**4. Simulation of network traffic in simulation tools**

One of the very important tasks in simulation is modeling the real network parameters and network elements for simulation purposes. The main goal in successful modeling of network traffic is to minimize discrepancies between the measured simulations and by simulations statistically-modeled and generated traffic. This means, that both traffics are similar within the different criteria, such as bit and packet-rate, bursts (Hurst's parameter), variance, etc.

Network traffic simulations are usually based on modeling of data sources or applications. One of the most known simulation tools is OPNET Modeler [22], [23]. A simulation of network traffic in this tool is based on the "on/off" models [41] or more often used traffic generators. Difference between these manners is in a modeling manner. In the first case, the arrival process is described by Hurst's parameter (*H*) and the data length process is

Modeling and Simulating the Self-Similar Network Traffic in Simulation Tool 365

In the IP station model, the traffic generator is placed above the IP encapsulation layer, which takes care of packets' formations and fragmentation. This is the process of segmentation of long data into the shorter packets, or vice versa, according to the RFC 793 [12]. Padding of the packet data payload with additional bits is also performed when data is shorter than a predefined minimal payload. Because the traffic is modeled, above IP level of the TCP/IP model, to the lengths of the generated data, 20 bytes of IP header are added. 18 bytes of information for MAC (14bytes) and CRC (4 bytes) are also further added. Structure of Ethernet frame used in the IP station model. Using this model, the applications' protocol does not impact the generated traffic. The model is suitable for the simulation cases, when we want to statistically model the network traffic, which can be caused by many arbitrary communications' applications. Using this approach, we can model such network traffic by

**5. Estimation of simulation parameters of measured network traffic** 

The main problem of measured packet network traffic modeling is to estimate the parameter, which is needed for modeling measured network traffic in simulation tools. It has already been mentioned that the parameters of data source traffic processes are needed. We already described that transformation from packet network traffic Z*p*[*n*] to data source

Fig. 8. Node model for used IP station in simulation.

single traffic source.

described by probability density function (*pdf*). In the second case, processes of data length and data inter-arrival time are both described by *pdf*.

In OPNET Modeler, two standard node models appear [9]:


Raw Packet Generator (RPG) is a traffic source model [16], [27] implemented specially to generate self-similar traffic, which is based on different fractal point processes (FPP) [41]. Self similar traffic is modeled with an arrival process, which is described by Hurst's parameter and the distribution probability for packet sizes. This arrival process can be based on many different parameters, such as Hurst parameter, average arrival rate, fractal onset time scale, source activity ratio and peak to mean ratio [16]. There are several different fractal point processes (FPP). In our case, we used the superposition of the fractal renewal process (Sub-FRP) model, which is defined as the superposition of *M* independent and probably identical renewal fractal processes. Each FRP stream is a point renewal processes and *M* numbers of independent sources compose the Sub-FRP model. Common inter-arrival probability density function *p(t)* of this process is:

$$p(t) = \begin{cases} \mathcal{Y}A^{-1}e^{-\mathcal{Y}t/A} & 0 \le t \le A \\\mathcal{Y}e^{-\mathcal{Y}}A^{\mathcal{Y}}t^{-(\mathcal{Y}+1)} & t \ge A \end{cases} \tag{21}$$

where 1 < *γ* < 2. Process FRP can be defined as Sup-FRP process, when the number of independent identical renewal processes *(M)* is equal to 1. A model Sub-FRP is described by three parameters: *γ*, *A* and *M*. *γ* represents the fractal exponent, *A* is the location parameter, and *M* is the number of sources. These three parameters are in relationship with three OPNET parameters. These parameters are Hurst's average arrival-rate *λ*, and fractal onset time-scale (FOTS). The relationships between these three parameters of Sub-FRP and parameters in OPNET model are:

$$H = (3 - \gamma) / 2$$

$$\lambda = M\gamma [1 + (\gamma - 1)^{-1} e^{\gamma \gamma}]^{-1} A^{-1} \tag{22}$$

$$T^{\alpha} = 2^{-1} \gamma^{-2} e^{-\gamma} (\gamma - 1)^{-1} (2 - \gamma) (3 - \gamma) [1 + (\gamma - 1) e^{\gamma}]^2 A^{\alpha} \tag{23}$$

where *γ* = 2 – *β*. Hurst parameter *H* is defined by equation (3). In the Sub-FRP model from OPNET, we can set Hurst's parameter (*H*), average arrival-rate (*λ*) and fractal onset timescale (FOTS) in seconds. The recommended value for the parameter FOTS in OPNET is 1 second.

