot of setbacks, we do not know how many, in the derivation of a tightened traffic bound as discussed in this article. In 2008, we obtained the results in this article.
Where do you see your research leading in the
future?
Our article may lead to two research topics. One is in the parameter estimations of large and small scale factors of traffic time series. The other is about applications of the present traffic bound to various issues in communication networks, such as packet delay. In addition, we believe that the results in this article may be useful for data modeling in cyber-physical networking systems.
Do you foresee any social or political
implications for your research?
The traffic bound of Cruz in network calculus implies a great idea in theory. It says that arrival traffic can be deterministically modeled instead of stochastically modeling as explained in conventional traffic theory. Therefore, the bound of Cruz substantially differs from extremes in the traditional theory of random processes. It regards arrival traffic that is conventionally considered as a random function as a deterministic one the form of which is unknown.
Our research followed that idea but developed a step further in theory like
this. While taking a random function as a deterministic one, we need the
self-knowledge that we are human beings. Thus, instead of finding an
analytical expression of arrival function, we tightened the bound of Cruz
based on fractals. Therefore, we need to note that the stochastic bound
discussed in our research is not in the field of extremes in the
traditional theory of random processes. More precisely, it is a result of
deterministic bound but tightened stochastically. We hope that the research
idea reflected in our research may have implications in thinking in the
aspect of social or political sciences.
Ming Li
Professor
East China Normal University
Shanghai, Peoples Republic of
China
Web
Wei Zhao
Rector
University of Macau
Macau
Web
KEYWORDS: TRAFFIC MODELING, TRAFFIC BOUND, BURSTINESS, LONG-TERM AVERAGE RATE, LOCAL SELF-SIMILARITY, LONG-RANGE DEPENDENCE, GENERALIZED CAUCHY PROCESS, COMMUNICATION NETWORKS, FRACTAL DIMENSION, ESTIMATORS, PERFORMANCE, CALCULUS, DELAY.