# NETWORK BURST MONITORING AND DETECTION BASED ON FRACTAL DIMENSION WITH ADAPTIVE TIME-SLOT MONITORING MECHANISM

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3 688 Journal of Marine Science and Technology, Vol. 21, No. 6 (213) constant. In contrast, the dynamic time-slot method is flexible in time scheduling, and its monitoring overhead relies on the process of determining the number of slots. III. TECHNIQUES METHOD OF BURSTINESS MEASUREMENT 1. Fractal Dimension of Traffic This study collected a sequence of network traffic data as a summation of flows within a period and then plotted the data on the Y-axis against the start time of each period on the X-axis. This study obtained the FD of the measured network traffic by applying the BCM to the plot. The FD of the curve represents the variation of traffic over a certain period and is referred to in this study as TFD. The TFD could reflect the complexity of the curve that represents the degree of the variation of the network traffic. In theory, a curve can be completely covered with N(l) contiguous square boxes with each box measured l l. As the size of the box approaches zero, the total area covered by the boxes converges to the measurement of the curve. In practice, the FD of the curve is estimated by first counting the number of boxes that is required to fully cover the curve for several box sizes, and then by fitting a regression line to the log-log plot of log Nl ( ) versus log l. The slope of the regression line log Nl ( ) versus log l is the FD of the curve that represents the TFD. 2. Fractal Dimension of Range Network traffic consists of several flows. The traffic can be bursty when a relatively large flow occurs. The measurement of the degree of the dispersal of flows in each interval is useful for detecting burstiness. The proposed method regards the difference between the maximal flow and minimal flow sizes within a time slot as the range. This study plotted the maximal flow and the minimal flow within a period on the Y-axis against the start time of each period on the X-axis; two curves were then obtained. The area between two curves represents the flow range. By applying (6) to the area, this study was able to estimate the FD of the area, which represents the RFD and reflects the degree of the flow dispersal and the variation of range trend (i.e., a smaller RFD indicates that the flow sizes are closer). The difference in the flow sizes increases in conjunction with the increase of the RFD. The RFD can be estimated by using the BCM. The estimation procedure is described as the follows: 1) choose a flow range of network traffic within period P and place the curves on a space. 2) Choose a set of boxes of various sizes, such that box length l tends to be zero. 3) Cover the area with the boxes. For each l, the corresponding number of boxes necessary to cover the entire range, N(l), is counted. 4) Plot log Nl ( ) against log1 l, for various l. By applying a process similar to the one in Section III.1 that solves (6), the FD of the range is readily available as the slope of the regression line. If the flow range of the network traffic is a fractal, then the logarithm plot is a straight line. 3. FD Based Detection of Bursty Traffic To estimate the burstiness of the traffic, this study designated two adjacent time windows: the reference window and target The designated window consists of a given number of time slots. The window size changes as the slot periods change. Within each of the alternating windows, traffic measurements are obtained and the two FDs discussed earlier are derived. By definition, bursty traffic has occurred when the FDs in the reference window are both less than their counterparts in the target window, each by a certain threshold. As the monitoring continues, the duration of the time slot for the next target window is determined by the result of the comparison between the FDs in the current reference and target windows. The mechanism for changing the duration of a time slot is described below: (a) Initially, both windows consist of n time slots of duration t. Hence, the size of each window is n t. Let the start point of the reference window be W s. Therefore, the start point of the target window is W s + nt, as shown in Fig. 1(a). (b) Let TFD be the difference between the TFD in the reference window and its counterpart in the target Similarly, let RFD be the difference between the RFD in the reference window and its counterpart in the target The following conditions are suggested for the detection of bursty traffic: { TFD threshold t } and { RFD threshold r } (7) where threshold t is the threshold of the FD of traffic and thresholdr is the threshold of the FD of range. Bursty traffic is detected when the traffic satisfies both conditions in (7). (c) If any condition in (7) is not satisfied, then bursty traffic has not occurred in the target In such a case, it is reasonable to decrease the monitoring frequency by increasing the duration of the time slots for the next target This study chose to double the duration of the time slots in the upcoming For the subsequent comparisons to be meaningful, the last original reference and target windows were combined into a new reference The new target window is the same size. The TFD and RFD of the new reference window are the means of the two respective counterparts from each of the two original windows. (d) If both of the conditions in (7) are satisfied, then bursty traffic is detected and the target window is a bursty Consequently, the duration of the time slots for the next target window reverts to the initial value and the size

