Generating Self-similar Traffic for Opnet Simulations

Self-similar (s-s) arrival processes are realistic models for many types of network traffic. Unfortunately, generating synthetic s-s arrivals and interarrival times for simulations is rather involved. This paper discusses six issues related to s-s traffic generation for discrete-event simulations: (i) what s-s processes are, and why they are important to network modelers; (ii) where to find a fast s-s generator; (iii) how to install the generator and synthesize s-s arrivals; (iv) how to convert s-s arrival counts to interarrival times; (v) how to build a simple OPNET process model for generating interarrivals; and (vi) how traffic from simulated s-s arrival processes compares with traffic from simulated bursty and Poisson arrival processes. 1. SELF-SIMILAR PROCESSES Network modelers used to routinely assume that arrival events were independent, or nearly so. The Poisson arrival process was convenient, was easy to model and analyze, and fit many types of network traffic reasonably well. More sophisticated models (e.g., based on Markov-modulated Poisson or Bernoulli processes) were used to convey the autocorrelation or short-range dependence (SRD) found in bursty empirical traffic traces. In the early 1990s, researchers found evidence of long-range dependence (LRD) in empirical traffic traces. This raised serious doubts about modeling network arrivals using Poisson and Markov-modulated processes, as these (if stationary) cannot convey LRD [1, 2]. There is convincing evidence that LRD is present in many types of network traffic, including: Ethernet LAN traffic, WAN traffic, coded video traffic, frame relay traffic, connectionless DQDB traffic, common channel signaling traffic in LEC networks, ATM WAN traffic, narrowband ISDN traffic, telnet packet arrivals, the sizes of FTP bursts, and some types of WWW traffic [4, 5, 6, 7]. LRD greatly lengthens the tail of queue waiting time distributions, so ignoring LRD can lead to overly optimistic estimates of performance in buffer dimensioning. This can result in more frequent buffer overflow in finite queues, in delays an order of magnitude longer than expected in some queues, and/or other manifestations of poor performance [1, 3]. This phenomenon is illustrated in Section 6. LRD is a characteristic of self-similar (s-s) processes, and so s-s processes are often used to generate synthetic arrivals in simulations when LRD is an important trait. Many s-s generators have been proposed. Most are based on fractional stochastic processes, fractals, chaotic maps, on/off models with heavy tails, superposed on/off sources, or wavelet transforms of s-s processes. We use Paxson’s generator fft_fgn [3, 8] to synthesize a s-s fractional Gaussian noise (FGN) process. The generator uses a fast Fourier transform to estimate the power spectrum of an FGN process. The generator is scalable, fast, efficient, comparatively simple to implement, and provides reproducible traces that are statistically indistinguishable from FGN. The fft_fgn generator has switches for specifying the trace size, Hurst number (the degree of LRD in the trace), and scaling factors for linearly transforming the trace to any mean and variance. SRD and LRD are both important in network simulations. E.g., in finite buffers, SRD and LRD influence the delay distribution of packet arrivals, and LRD influences packet drops [3]. Carriers have begun using LRD models to engineer data networks, and are finding them to be more robust than their SRD counterparts [4]. ATM researchers have found that the s-s trait is robust and cannot be removed by shaping; at short time scales, SRD is reduced by shaping but LRD is not [5]. Finally, there is conflicting evidence about the impact of LRD at very short time scales. Some believe that SRD dominates, and that LRD has little influence on queue lengths at these time scales [6]. The simulation results summarized in Section 6 generate packet arrivals on the order of 0.01 seconds. The LRD phenomenon is clearly influential at this time scale. Peak queue lengths for s-s traffic are 4.5 times larger than for bursty traffic, and 35 times larger than for Poisson traffic.