Introduction

Many perspectives appear when observing the good performance of NN (optimization issues, tuning of parameters, ...). We are interested here in predicting the behavior of network and the applications running over it. One of the hot research topics in traffic engineering is traffic prediction. Traffic prediction is an important subject because there are many applications in networking that can be efficiently implemented based on a good traffic predictor. Traffic prediction is crucial for successful congestion control, congestion avoidance, dynamic bandwidth allocation, dynamic contract negotiation, traffic shaping and engineering, etc. However, there are some difficulties that prevent providing so far a good traffic predictor that can work in real situations. This is because networks traffic is, in general, a complex, time-variant, nonlinear, and non-stationary process (see for instance [27] for the case of high speed networks). Furthermore, this process is governed by parameters that are difficult to measure [56]. Sometimes, there are completely non-predictable portions of this time-variant process (The so-called ``spiky'' samples). Therefore, a precise model of this process becomes difficult as its complexity increases. Despite these problems, traffic prediction is possible because, as the measurements and previous studies have shown, there coexist both long-range and short-range dependencies in network traffics [54,85,27]. For example, the amount of traffic differs from the week-end to that in the week-days. However, it is statistically similar for all the week-ends. Also during the same day, in the morning, and at night, at some specific time of the day, etc. The traffic prediction problem has been tackled by several techniques; least mean square filter or similar methods [85], regression and statistical models (AR, ARIMA, FARIMA, etc.) [27,121,85], and fuzzy logic with regression [120,27]. Recently, Neural Networks (NN) have been found to be a powerful method to efficiently describe a real, complex, and unknown process, with non-linear and time-varying properties. There are several proposals using the NN to model the traffic process [156,157,39,88,133]. The first one seems to be [133], in 1993. However, the existing proposals concentrate only on the short-range dependencies and neglect the long-range ones. Thus, when testing these models on real traces lasting for several minutes or hours, they give good performance. However, when employing them for predicting the traffic for days or weeks, their performance degrades significantly [56]. Our aim in this study is to present and evaluate a new model for traffic prediction that can work well for IP and ATM networks. However, we have tested it only on IP real traces. The advantage of our model is that it makes use of the long-range information as well as the traditional short-range information in the past history, to predict efficiently the future arrivals of packets or cells. We used the NN as a tool to predict the traffic after training them with the information from the past history. It is not a problem to use either ANN or RNN, because both give similar results. However, RNN as stated in Section 4.5 is faster with respect to ANN, which makes it a good candidate when a light-weight application is targeted (to be used for example in a critical router). For our model to be efficient and light, the NN can be trained either on-line, or periodically off-line. This is to take into account the system variation with time. (For example, in the case of the Internet, it is known that the traffic increases continuously.) Thus, we can track this variation without rebuilding a new predictor. We validated our model by using real data and, at the same time, explored its efficiency in a real situation. It should be noted that many of the existing models were validated using data produced by simulation [88], or with artificially generated data (by simple equations) [157,156], or considering ``easy-to-predict'' traffic (MPEG traces that have some kind of periodicity due to the frame types) [39,133,156]. These models work quite well for their associated data, but fail once they are applied to real ones. This limits their applicability to real applications [56]. On the other hand, other studies that have been validated by real traces concern short time periods (i.e. two hours). When these models are used to predict longer time periods or when the size of the time step⁹¹ becomes larger, the performance degrades [27,120]. The outline of this Chapter is as follows. In Section 9.2, we describe our model. Then in Section 9.3, we evaluate it by means of several experiments. Some possible applications that can benefit from our technique are discussed in Section 9.5. A comparison between our model and some existing ones is the subject of Section 9.4. Finally the conclusions are given in Section 9.6.