4 H.-W. Tin et al.: Network Burst Detection Based on Fractal Dimension with Adaptive Time-Slot Mechanism 689 Starting point of the reference window (W s) Starting point of the target window (W s + n t) Reference window Target window Time slot of duration t Obtain TFD r and RFD r in the reference Obtain TFD t and RFD t in the target In this example, the target window and the reference window have equal size w = n t, where n = 2. (a) Initial step: setting the initial values. The original reference window and target window are combined as the new reference window W s. Reference window Target window Next Target window t is increased to t next. Let the means RFD and TFD be RFD r and TFD r in the new reference The duration of the next target window is n t next. (b) If any of the differences of FDs between the target window and reference window is less than the threshold, non-bursty traffic is detected in the target Hence, the duration of the time slot is increased. This target window becomes the new reference Target window Next Target Window Set the duration of the time slot to t. Size of the next target window is w = n t. (c) If both of the FDs in the target window are greater than the FDs in the reference window and the differences of the FDs are greater than or equal to the thresholds, a bursty traffic is detected. That is, the target window is a bursty So, set the duration of time slots to the default value for the next target window and let the current target window be the new reference Fig. 1. Adaptive time-slot monitoring mechanism. of the next target window is also restored to the initial value. The duration of the time slots reverts to the initial values, indicating that the size of the next target window also reverts to the initial length as presented in Fig. 1(c). The adaptive time-slot monitoring mechanism shown in Figs. 1(b) and 1(c) is summarized by (8): t next t = t initial current, If both of the conditions in (7) hold + t initial,otherwise (8) where t initial is the duration of the time slot at the initial step, t current is the duration of the time slot in the current target window, t next is the new duration of the time slot for the next target IV. SIMULATION SCENARIO AND ANALYSIS 1. Network Traffic Model This study used the Pareto ON/OFF model; the connectionlevel traffic model [13] for both models have been used in

5 69 Journal of Marine Science and Technology, Vol. 21, No. 6 (213) Table 1. Link parameters of the Pareto ON/OFF model. Link Bandwidth (Kbps) Latency (ms) D clients 5 1 A B 2 2 B D 2 2 A servers 1 2 Table 2. Topology parameters of the Pareto ON/OFF model. Parameter Value Number of server 4 Number of clients 9 Mean ON time.5 sec Mean OFF time.5 sec Pareto parameter α 1.2 Burst Rate 2 k Packet size Time (sec) (dutation of time slot = 1 ms) Fig. 3. TCP traffic in the Pareto ON/OFF model. Servers E P Clients Servers Clients F P 1 S C G A B D S 1 C 1 A B D H P n S n C n Fig. 4. Topology of the connection-level traffic model. Fig. 2. Topology of the Pareto ON/OFF model. major studies on bursty traffic, such as Willinger et al. [18] and Sarvotham et al. [13]. This study set the simulation of TCP flow at the packet level to simplify the experimental conditions. Simulation 1. Pareto ON/OFF Model: The simulator transmits the packets according to parameter α = 1.2, which is the same value used by Sarvotham et al. [13]. The OFF state of the Pareto ON/OFF model is the idle time during which packets are not transmitted. The waiting time depends on parameters γ and ω, where γ = 1.1 and ω =.36. The topology is depicted in Fig. 2. The parameters used in the experiment are presented in Tables 1 and 2. These values were selected according to the NS2 parameters used in Savotham et al. [13] as well as the parameters recommended in the user guide of the NS2. Overall, 4 sources, 9 clients, and 3 middle nodes were included in the simulation. A total of 9 flows between the source nodes and client nodes were established as evenly as possible. The observation period was 1 s, and the time slot was set to.1 s. Therefore, the number of measurements was 1. Node A in Fig. 2 is designated as the observation point for this topology. This study collected the packets that were generated by 9 flows passing through node A and plotted the data, as shown in Fig. 3. Simulation 2. Connection-Level Traffic Model: The topology of the connection-level traffic model is depicted in Fig. 4 based on the model used in the Sarvotham et al. experiment [13]. The parameters of this model are presented in Tables 3 and 4. As shown in Fig. 4, four transmission nodes, from E to H, were established on the Server side. Each transmission node connects to 1 source nodes. On the client side, six receiver nodes each connect to 15 destination nodes. Two sides are connected by three middle nodes. The source nodes and destination nodes were connected as evenly as possible. The observation period was 1 s, and the time slot was.1 s. Overall, 1 measurements were performed. For this topology, node A is the observation point, and the packets from 9 flows were collected. Fig. 5 shows the results of the observation over the entire period.

