Implementation of an Advanced Traffic Model in OPNET Modeler J. Potemans1, B. Van den Broeck, Y. Guan, J. Theunis, E. Van Lil, A. Van de Capelle Katholieke Universiteit Leuven Department of Electrical Engineering – ESAT-TELEMIC division Kasteelpark Arenberg 10, B-3001 Leuven, Belgium E-mail:
[email protected] Abstract Traditional traffic models like the Poisson model are inappropriate to accurately model the bursty behavior of real network traffic. Performance analysis based on these models can lead to a severe underestimation of packet delay or loss, with badly dimensioned networks as a result. Our group developed a new traffic model, which is based on a hierarchical scheme of Bernoulli sources and was presented at ICC2003. Contrary to most other self-similar traffic models, this model allows to efficiently generate traffic of which the mean, the variance and the Hurst parameter can be set in an easy way. In this paper we describe how we implemented the generator in OPNET Modeler. The benefits of the method will be made clear by means of a case study in which our model is compared to the models available in the Raw Packet Generator (RPG).
This paper is organized as follows. In a first section, we give an overview of the model we propose. In a second section, we briefly comment on how we implemented the model in OPNET Modeler. In a third section, we compare our model to the models which are available in the Raw Packet Generator. Finally, we end this paper with some conclusions and directions for future work. ESAT-TELEMIC participates in OPNET’s University Program both for educational [12-14] and for research purposes [15-18]. This paper fits into our research on advanced traffic models, performance analysis and hybrid simulation techniques. Model overview The model we developed in [10] is a discrete model. It indicates the number of packets to be generated in each subsequent time interval, resulting in vector X(k) representing the traffic load.
Introduction Since the discovery of the self-similar nature of data traffic [1,2], it is clear that the Poisson model is no longer suitable to accurately describe the bursty behavior of real traffic. On a wide range of time scales, peaks appear in the traffic load. This peak behavior can be very harmful: queues not able to handle the large amounts of traffic, induce large packet delays or losses. Especially multimedia applications are very sensitive to these Quality of Service (QoS) characteristics.
Based on the fact that self-similar traffic looks similar on a wide range of time scales, we worked out a model which consists of a superposition of a number of independent Bernoulli (ON/OFF) sources Si(k), each working on a different time scale: the first source S1(k) can switch its state every interval, the second source S2(k) every two intervals, the third source S3(k) every four intervals, the fourth source S4(k) every eight intervals, etc … Figure 1 depicts this procedure in case 5 sources are used. The resulting traffic trace is obtained by simply summing the number of packets for each interval.
Accurate traffic models are needed to predict realistic packet delay and loss values in simulations. This is a fundamental requirement to dimension data networks optimally. Poor traffic models can result in a severe underestimation of packet delay and loss, and thus in a too optimistic view on reality.
Each of the Bernoulli sources Si(k) is defined by two parameters: pi the probability that the source is in an ON-state and Ni the number of packets generated per interval during an ON-state. No packets are generated in an OFF-state. These source parameters are determined by fitting the variance-time behavior of the desired trace. A variance-time plot is often used to characterize self-similar traffic. Plotting the variance as a function of the aggregation level on a log-log scale results in a straight line of which the slope is 2H-2, with H the Hurst parameter. A Hurst parameter of 1 equals a slope of 0 and represents very bursty, long-range dependent traffic. A Hurst parameter of 0.5 equals a slope of -1 and represents short-range dependent, Poisson-like traffic. By choosing the length of the sources as described above, it is possible to fit the variance-time curve at aggregation levels of power 2. The number of sources determines the maximum aggregation level at which the curve is fitted.
