New source-level models for aggregated HTTP traffic and a design for their integration with the TCP transport layer are built and validated using two large-scale collections of TCP/IP packet header traces. An implementation of the models and the design in the ns network simulator can be used to generate web traffic in network simulations.

Network devices put packets on an Internet link, and multiplex, or superpose, the packets from different active connections. Extensive empirical and theoretical studies of packet traffic variables --- arrivals, sizes, and packet counts --- demonstrate that the number of active connections has a dramatic effect on traffic characteristics. At low connection loads on an uncongested link --- that is, with little or no queueing on the link-input router --- the traffic variables are long-range dependent, creating burstiness: large variation in the traffic bit rate. As the load increases, the laws of superposition of marked point processes push the arrivals toward Poisson, the sizes toward independence, and reduces the variability of the counts relative to the mean. This begins a reduction in the burstiness; in network parlance, there are multiplexing gains. Once the connection load is sufficiently large, the network begins pushing back on the attraction to Poisson and independence by causing queueing on the link-input router. But if the link speed is high enough, the traffic can get quite close to Poisson and independence before the push-back begins in force; while some of the statistical properties are changed in this high-speed case, the push-back does not resurrect the burstiness. These results reverse the commonly-held presumption that Internet traffic is everywhere bursty and that multiplexing gains do not occur. Very simple statistical time series models --- fractional sum-difference (FSD) models --- describe the statistical variability of the traffic variables and their change toward Poisson and independence before significant queueing sets in, and can be used to generate open-loop packet arrivals and sizes for simulation studies. Both science and engineering are affec...

We study traffic streams through their counting process representation. We examine the longrange-dependent (LRD) characteristics of such processes. We first show that the measured LRD traffic, as described by the interarrival time and packet size sequences, is sufficiently well approximated by a synthesized stream formed by recording the counting state of the traffic at the start of each time slot. We then model these counting processes by constructing a multiplicative multifractal process. The model only contains two parameters. One is used to indicate the mean of the counting process; the other is employed to describe the variation of the traffic around the mean function. We show that this multifractal traffic characterization has well defined burstiness descriptors, and is easy to construct. We consider a single server queueing system which is loaded, on one hand, by the measured processes, and, on the other hand, by properly parameterized multifractal processes. In comparing the system-size tail distributions, we demonstrate our model to effectively track the behavior exhibited by the system driven by the actual traffic processes.

As the number of active connections (NAC) on an Internet link increases, the long-range dependence of packet traffic changes due to increased statistical multiplexing of packets from different connections. Four packet traffic variables are studied as time series --- inter-arrival times, sizes, packet counts in 100 ms intervals, and byte counts in 100 ms intervals. Results are based on the following: (1) the mathematical theory of marked point processes; (2) empirical study of 2526 packet traces, 5 min or 90 sec in duration, from 6 Internet monitors measuring 15 interfaces ranging from 100 mbps to 622 mbps; (3) simple statistical models for the traffic variables; and (4) network simulation with NS. All variables have components of long-range dependence at all levels of the NAC. But the variances of the long-range dependent components of the sizes and of the inter-arrivals decrease to zero as the NAC increases; the sizes tend toward independent, and the inter-arrivals tend toward independent or very short range dependent. These changes in the sizes and inter-arrivals are not arrested by the increased upstream queueing that eventually occurs as the NAC increases. The long-range dependence of the count variables does not change with the NAC, but their standard deviations relative to the means decrease like one over the square root of the NAC, making the counts smooth relative to the mean. Theory suggests that once the NAC is large enough, increased upstream queueing should alter these properties of the counts, but in the empirical study and in the simulation study the NAC was not large enough to observe an alteration for 100 ms counts. The change in the long-range dependence of the sizes and inter-arrivals does not contradict the constancy of the long-range dependence of th...

The Internet of the future and next generation wireless systems are expected to carry to a large extent video of heterogeneous quality and video that is scalable encoded (into multiple layers). However, due to a lack of long traces of heterogeneous and scalable encoded video, most video networking studies are currently conducted with traces of single layer (non–scalable) encoded video. In this technical report we present a publicly available library of traces of heterogeneous and scalable encoded video. The traces have been generated from over 15 videos of one hour each, which have been encoded into two layers using the temporal scalability and spatial scalability modes of MPEG–4. We provide both the frame sizes as well as the frame qualities (PSNR values) in the traces. We study the statistical characteristics of the traces, including their long–range–dependence and multi–fractal properties.

