Traffic variables on an uncongested Internet wire exhibit a pervasive nonstationarity. As the rate of new TCP connections increases, arrival processes (packet and connection) tend locally toward Poisson, and time series variables (packet sizes, transferred file sizes, and connection round-trip times) tend locally toward independent. The cause of the nonstationarity is superposition: the intermingling of sequences of connections between different source-destination pairs, and the intermingling of sequences of packets from different connections. We show this empirically by extensive study of packet traces for nine links coming from four packet header databases. We show it theoretically by invoking the mathematical theory of point processes and time series. If the connection rate on a link gets sufficiently high, the variables can be quite close to Poisson and independent; if major congestion occurs on the wire before the rate gets sufficiently high, then the progression toward Poisson and independent can be arrested for some variables.

The burstiness of Internet traffic was established in pioneering work in the early 1990s, which demonstrated that packet arrival times are not Poisson, and packet and byte counts in fixed-length intervals are long-range dependent [17, 20]. Here we demonstrate that these results are one end of a continuum of traffic characteristics. At the other end are Poisson behavior and independence. Our study focuses on packets, what devices actually see; we study the statistical properties of packet inter-arrival times and packet sizes. As the traffic load increases --- that is, as the number of simultaneous transport connections increases --- arrivals tend to Poisson and sizes tend to independence. More specifically, long-range dependence of inter-arrivals and sizes decreases to independence, and the marginal distribution of inter-arrivals tends toward exponential; this happens (1) through time on a single link as the load increases due to daily variation, or (2) at a single point in time as the load increases going from lightly loaded links at the edges of the Internet to heavily loaded links at the core. Convergence is rapid; the packet traffic gets quite close to Poisson and independent loads far less than the maximum we observe.

Abstract not found

As the active connection load (ACL) on an Internet link increases, the statistical properties of packet inter-arrivals and sizes change due to increased statistical multiplexing of packets from different connections. Chief among these results is that the long-range dependence of the inter-arrivals and sizes goes locally to independence. The results are based on (1) the mathematical theory of superposition of marked point processes, and (2) empirical study of 3026 packet traces, each 5 minutes or 90 seconds in duration, from 6 monitors on Internet links ranging from 100 mbps to 622 mbps. An understanding of packet inter-arrivals and sizes is important because it is packets that devices must send and receive, and the burstiness of traffic as seen by the devices is determined by the statistical characteristics of these two variables. The results for inter-arrivals and sizes do not conflict with previous well known results about the statistical properties of packet and byte counts in fixed time intervals, but the counts do have a different change in statistical properties with the ACL. 1.

We describe a new methodology for analyzing Internet traffic based on an abstract model of application-level communication and statistical cluster analysis, and argue that this method of analysis can serve as a foundation for building flexible traffic generation tools. We present the details of two case studies in which the new analysis tools are applied to data from the University of North Carolina at Chapel Hill and Internet2. 1

Abstract not found

Campus wireless LANs (WLANs) are complex systems with hundreds of access points (APs) and thousands of users. Their performance analysis calls for realistic models of their elements, which can be input to simulation and testbed experiments but also taken into account for theoretical work. However, only few modeling results in this area are derived from real measurement data, and rarely do they provide a complete and consistent view of entire WLANs. In this work, we address this gap relying on extensive traces collected from the large wireless infrastructure of the University of North Carolina. We present a first system-wide, multi-level modeling approach for characterizing the traffic demand in a campus WLAN. Our approach focuses on two structures of wireless user activity, namely the wireless session and the network flow. We propose statistical distributions for their attributes, aiming at a parsimonious characterization that can be the most flexible foundation for simulation studies. We simulate our models and show that the synthesized traffic is in good agreement with the original trace data. Finally, we investigate to what extent these models can be valid at finer spatial aggregation levels of traffic load, e.g., for modeling traffic demand in hotspot APs. ∗ Dr. Hernández-Campos is currently with Google Inc. † Prof. Papadopouli is also affiliated with the Institute of