Fast and physically-based generation of self-similar network traffic with applications to ATM performance evaluation

Abstract

Self-similarity concepts relate statistical properties of processes observed at different time scales through judicious scaling of time and space. They have recently been shown to be ideally suited to account for the surprising scaling properties that measured network traffic (e.g., number of packets/bytes per time unit) exhibits over a wide range of time scales, from milliseconds to seconds to minutes and beyond. The observed self-similar property in measurements from working packet networks is in sharp contrast to commonly made assumptions about the bursty nature of network traffic and challenges many of the traditional approaches to traffic and performance modeling. In this paper, we illustrate how the self-similar finding gives rise to new mathematical results that (i) clear the way for physically-based approaches to network traffic modeling, (ii) can be combined with high-performance computing capabilities to yield new and fast (i.e., linear in the number of observations) methods for generating self-similar traces, and (iii) provide new insights into the potential performance implications that self-similar traffic can have on the design of network equipment and on the perceived quality-of-service experienced by some of the dominant applications and services. In particular, studying the cell loss dynamics (rather than the traditional long-term cell loss rate) observed at an ATM switch that is fed by self-similar traffic, we discuss the impact of network traffic self-similarity on broadband services such as VBR video and on popular network protocols such as TCP/IP. ample evidence that actual network traffic is fractal in nature in that it exhibits statistical features over many timescales. In particular, these studies have demonstrated that measured traffic rates (i.e., number of packets or cells or bytes per time unit) in LAN/MAN/WAN environments, where data transfer rates typically vary between 1.5 - 155 Mbps, exhibit surprising scaling properties over a wide range of time scales; that is, actual network traffic looks statistically the same in the small (i.e., at small time scales, on the order of imilliseconds or seconds) and in the large (i.e., at time scales on the order of seconds and beyond) , and rto natural length of a “burst” is discernible: at every time scale ranging from milliseconds to seconds to minutes and beyond, bursts have the same qualitative appearance and cause the resulting traffic to exhibit fractal-like characteristics. The observed self-similarity properties in measurements from working packet networks is in sharp contrast to commonly made modeling choices in today’s traffic theory and practice (where the focus remains on reproducing the bursty behavior of network traffic time scale by time scalle) and challenges traditional approaches to traffic and performance modeling. At the same time, it provides new insights into the dynamic nature of actual network traffic, gives rise to novel modeling approaclies that take into account the specific features of the underlying networking structure and hence allows for plausible physical explanations of observed traEic characteristics in the networking context. For example, not only can the observed self-similar natuire of Ethernet LAN traffic at the aggregate level (Le., aggregated over all active hosts on the network; see Leland, Taqqu, Willinger,