A large number of models are described in the literature [3-9], but most of them have one or more of the following problems. Many models have difficulties to accurately fit the Hurst parameter, which is a measure for the burstiness of the traffic. A lot of models do not allow generating traffic with an arbitrary combination of average arrival rate, variance and Hurst parameter. Several models make use of parameters which do not represent characteristics that can be easily measured in real-life traffic traces. This makes the parameterization of these models very awkward [15]. To overcome these problems we developed a new traffic model which is based on a hierarchical scheme of Bernoulli sources [10,11]. We implemented the model in OPNET Modeler and used it in a case study in which we show its benefits. 1
Research Assistant of the Fund for Scientific Research – Flanders (Belgium) (F.W.O.-Vlaanderen) 1
S1(k) + S2(k) + S3(k) + S4(k) + S5(k)
~ = X(k) 123
k
Figure 1: Traffic generated by a superposition of independent Bernoulli sources, each working on a different time scale By fitting the variance-time plot, both the variance and the Hurst parameter can be configured independently. In [10] we described the mathematical procedure needed to calculate the source parameters when also fitting the average arrival rate. In [11] we presented a more sophisticated version of the model in which also third-order moments can be fitted and non-stationary effects can be compensated for. These enhancements make the model more accurate for imitating the queuing behavior of real traffic.
Figure 2: Traffic generation parameters of the implemented model Figure 4 depicts the implemented SS_simplified_rpg_dispatcher process model. After initialization, the state (ON or OFF) of every source needs to be set. The total number of packets to be generated in the first interval depends on the state of each of the sources. Since the generation of a packet requires a specific time stamp, the packets are sent uniformly, equally spaced in time throughout the interval. Each time a packet arrives, the statistics variables are updated and the packet is destroyed. Each time a minimal time interval has passed, the program checks which of the sources need to be reset and calculates the new number of packets to transmit in the new interval.
Implementation of the model In this section we give a brief overview of the implementation in OPNET Modeler. Similar to the Raw Packet Generator, we developed a PPP workstation able to send and receive selfsimilar traffic. The attributes of the workstation are depicted in Figure 2. As stated before, our model is a discrete model: the Minimal Time Interval parameter indicates the interval length the first source S1(k) is working on. The Additive Packet Complement is a constant number of packets that needs to be added or subtracted in each interval (used in the sophisticated version of the model). The Destination IP Address indicates where the packets need to be sent to. In this implementation the Packet Size is constant. A future version will include the ability to choose a packet size distribution. Start Time specifies when the traffic generator is started. In this implementation the Ni and pi parameters need to be entered manually for each source. The source parameter calculation methods described in [10] and [11] are not yet included in the implementation. At this moment, the source parameters need to be calculated in another program. We use MATLAB for this purpose. Figure 3 gives an overview of the implemented SS_ppp_simple_rpg_wkstn_adv node model. The rpg module is able to generate and receive packets. Once a data packet is generated, it is encapsulated in an IP-packet and transmitted via the tx-interface. For packets received by the rx-interface, the data is taken out of the IP-packet and delivered to the rpg module.
Figure 3: Node model of the implemented traffic generator 2
Figure 4: Process model of the packet generator Case study To point out the benefits of the model described above, we use the implemented generator in a case study in which we compare its ease of use and accuracy to the self-similar generators that are available in OPNET’s Raw Packet Generator (RPG).
Figure 6: Adjusting the capture mode of the packets/sec statistic The Raw Packet Generator offers various traffic generation methods based on Fractal Point Processes (FPP): Sup-FRP, PowON-PowOFF, PowON-ExpOFF, ExpON-PowOFF, HFSNDP, F-FSNDP-EF and F-FSNDP-FF. For more information regarding the theory of these models we refer to [8,9].
The aim of the case study is to send self-similar traffic from workstation Alice to workstation Bob. Figure 5 depicts the simple project scenario: two PPP workstations interconnected by an OC-12 link. The traffic should have an average arrival rate of 10,000 packets/sec, a Hurst parameter of 0.7 and a variance of 100 at an aggregation level of 1 ms. Each of these macroscopic characteristics can be easily measured in real traffic traces. The values are chosen arbitrarily but are representative for a realistic scenario. The link bandwidth is high enough to avoid saturation.
In this case study we use the PowON-ExpOFF, the ExpONPowOFF, the PowON-PowOFF and the Sup-FRP model. The FSNDP models are not used because they are flow-based and no specific information regarding the characteristics of these flows is given in the case study objectives. This makes a good parameterization nearly impossible. In case of the F-FSDNP-EF model, it is also impossible to specify the Hurst parameter.
