Origin of Critical Behavior in Ethernet Traffic

We perform a simplified Ethernet traffic simulation in order to clarify the physical mechanism of the phase transition behavior which has been experimentally observed in the flow density fluctuation of Internet traffic. In one phase traffics from nodes connected with an Ethernet cable are mixed, and in the other phase, the nodes alternately send bursts of packets. The competition of sending packets among nodes and the binary exponential back-off algorithm are revealed to play important roles in producing $1/f$ fluctuations at the critical point.Comment: 14 pages, 9 figures. To appear physica

Understanding Internet topology: principles, models, and validation

Building on a recent effort that combines a first-principles approach to modeling router-level connectivity with a more pragmatic use of statistics and graph theory, we show in this paper that for the Internet, an improved understanding of its physical infrastructure is possible by viewing the physical connectivity as an annotated graph that delivers raw connectivity and bandwidth to the upper layers in the TCP/IP protocol stack, subject to practical constraints (e.g., router technology) and economic considerations (e.g., link costs). More importantly, by relying on data from Abilene, a Tier-1 ISP, and the Rocketfuel project, we provide empirical evidence in support of the proposed approach and its consistency with networking reality. To illustrate its utility, we: 1) show that our approach provides insight into the origin of high variability in measured or inferred router-level maps; 2) demonstrate that it easily accommodates the incorporation of additional objectives of network design (e.g., robustness to router failure); and 3) discuss how it complements ongoing community efforts to reverse-engineer the Internet

A method to assess demand growth vulnerability of travel times on road network links

Many national governments around the world have turned their recent focus to monitoring the actual reliability of their road networks. In parallel there have been major research efforts aimed at developing modelling approaches for predicting the potential vulnerability of such networks, and in forecasting the future impact of any mitigating actions. In practice-whether monitoring the past or planning for the future-a confounding factor may arise, namely the potential for systematic growth in demand over a period of years. As this growth occurs the networks will operate in a regime closer to capacity, in which they are more sensitive to any variation in flow or capacity. Such growth will be partially an explanation for trends observed in historic data, and it will have an impact in forecasting too, where we can interpret this as implying that the networks are vulnerable to demand growth. This fact is not reflected in current vulnerability methods which focus almost exclusively on vulnerability to loss in capacity. In the paper, a simple, moment-based method is developed to separate out this effect of demand growth on the distribution of travel times on a network link, the aim being to develop a simple, tractable, analytic method for medium-term planning applications. Thus the impact of demand growth on the mean, variance and skewness in travel times may be isolated. For given critical changes in these summary measures, we are thus able to identify what (location-specific) level of demand growth would cause these critical values to be exceeded, and this level is referred to as Demand Growth Reliability Vulnerability (DGRV). Computing the DGRV index for each link of a network also allows the planner to identify the most vulnerable locations, in terms of their ability to accommodate growth in demand. Numerical examples are used to illustrate the principles and computation of the DGRV measure