6 H.-W. Tin et al.: Network Burst Detection Based on Fractal Dimension with Adaptive Time-Slot Mechanism 691 Table 3. Link parameters of the connection-level traffic model. Link Bandwidth (Kbps) Latency (ms) D P 12 2 D P 1 to D P n Unif (5,12) 2 P i clients 5 1 A B 2 2 B D 2 2 A E to A H 1 2 E servers to H servers 1 Unif (1,1) Table 4. Topology parameters of the connection-level traffic model. Parameter Value Number of servers per E H 1 Number of nodes P i 15 Number of clients per P i 6 Mean ON time.5. Mean OFF time.5 Pareto parameter α 1.2 Burst Rate 2 k Packet size Time (sec) (dutation of time slot = 1 ms) Fig. 5. TCP traffic in the connection-level traffic model. 2. Measuring Burstiness by Using Adaptive Time-Slot Monitoring Mechanism By applying the adaptive time-slot monitoring mechanism, the size of the reference window and the size of the target window were initialized to the same value n t. Let n = 2, t =.1, and the starting point of reference window W s =. This study applied Fractalyse version [14] to obtain the FDs. The plots of the traffic data and their corresponding TFD are depicted in Figs. 6 and 7. The plots of the range data and the corresponding RFD are shown in Figs. 8 and 9. The following two experiments are presented as examples to explain the function of the proposed mechanism based on 12 1 size of the reference window is 2.1 = 2 (sec) size of the target window is 2.1 = 2 (sec) 8 7 period #1 period #2 6 FD =.9343 FD = Time (sec) (dutation of time slot = 1 ms) Fig. 6. Analysis of the TFD in the Pareto ON/OFF model with the duration of the time slots =.1 sec size of the reference window is 2.1 = 2 (sec) size of the target window is 2.1 = 2 (sec) 8 7 period #1 period #2 6 FD = FD = Time (sec) (dutation of time slot = 1 ms) Fig. 7. Analysis of the TFD in the connection-level traffic model with the duration of the time slots =.1 sec size of the reference window is 2.1 = 2 (sec) size of the target window is 2.1 = 2 (sec) 1 12 period #1 period #2 1 FD = FD = Time (sec) (dutation of time slot = 1 ms) Fig. 8. Analysis of the RFD in the Pareto ON/OFF model with the duration of the time slots =.1 sec size of the reference window is 2.1 = 2 (sec) size of the target window is 2.1 = 2 (sec) 1 12 period #1 period #2 1 FD = FD = Time (sec) (dutation of time slot = 1 ms) Fig. 9. Analysis of the RFD in the connection-level traffic model with the duration of the time slots =.1 sec.

7 692 Journal of Marine Science and Technology, Vol. 21, No. 6 (213) Previous reference Size is 2.1 = 2 (sec) Previous reference t =.1 (sec) Previous target windows. Size is 2.1 = 2 (sec) Previous target t =.1 (sec) New target Size is 2.2 = 4 (sec) t new =.2 (sec) Time (sec) Fig. 1. In the Pareto ON/OFF model, the duration of the time slot in the next target window is increased if no bursty TCP traffic is detected Previous reference Size is 2.1 = 2 (sec) Previous reference t =.1 (sec) Previous target windows. Size is 2.1 = 2 (sec) Previous target t =.1 (sec) New target Size is 2.2 = 4 (sec) t new =.2 (sec) Time (sec) Fig. 11. In the connection-level traffic model, the duration of the time slot in the next target window is increased if no bursty TCP traffic is detected. the FDs. The first experiment demonstrated a situation in which bursty traffic was undetected; therefore, the system increased the duration of the time slot in the next target window as depicted in Fig. 1(b). The second experiment shows cases in which bursty traffic exists. Upon detection of bursty traffic, the system reset the duration of the time slot in the next target window as shown in Fig. 1(c). Experiment 1. Non-Bursty TCP Traffic In a situation where bursty traffic is undetected, assume threshold traffic = 2 and threshold range = 2. With the Pareto ON/OFF model, the difference of the TFD between the first reference window (Period #1 in Fig. 6) and the first target window (Period #2 in Fig. 6) is TFD = The difference of the FD range between the first reference window (Period #1 in Fig. 8) and the first target window (Period #2 in Fig. 8) is RFD = Because either TFD or RFD does not satisfy the conditions expressed in (7), the new duration of the time slot for the next target window is t new = t current + t =.2. The adjustment is depicted in Fig. 1. In the connection-level traffic model, the difference of the TFD between the first reference window (Period #1 in Fig. 7) and the first target window (Period #2 in Fig. 7) is TFD = The difference of the RFD between the first reference window (Period #1 in Fig. 9) and the first target window (Period #2 in Fig. 9) is RFD = Again, neither TFD nor RFD satisfy the conditions expressed in (7). The new duration of the time slot for the next target window should be t new = t current + t =.2. The adjustment is shown in Fig. 11. Experiment 2. Bursty TCP Traffic In a situation where bursty traffic exists, let threshold traffic =.1 and threshold range =.1. In the Pareto ON/OFF model, TFD =.1629, RFD =.1852, and both conditions in (8) are satisfied. The new duration of the time slot for the next target window was reset size of the reference window is 2.1 = 2 (sec) (previous target window) size of the target window is 2.1 = 2 (sec) Reset the size of the target window to the initial values Time (sec) Fig. 12. When a bursty TCP traffic is detected in the Pareto ON/OFF model, reset the duration of the time slot in the next target size of the reference window is 2.1 = 2 (sec) (previoustarget window) size of the target window is 2.1 = 2 (sec) Reset the size of the target window to the initial values Time (sec) Fig. 13. When a bursty TCP traffic is detected in the connection-level traffic model, reset the duration of the time slot in the next target