MATLAB is used to check the above mentioned characteristics of the generated traces. To obtain traces indicating the number of packets generated per ms (needed to calculate the characteristics), we configure the capture mode as indicated in Figure 6. The trace data are written to a txt-file by exporting the packets/sec graph.
Generated traces The PowON-ExpOFF model is based on a superposition of ON/OFF sources of which the ON-times have a heavy-tailed distribution and the OFF-times an exponential distribution. The model has five parameters: the average arrival rate, the Hurst parameter, the Fractal Onset Time Scale (FOTS), the source activity ratio and the peak-to-mean ratio. Unfortunately we can not choose the variance. We are forced to vary the other parameters in order to examine their impact on the variance of the generated trace. For the first trace we enter the values as depicted in Figure 7: 10,000 packets/sec, 0.7, 0.001 sec, 75 % and 4 respectively. Six other traces are obtained by changing the source activity ratio to 50 and 90 %, by shifting the peak-to-mean ratio to 2 and 10, and by altering the FOTS to 0.0001 and 0.01 sec respectively. Table 1 summarizes the PowON-ExpOFF trace configurations. The ExpON-PowOFF model is similar to the PowON-ExpOFF model. In this case the ON-times have an exponential distribution and the OFF-times a heavy-tailed distribution. The model has the same parameters as the PowON-ExpOFF model.
Figure 5: Project scenario used in the case study 3
This model has only four parameters: the average arrival rate, the Hurst parameter, the Fractal Onset Time Scale (FOTS) and the source activity ratio. The values for the parameters are equal to the ones of the traces above. Table 3 gives an overview of the five different configurations.
Trace 15 Trace 16 Trace 17 Trace 18 Trace 19
Trace 1 Trace 2 Trace 3 Trace 4 Trace 5 Trace 6 Trace 7
Source Activity Ratio 75 % 50 % 90 % 75 % 75 % 75 % 75 %
Peak-toMean Ratio 4 4 4 2 10 4 4
The Sup-FRP model consists of a superposition of fractal renewal processes. The model has only three parameters: the average arrival rate, the Hurst parameter and the Fractal Onset Time Scale (FOTS). Three different traces are obtained by varying the FOTS.
Trace 20 Trace 21 Trace 22
Table 1: Different PowON – ExpOFF trace configurations, the average arrival rate is always 10,000 packets/sec, the Hurst parameter 0.7.
Trace 8 Trace 9 Trace 10 Trace 11 Trace 12 Trace 13 Trace 14
Source Activity Ratio 75 % 50 % 90 % 75 % 75 % 75 % 75 %
Fractal Onset Time Scale 0.001 s 0.0001 s 0.01 s
Table 4: Different Sup-FRP trace configurations, the average arrival rate is always 10,000 packets/sec, the Hurst parameter 0.7.
Analogously to the PowON-ExpOFF case, seven traces are obtained by configuring the parameters as shown in table 2
Fractal Onset Time Scale 0.001 s 0.001 s 0.001 s 0.001 s 0.001 s 0.0001 s 0.01 s
Source Activity Ratio 75 % 50 % 90 % 75 % 75 %
Table 3: Different PowON – PowOFF trace configurations, the average arrival rate is always 10,000 packets/sec, the Hurst parameter 0.7.
Figure 7: Configuring the arrival process of the RPG model
Fractal Onset Time Scale 0.001 s 0.001 s 0.001 s 0.001 s 0.001 s 0.0001 s 0.01 s
Fractal Onset Time Scale 0.001 s 0.001 s 0.001 s 0.0001 s 0.01 s
Trace 23 is generated using our model. By using 12 sources the variance-time behavior can be fitted up to aggregation levels of 211. The source parameters are calculated in MATLAB using the method described in [10], which does allow choosing a specific variance. This calculation only takes very little time and memory and can be included in OPNET in a future version of our traffic generator. Figure 8 shows the configuration of each of the Bernoulli sources.
Peak-toMean Ratio 4 4 4 2 10 4 4
For each scenario we generate a trace of 100 s. The number of packets generated in each interval of 1 ms, can be calculated by dividing the number of packets/sec by 1000. Figure 9 depicts trace 23 at aggregation levels of 1, 10, 100, and 1000 respectively. On each of these time scales, the generated traffic exhibits a peak behavior, which indicates that the trace is selfsimilar.