Sea clutter refers to the backscattered returns from a patch of the sea surface illuminated by a transmitted radar pulse. Since the complicated sea clutter signals depend on the complex wave motions on the sea surface, it is reasonable to study sea clutter from nonlinear dynamics, especially chaos, point of view, instead of simply based on random processes. In the past decade, Dr. Simon Haykin's group at the McMaster University of Canada carried out analysis of some sea clutter data using chaos theory, based on the the assumption that a chaotic attractor is fully characterized by a non-integer fractal dimension and a positive Lyapunov exponent. Thus, they concluded that sea clutter signals are chaotic. In other words, the complicated sea clutter wave forms are generated by nonlinear deterministic interactions of a few modes (i.e., number of degrees of freedom). However, a numerically estimated non-integral fractal dimension and a positive Lyapunov exponent may not be sufficient indication of chaos. Recently, Cowper and Mulgrew, Noga, and Davies separately have questioned the chaoticness of the radar sea clutters. In this paper, we show, using the direct dynamical test for deterministic chaos developed by Gao and Zheng, which is one of the more stringent criteria for low-dimensional chaos, a two minute duration sea clutter data is not chaotic. We also carry out a multifractal analysis of this sea clutter data set, and find that the original sea clutter amplitude signal is approximately multifractal, while the envelope signal, formed by picking up the successive local maxima of the amplitude signal, thus measuring the energy of successive waves on the sea surface, is well modeled as multifractals. A possible interpretation for this difference is that when time scales are ...

Video traces for the evaluation of network performance... In this report, we introduce interfaces from different video traces to three major simulators.

Source traffic streams as well as aggregated traffic flows often exhibit long-range-dependent (LRD) properties. In this paper, we model each traffic stream component through the multiplicative multifractal counting process traffic model. We prove that the superposition of a finite number of multiplicative multifractal traffic streams results in another multifractal stream. This property makes the multifractal traffic model a versatile tool in modeling traffic streams in computer communication networks. There, a node is loaded by a traffic flow resulting from the superposition of source streams and aggregated LRD (and other) streams. The structure and the burstiness of the superimposed process is studied, and useful mathematical relations are obtained.

A fundamental problem of Internet traffic engineering is bandwidth estimation: determining the band-width (bits/sec) required to carry traffic with a specific bit rate (bits/sec) offered to an Internet link and satisfy quality-of-service requirements. The traffic is packets of varying sizes arriving for transmission on the link. Packets can queue up and are dropped if the queue size (bits) is bigger than the size of the buffer (bits) for the queue. For the predominant traffic on the Internet, best-effort traffic, quality metrics are the packet loss (fraction of lost packets), a queueing delay (sec), and the delay probability (probability of a packet exceed-ing the delay). This article presents an introduction to bandwidth estimation and a solution to the problem for best-effort traffic for the case where the quality criteria specify negligible packet loss. The solution is a simple statistical model: (1) a formula for the bandwidth as a function of the delay, the delay probability, the traffic bit rate, and the mean number of active host-pair connections of the traffic, and (2) a random error term. The model is built and validated using queueing theory and extensive empirical study; it is valid for traffic with 64 host pair connections or more, which is about 1 megabit/sec of traffic. The model provides for Internet best-effort traffic what the Erlang delay formula provides for queueing systems with Poisson arrivals and i.i.d. exponential service times.

In order to ensure continued availability of high performance network for the nation's research and education community and to continue supporting the development of new high performance Internet capabilities, the National Science Foundation (NSF) established the very-high-speed Backbone Network Service (vBNS) through a cooperative agreement with MCI telecommunications Corporation. To ensure quality of service (QoS) provided by vBNS, an important task is to understand characteristics of vBNS traffic. In this paper we show that vBNS traffic has longrange-dependent (LRD) properties, which have been observed in LAN, WAN, WWW, and VBR video traffic traces. However, we also show that the burstiness of vBNS trac varies from trace to trace, indicating considerable spatial variations of traffic features, and cannot be characterized by the Hurst parameter. We develop a generalized multifractal model for vBNS traffic. The model contains two parameters, is easy to construct, and generates short-range-dependent processes, conventional long-range-dependent processes, and ideal multiplicative multifractal processes as special cases. The power of the proposed process in modeling the vBNS traffic is demonstrated.