Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 wide-area traces, investigating a number of wide-area TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that user-initiated TCP session arrivals, such as remotelogin and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib [Danzig et al, 1992] interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into “connection bursts,” the largest of which are so large that they completely dominate FTP data traffic. Finally, we offer some results regarding how our findings relate to the possible self-similarity of widearea traffic.

Recent traffic measurement studies from a wide range of working packet networks have convincingly established the presence of significant statistical features that are characteristic of fractal traffic processes, in the sense that these features span many time scales. Of particular interest in packet traffic modeling is a property called long-range dependence, which is marked by the presence of correlations that can extend over many time scales. In this paper, we demonstrate empirically that, beyond its statistical significance in traffic measurements, long-range dependence has considerable impact on queueing performance, and is a dominant characteristic for a number of packet traffic engineering problems. In addition, we give conditions under which the use of compact and simple traffic models that incorporate long-range dependence in a parsimonious manner (e.g., fractional Brownian motion) is justified and can lead to new insights into the traffic management of high-speed networks. 1...

In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with longrange-dependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing N-point data sets. We study both the second-order and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variance-time plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.

High-resolution traffic measurements from modern communications networks provide unique opportunities for developing and validating mathematical models for aggregate traffic. To exploit these opportunities, we emphasize the need for structural models that take into account specific physical features of the underlying communication network structure. This approach is in sharp contrast to the traditional black box modeling methodology from time series analysis that ignores, in general, specific physical structures. We demonstrate, in particular, how the proposed structural modeling approach provides a direct link between the observed self-similarity characteristic of measured aggregate network traffic, and the strong empirical evidence in favor of heavy-tailed, infinite variance phenomena at the level of individual network connections.

In this paper we report on an ongoing statistical analysis of actual CCSN traffic data. The data consist of approximately 170 million signaling messages collected from a variety of different working CCS subnetworks. The key findings from our analysis concern: (1) the characteristics of both the telephone call arrival process and the signaling message arrival process, (2) the tail behavior of the call holding time distribution, and (3) the observed performance of the CCSN with respect to a variety of performance and reliability measurements. 1.

We measure and analyze the single-hop packet delay through operational routers in a backbone IP network. First we present our delay measurements through a single router. Then we identify stepby -step the factors contributing to single-hop delay. In addition to packet processing, transmission, and queueing delays, we identify the presence of very large delays due to non-work-conserving router behavior. We use a simple output queue model to separate those delay components. Our step-by-step methodology used to obtain the pure queueing delay is easily applicable to any single-hop delay measurements.

Traffic models are at the heart of any performance evaluation of telecommunications networks. An accurate estimation of network performance is critical for the success of broadband networks. Such networks need to guarantee an acceptable quality of service (QoS) level to the users. Therefore, traffic models need to be accurate and able to capture the statistical characteristics of the actual traffic. In this article we survey and examine traffic models that are currently used in the literature. Traditional short-range and non-traditional long-range dependent traffic models are presented. Number of parameters needed, parameter estimation, analytical tractability, and ability of traffic models to capture marginal distribution and auto-correlation structure of actual traffic are discussed. n Figure 1. Finite state model for voice. This research was supported in part by the National Science Foundation under grant NCR-9396299. This article is based on Georgia Tech technical report G...

this paper, we analyze a fluid or storage queueing system with LRD input. Fluid systems have been used before (e.g. Bensaou et al. [2], Guibert [7]) to model bursty traffic fed into ATM multiplexer queues, when considering time scales where the granularity of the ATM cells no longer dominates. The input sources are assumed to be of On/Off type, that is, with mutually independent, alternating silence periods (no work arriving) and activity periods (work arriving at a constant rate). We consider a superposition of N identical, independent On/Off sources flowing into an infinite reservoir with fixed output rate C. The object of study is the complementary distribution function Q of the stationary queue content. F. Brichet et al. / Heavy traffic analysis with LRD sources 3 If is the mean arrival rate for a single source, we require C ? N for stability. For N sufficiently large, C then exceeds the peak rate of an individual source. If this rate is proportional to C=N , so that it decreases with N , then we are in the realm of "small" sources. The M=G=1 example above represents the limiting form of the alternative assumption, where instantaneous arrivals idealize the case of a capacity significantly smaller than the individual arrival rate. By selecting "heavy" tails (as defined in section 4) for the silence and/or activity periods, the input process becomes long range dependent and the queueing problem is fundamentally non-Markovian. Despite this, a useful lower bound L to

Abstract—We measure and analyze the single-hop packet delay through operational routers in the Sprint Internet protocol (IP) backbone network. After presenting our delay measurements through a single router for OC-3 and OC-12 link speeds, we propose a methodology to identify the factors contributing to single-hop delay. In addition to packet processing, transmission, and queueing delay at the output link, we observe the presence of very large delays that cannot be explained within the context of a first-in first-out output queue model. We isolate and analyze these outliers. Results indicate that there is very little queueing taking place in Sprint’s backbone. As link speeds increase, transmission delay decreases and the dominant part of single-hop delay is packet processing time. We show that if a packet is received and transmitted on the same linecard, it experiences less than 20 s of delay. If the packet is transmitted across the switch fabric, its delay doubles in magnitude. We observe that processing due to IP options results in single-hop delays in the order of milliseconds. Milliseconds of delay may also be experienced by packets that do not carry IP options. We attribute those delays to router idiosyncratic behavior that affects less than 1 % of the packets. Finally, we show that the queueing delay distribution is long-tailed and can be approximated with a Weibull distribution with the scale parameter aHS and the shape parameter aHT to 0.82. Index Terms—Link utilization, queueing delay, single-hop delay measurement. I.

Abstract—Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of long-range dependence (LRD) and marginal statistics still remains on unsure footing. In this paper, we study these two issues by introducing a multiscale traffic model and a novel multiscale approach to queuing analysis. The multifractal wavelet model (MWM) is a multiplicative, wavelet-based model that captures the positivity, LRD, and “spikiness ” of non-Gaussian traffic. Using a binary tree, the model synthesizes an-point data set with only computations. Leveraging the tree structure of the model, we derive a multiscale queuing analysis that provides a simple closed form approximation to the tail queue probability, valid for any given buffer size. The analysis is applicable not only to the MWM but to tree-based models in general, including fractional Gaussian noise. Simulated queuing experiments demonstrate the accuracy of the MWM for matching real data traces and the precision of our theoretical queuing formula. Thus, the MWM is useful not only for fast synthesis of data for simulation purposes but also for applications requiring accurate queuing formulas such as call admission control. Our results clearly indicate that the marginal distribution of traffic at different time-resolutions affects queuing and that a Gaussian assumption can lead to over-optimistic predictions of tail queue probability even when taking LRD into account. I.