Network traffic forecasting model based on long-term intuitionistic fuzzy time series
Introduction
With the rapid expansion of network scale, the quantity and complexity of traffic information increase sharply. The network traffic is the most important index to measure load and status of network operation. The traffic characteristic modeling and simulation are effective methods of network supervision and control. The characteristics of network traffic include non-stationary, non-linear, burstiness, multi-fractal, periodicity, chaotic, self-similarity, long-rage dependence and short-rage dependence [3]. Network resource allocating is the major part of network management, operation and maintenance work. According to the traffic forecasting scheme, the network managers expect to distribute resource reasonably and avoid traffic blocking. Besides, anomaly network actions may cause network traffic variation easily, which is an obvious signal of network attack. Network traffic forecasting is a practical method in the network security field [7].
Network traffic is typical time series data. Many scholars have been working on traffic forecasting theory based on time series analysis. The classical linear time series model includes auto regressive moving average (ARMA) [25], auto regressive integrated moving average (ARIMA) and fractional auto regressive integrated moving average (FARIMA) [40]. The main strategy of traditional time series forecasting models based on regression analysis is to fit the time series tendency, evaluate the parameters and construct the regression equation. And then, the forecasting values are calculated by regression equation. Considering the non-linear character of network traffic, some other time series forecasting models based on echo network [39], particle swarm optimization support vector machine [32], fruit fly optimization [30], relevance vector machine [37] and Fuzzy C-Regression [12] were proposed in succession. With the integration and application of intelligent information processing methods, the ability to handle complex problems is enhanced.
The traditional time series analysis forecasting models usually drafted accurate historical values, thus they were invalid in processing of fuzz or uncertain information such as linguistic variable. Song and Chissom first proposed the concept of the fuzzy time series (FTS) and FTS forecasting model [42], [43]. After that, several fuzzy time series theories were presented in succession [8], [27]. Fuzzy time series integrating with other intelligent algorithm performed better in fuzzy data forecasting. The neural networks [21] FTS and the particle swarm optimization FTS [38] models were applied to forecast Taiwan Futures Exchange (TAIFEX) dataset. A linear FTS model by defining fuzzy plus and minus operators based on autocorrelation functions were proposed [44]. A fuzzy time series forecasting method based on trapezoid fuzzification and entropy-based was presented [11]. Focusing on the fuzzy nonlinear control problem, the adaptive fuzzy asymptotical tracking control of nonlinear systems was proposed [48], [49]. Considering the multiple attributes on input, a multivariate stochastic fuzzy [23] and an adaptive expectation forecasting models [35] were proposed.
To improve the forecasting accuracy, some scholars proposed the high-order fuzzy time series substituting the first-order model [9], [17]. FTS models were reformed to multi-factor forecasting model [10] or integrated high-order and multi-factor model [5], [26] at the same time. Some scholars put forward that the intervals length of universe of discourse influenced forecasting accuracy. Fuzzy clustering was the most popular intervals partition method [15], [23], [31]. PSO [20], [22], [24], Tabu Search [2], information granules [13] and ant colony optimization [4] were employed to search appropriate intervals. The intuitionistic fuzzy sets (IFS) theory was an extension of fuzzy sets, which depicted the fuzzy object more clearly [1]. IFS theory was applied in attribute decision making, field [6], [34], [45], [47]. Few time series analysis models based on IFS were proposed [14], [18]. To optimize intuitionistic fuzzy time series (IFTS) model, a long-term intuitionistic fuzzy time series (LT-IFTS) forecasting model was proposed [16].
The network traffic forecasting scheme aims to provide reliable traffic variation expectation according to changing patterns in historical data. Because forecasting values have close connection with nearby time series values, time series forecasting model could fit traffic variation well. The traditional time series analysis is based on regression theory, while the (intuitionistic) fuzzy time series fuzzy reasoning. It indicates that the principles of the two kinds of time series theories are different. The FTS and IFTS models focus on describing the fuzziness and uncertainty characteristics of data. Due to the mass uncertain information and messages contained in the network traffic, we propose a network traffic forecasting model based on long-term intuitionistic fuzzy time series analysis, expressing the fuzziness and the uncertainty features of network traffic exactly. In this paper, network traffic forecasting scheme combines with the IFTS theory, the time series segments are quantified, IFTS forecasting model is constructed, and the fuzziness and uncertainty characteristic of network are extracted and intuitionistic fuzzified. The proposed model includes training stage and forecasting stage. In the training stage, the IFCM clustering method is optimized, the intuitionistic fuzzy time series vector distance is modified based on an improved vector changing pattern. The clustering centroid calculated by the proposed model is more accurate. Besides, different from single output forecasting models, the proposed model holds long-term and milt forecasting output capacity. The accuracy of traditional fuzzy time series forecasting models is relative to universe of discourse partition. The rougher interval partition leads to decreasing of forecasting accuracy. Not considering the universe of discourse partition, the proposed model reduces the computational complexity by IFTSVQ algorithm and increases the forecasting system efficiency.
Frame of the paper: in Section 2, some fundamental theories of LT-IFTS, time series vector quantization and network traffic forecasting principle are given. In Section 3, the framework of the network traffic forecasting model based on LT-IFTS is constructed. In Section 4, the details of the proposed traffic forecasting model are presented and experimented on network traffic dataset MAWI (Measurement and Analysis on the WIDE Internet). And then, our model is deployed on different time-scales to certify the availability. In Section 5, the conclusions are drawn.
Section snippets
Fundamental theories
This section, the fundamental theories of research are presented briefly, including definitions of LT-IFTS, time series vector quantization, intuitionistic fuzzy vector clustering and network traffic forecasting. These relevant theories are basic stones of our research.
Network traffic forecasting principle
The characteristic description of network traffic is important evidence for network management. Modeling and forecasting network traffic according characteristic is an effective measure of anomaly detection and supervision. A small scale network traffic prediction model was proposed based on local relevance vector machine regression. The model imitated nonlinear features of network [37]. Preprocessing network traffic predicted method and chaos theory were applied in DDoS anomaly detection [7].
MAWI network traffic forecasting
In this section, we implement our model on network traffic data set to test performance of proposed method. The experiment data derives from the MAWI working group of the WIDE (Widely Integrated Distributed Environment) project collecting the traffic in Pacific Ocean backbone network [36]. The working group deployed 6 different sample points (sample point A- sample point F), which gathers whole year trace flow to offer analyzing and experiment data. The MAWI is a database that assists
Conclusions
In this paper, a network traffic forecasting model based on intuitionistic fuzzy time series is proposed. As plenty of complex and changeable features exist in network traffic, intuitionistic fuzzy time series model is applied in traffic forecasting field. The fuzziness and uncertainty of network flow data are described by IFTS theory effectively. The long-term intuitionistic fuzzy time series is defined. (p−q) IFTS is a multi-input multi-output intuitionistic fuzzy time series forecasting
Declaration of Competing Interest
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
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