Table 2: Different ExpON – PowOFF trace configurations, the average arrival rate is always 10,000 packets/sec, the Hurst parameter 0.7.
Analysis of the traces Each of the traces is analyzed in more detail by calculating the mean number of packets per interval of 1ms, the variance, and the Hurst parameter. Both the variance-time (VT) plot and the rescaled adjusted range statistic (R/S) are used to determine the Hurst parameter.
The PowON-PowOFF model is based on a superposition of ON/OFF sources of which both the ON-times and the OFF-times have a heavy-tailed distribution. 4
Trace 8 Trace 9 Trace 10 Trace 11 Trace 12 Trace 13 Trace 14
Mean
Variance
9.97 9.97 9.99 10.01 10.02 10.05 10.02
19.92 19.53 20.12 19.03 22.47 35.92 13.81
Hurst VT 0.69 0.67 0.67 0.65 0.65 0.63 0.64
Hurst R/S 0.61 0.53 0.69 0.58 0.65 0.63 0.56
Table 6: Measured mean, variance and Hurst parameter of the generated ExpON-PowOFF traces.
Mean
Variance
10.00 9.99 9.97 9.97 10.02
17.55 18.32 16.61 24.31 13.34
Figure 8: Bernoulli source configuration for Trace 23
Aggregation level 1
Trace 15 Trace 16 Trace 17 Trace 18 Trace 19
Aggregation level 10
60
400
50 300
Hurst VT 0.66 0.61 0.64 0.65 0.67
Hurst R/S 0.56 0.56 0.64 0.78 0.60
40 30
200
Table 7: Measured mean, variance and Hurst parameter of the generated PowON-ExpOFF traces.
20 100 10 0
0
2
4
6
8
0
10
0
2000
4000
6000
8000
10000
4
x 10
4
Aggregation level 100 2500
2
2000
Aggregation level 1000
x 10
Trace 20 Trace 21 Trace 22
1.5
1500 1
Mean
Variance
10.03 10.09 10.11
11.03 20.11 10.19
Hurst VT 0.72 0.69 0.65
Hurst R/S 0.72 0.66 0.65
1000 0.5
500 0
0
200
400
600
800
1000
0
Table 8: Measured mean, variance and Hurst parameter of the generated Sup-FRP traces. 0
20
40
60
80
100
Figure 9: Trace 8 at different aggregation levels Tables 5, 6, 7, 8 and 9 summarize the measured statistics for the PowON-ExpOFF model, the ExpON-PowOFF model, the PowON-PowOFF model, the Sup-FRP model, and our model respectively.
Trace 1 Trace 2 Trace 3 Trace 4 Trace 5 Trace 6 Trace 7
Mean
Variance
9.98 10.00 9.97 9.92 10.00 9.92 10.00
18.69 19.35 18.26 18.58 18.66 29.41 13.61
Hurst VT 0.62 0.66 0.64 0.54 0.61 0.62 0.58
Trace 23
Mean
Variance
10.19
100.55
Hurst VT 0.72
Hurst R/S 0.67
Table 9: Measured mean, variance and Hurst parameter of the trace generated with our model.
Hurst R/S 0.62 0.56 0.64 0.55 0.69 0.63 0.56
Mean The mean is fitted very well for all traces. The small deviations are purely probabilistic and depend on the seed of the random number generator. These deviations will become smaller if the simulation time is increased. Variance A variance of 100 is only achieved for Trace 23, which is generated by using our model. This is not surprising since only our model offers the ability to configure the variance. Changing the source activity ratio or the peak-to-mean ratio for the PowON-ExpOFF model, does not have a significant impact on the generated variance.
Table 5: Measured mean, variance and Hurst parameter of the generated PowON-ExpOFF traces. 5
Altering the FOTS however, does change the variance. When the fractal behavior starts at a smaller time scale, the variance at aggregations levels of 1 ms increases. A trial-and-error strategy is needed to obtain the correct FOTS value to generate the desired variance. This makes the parameterization of the built-in models very awkward.
