Source traffic streams as well as aggregated traffic flows often exhibit long-rangedependent (LRD) properties. In this work, we model traffic streams using multiplicative multifractal processes. We develop two type of models, the multifractal point processes and multifractal counting processes. We demonstrate our model to effectively track the behavior exhibited by the system driven by the actual traffic processes. We also study the superposition of LRD flows. We prove that the superposition of a finite number of multiplicative multifractal traffic streams results asymptotically in another multifractal stream. Furthermore we demonstrate numerically that the superimposed process can be effectively modeled by an ideal multiplicative process.

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.

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.

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.

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