9 694 Journal of Marine Science and Technology, Vol. 21, No. 6 (213) 62 (26). 6. Leland, W. E., Taqqu, M. S., Willinger, W., and Wilson, D. V., On the self-similar nature of Ethernet traffic (extended version), IEEE/ACM Transactions on Networking, Vol. 2, No. 1, pp (1994). 7. Li, J., Sun, C., and Du, Q., A new box-counting method for estimation of image fractal dimension, 26 IEEE International Conference on Image Processing, pp (26). 8. Liu, S. T., An improved differential box-counting approach to compute fractal dimension of gray-level image, Information Science and Engieering, Vol. 1, pp (28). 9. Mandelbrot, B. B., Fractal Geometry of Nature, Fkeeman Press, San Fkancisco (1982). 1. Mansfield, G., Roy, T. K., and Shiratori, N., Self-similar and fractal nature of Internet traffic data, 15th International Conference on Information Networking, pp (21). 11. Paxson, V. and Floyd, S., Wide area traffic: the failure of poisson modeling, IEEE/ACM Transactions on Networking, Vol. 3, pp (1995). 12. Riihijarvi, J., Wellens, M., and Mahonen, P., Measuring complexity and predictability in networks with multiscale entropy analysis, IEEE INFOCOM 29, pp (29). 13. Sarvotham, S., Riedi, R., and Baraniuk, R., Connection-level analysis and modeling of network traffic, ACM SIGCOMM Internet Measurement Workshop, pp (21). 14. Sasaki, H., Shibata, S., and Hatanaka, T., An evaluation method of ecotypes of Japanese lawn grass (Zoysia japonica STEUD.) for three different ecological functions, Bulletin of the National Grassland Research Institute, Vol. 49, pp (1994) 15. Tin, H. W., Leu, S. W., and Chang, S. H., Measurement of flow burstiness by fractal technique, 21 International Computer Symposium, pp (21). 16. Wang, T., Yu, Q., and Mao, Y., Fractal characteristics analysis of wireless network traffic based on Hurst parameter, ICCCAS 29, pp (29). 17. Wei, D. X., Cao, P., and Low, S. H., Packet loss burstiness: measurements and implications for distributed applications, IPDPS 27, pp. 1-8 (27). 18. Willinger, W., Taqqu, M. S., Sherman, R., and Wilson, D. V., Selfsimilarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level, IEEE/ACM Transactions on Networking, Vol. 5, No. 1, pp (1997). 19. Xu, Z., Xing, L., Zhou, F., and Wang, Y., Fractal characteristics of transportation network of Tianjin city, 21 International Conference on Mechatronics and Automation (ICMA), pp (21). 2. Zhang, J., Xiang, Y., Wang, Y., Zhou, W., Xiang, Y., and Guan, Y., Network traffic classification using correlation information, IEEE Transactions on Parallel and Distributed Systems, Vol. 24, pp (213). 21. Zhang, K., Ge, X., Liu, C., and Xiang, L., Analysis of frame traffic characteristics in IEEE networks, ChinaCOM 29, pp. 1-5 (29).

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