2 ideal expON−powOFF
Logarithm of variance
1
Hurst parameter None of the PowON-ExpOFF traces is able to accurately fit the Hurst parameter, as can be read from Table 5. They all generate traffic of which the burstiness is not high enough. This results in variance-time plots of which the slope is too steep. Figure 10 depicts this behavior.
0 −1 −2 −3 −4 −5
2 1 0
1
2 3 4 Logarithm of aggregation level
5
Figure 11: Variance-time plots of the generated ExpON-PowOFF traces
−1 −2
2
−3
1
−4
0
Logarithm of variance
Logarithm of variance
−6 0
ideal powON−expOFF
−5 −6 0
1
2 3 4 Logarithm of aggregation level
5
Figure 10: Variance-time plots of the generated PowON-ExpOFF traces
ideal powON−powOFF
−1 −2 −3 −4 −5
The Hurst parameter fit is slightly better in case of the ExpONPowOFF model. The slopes of the curves in Figure 11 are closer to the slope of the ideal case. However, some of the plotted curves exhibit a significant deviation from a straight line. This behavior can be explained only for the trace with the FOTS of 0.01 s, which corresponds to the lowest curve.
−6 0
1
2 3 4 Logarithm of aggregation level
5
Figure 12: Variance-time plots of the generated PowON-PowOFF traces
The same conclusions can be drawn for the PowON-PowOFF and the Sup-FRP model. Figure 12 and 13 respectively depict their variance-time behavior. Note that the Sup-FRP traces remain parallel to the ideal line up to aggregation levels much higher than the other models.
Simulation complexity Tables 10, 11, 12, 13, and 14 respectively give an overview of the number of events, the simulation time and the memory that is needed to generate the traces in case the PowON-ExpOFF, the ExpON-PowOFF, the PowON-PowOFF, the Sup-FRP, and our model is used. Varying the parameters of the built-in RPG models clearly influences the number of events and the simulation time needed. Reducing the source activity ratio increases the number of events. Except for the Sup-FRP model, a higher FOTS results in a serious increase of the number of events. The simulation time changes more or less proportionally in most cases. The memory usage remains rather constant. The Sup-FRP is the fastest of the built-in models. Our model has a comparable speed but uses less memory.
As indicated in Figure 14, our model is able to accurately fit the desired variance-time behavior, and thus the Hurst parameter. Not only the slope of the curve is ideal, the curve also intersects the y-axis at the correct value, which indicates that the variance is also fitted. To be sure that this good result is not a coincidence, several traces were generated with different seed values. The results do not significantly differ from Trace 23. 6
2 ideal Sup−FRP
Logarithm of variance
1
Trace 8 Trace 9 Trace 10 Trace 11 Trace 12 Trace 13 Trace 14
0 −1 −2 −3
Number of events 17,008,931 19,713,959 16,181,557 15,882,194 16,647,231 14,629,475 28,779,175
Simulation time 9m46s 10m08s 9m22 8m57s 9m30s 9m53s 11m43
Memory usage ± 5.9 MB ± 5.9 MB ± 5.9 MB ± 5.8 MB ± 5.9 MB ± 5.9 MB ± 5.9 MB
Table 11: Simulation complexity for the different ExpON-PowOFF traces.
−4 −5 −6 0
1
2 3 4 Logarithm of aggregation level
5
Trace 15 Trace 16 Trace 17 Trace 18 Trace 19
Figure 13: Variance-time plots of the generated Sup-FRP traces
Number of events 20,199,706 23,932,580 18,686,434 15,196,759 43,408,980
Simulation time 10m16s 10m52s 9m57s 8m55s 14m33s
Memory usage ± 5.9 MB ± 5.9 MB ± 5.9 MB ± 5.9 MB ± 5.9 MB
2 ideal our model
Logarithm of variance
1
Table 12: Simulation complexity for the different PowON-PowOFF traces.
0 −1
Trace 20 Trace 21 Trace 22
−2 −3 −4
Number of events 13,907,762 13,991,038 14,018,558
Simulation time 9m07s 8m45s 9m21s
Memory usage ± 5.9 MB ± 5.9 MB ± 6.0 MB
Table 13: Simulation complexity for the different Sup-FRP traces.
−5 −6 0
1
2 3 4 Logarithm of aggregation level
5
Trace 23
Figure 14: Variance-time plot of the trace generated with our model
Trace 1 Trace 2 Trace 3 Trace 4 Trace 5 Trace 6 Trace 7
Number of events 20,502,223 26,131,188 18,692,949 15,769,295 25,785,389 15,192,933 44,797,060
Simulation time 10m05s 11m13s 10m28s 9m20s 11m53s 9m26s 14m07s
Number of events 14,223,060
Simulation time 8m54s
Memory usage ± 4.8 MB
Table 14: Simulation complexity for our model.
Conclusions This paper describes a new traffic model we implemented in OPNET Modeler. The model is based on a superposition of independent Bernoulli sources, each working on a different time scale. The model is used in a case study to generate self-similar traffic of which the mean, the variance and the Hurst parameter are given. These parameters were chosen because they can be easily measured in real traffic traces. Compared to the models which are included in OPNET’s Raw Packet Generator, our model can fit the variance without any problem. It is more accurate in fitting the Hurst parameter and it requires less simulation time and memory. Our model in not difficult to parameterize, which makes it a valid alternative for the built-in models.
Memory usage ± 5.9 MB ± 5.9 MB ± 5.9 MB ± 5.9 MB ± 5.9 MB ± 5.9 MB ± 5.9 MB
Table 10: Simulation complexity for the different PowON-ExpOFF traces. 7
[7] T. Yoshihara, S. Kasahara, and Y. Takahashi, “Practical Time-Scale Fitting of Self-Similar Traffic with Markov-Modulated Poisson Process,” Telecommunication Systems, vol.17, no. 1-2, pp.185-211, 2001.
The current implementation of our model can be further improved by including the source parameter calculation. This way the user can simply enter the required average arrival rate, the variance and the Hurst parameter and does no longer have to worry about the calculation. An advanced version of the implementation could also support more sophisticated features of the model, which include the fitting of third-order moments or compensation for non-stationary effects. All implementations will be made available at our website [19].
[8] B. Ryu and S. Lowen, “Point process models for self-similar network traffic, with applications,” Stochastic Models, 14(3), pp. 735761, 1998. [9] B. Ryu, “A Tutorial on Fractal Traffic Generators in OPNET for Internet Simulation,” OPNETWORK 2000, Washington D.C., USA, August 2000.
Acknowledgements A first implementation of the traffic generator was created by Ye Guan in the framework of his Master thesis at our department. We want to thank him for his interest in our research and his enthusiastic attitude. We are grateful to Bart Van den Broeck for his numerous comments and efforts to further improve and extend the code. His contributions proved to be vital. We are also indebted to the Flemish government, which partly sponsors this research through the generic university basic research program (GBOU) "End-to-End QoS in an IP Based Mobile Network".
[10] J. Potemans, B. Van den Broeck, J. Theunis, P. Leys, E. Van Lil, and A. Van de Capelle, “A Tunable Discrete Traffic Generator based on a Hierarchical Scheme of Bernoulli Sources”, Proc. of ICC’03, Anchorage, Alaska, USA, May 2003. [11] J. Potemans, J. Theunis, P. Leys, B. Van den Broeck, E. Van Lil and A. Van de Capelle, “Advanced Traffic Modeling: Fitting Third Order Moments”, to appear in Proc. of Globecom’03, San Francisco, California, USA, December 2003. [12] J. Theunis, P. Leys, J. Potemans , Bart Van den Broeck, E. Van Lil and A. Van de Capelle, “Advanced Networking Training for Master Students Through OPNET Projects”, OPNETWORK 2003, Washington D.C., USA, August 2003. [13] J. Theunis, B. Van den Broeck, P. Leys, J. Potemans, E. Van Lil and A. Van de Capelle, “OPNET in Advanced Networking Education”, OPNETWORK 2002, Washington D.C., USA, August 2002.
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[19] http://www.esat.kuleuven.ac.be/telemic/networking/opnet.php
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