The IP station [16] can contain an arbitrary number of independent simultaneous workingtraffic generators. Each generator enables the use of heavy-tailed distributions, such as Pareto or Weibull, for the generation of a self-similar network traffic by two distributions, one for length of a data source process and another for data inter-arrival time process. In our research, a traffic generator contained in an Ethernet IP station model of the OPNET Modeler simulation tool is used, as shown in the Figure 8.

described by probability density function (*pdf*). In the second case, processes of data length

Raw Packet Generator (RPG) is a traffic source model [16], [27] implemented specially to generate self-similar traffic, which is based on different fractal point processes (FPP) [41]. Self similar traffic is modeled with an arrival process, which is described by Hurst's parameter and the distribution probability for packet sizes. This arrival process can be based on many different parameters, such as Hurst parameter, average arrival rate, fractal onset time scale, source activity ratio and peak to mean ratio [16]. There are several different fractal point processes (FPP). In our case, we used the superposition of the fractal renewal process (Sub-FRP) model, which is defined as the superposition of *M* independent and probably identical renewal fractal processes. Each FRP stream is a point renewal processes and *M* numbers of independent sources compose the Sub-FRP model. Common inter-arrival

1

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 γ

γ

Modeler simulation tool is used, as shown in the Figure 8.

γ γ γ

*p t e At t A* γ

where 1 < *γ* < 2. Process FRP can be defined as Sup-FRP process, when the number of independent identical renewal processes *(M)* is equal to 1. A model Sub-FRP is described by three parameters: *γ*, *A* and *M*. *γ* represents the fractal exponent, *A* is the location parameter, and *M* is the number of sources. These three parameters are in relationship with three OPNET parameters. These parameters are Hurst's average arrival-rate *λ*, and fractal onset time-scale (FOTS). The relationships between these three parameters of Sub-FRP and

> *H* = − ( )/ 3 2 γ

2 1 <sup>2</sup> 12 3 1 1 -1 *T e* 2 ( ) ( )( )[ ( ) ] , *e A*

−− − = − − − +−

 γγ

where *γ* = 2 – *β*. Hurst parameter *H* is defined by equation (3). In the Sub-FRP model from OPNET, we can set Hurst's parameter (*H*), average arrival-rate (*λ*) and fractal onset timescale (FOTS) in seconds. The recommended value for the parameter FOTS in OPNET is 1

The IP station [16] can contain an arbitrary number of independent simultaneous workingtraffic generators. Each generator enables the use of heavy-tailed distributions, such as Pareto or Weibull, for the generation of a self-similar network traffic by two distributions, one for length of a data source process and another for data inter-arrival time process. In our research, a traffic generator contained in an Ethernet IP station model of the OPNET

<sup>1</sup> 1 1 - -1 -1 *M* [( ) ] *e A*

γ

<sup>−</sup> = +− (22)

 γ

 γ α

1 0 / ( )

(21)

*t A A e tA*

and data inter-arrival time are both described by *pdf*.

probability density function *p(t)* of this process is:

• Raw Packet Generator (RPG)

parameters in OPNET model are:

second.

α

• IP station

In OPNET Modeler, two standard node models appear [9]:

Fig. 8. Node model for used IP station in simulation.

In the IP station model, the traffic generator is placed above the IP encapsulation layer, which takes care of packets' formations and fragmentation. This is the process of segmentation of long data into the shorter packets, or vice versa, according to the RFC 793 [12]. Padding of the packet data payload with additional bits is also performed when data is shorter than a predefined minimal payload. Because the traffic is modeled, above IP level of the TCP/IP model, to the lengths of the generated data, 20 bytes of IP header are added. 18 bytes of information for MAC (14bytes) and CRC (4 bytes) are also further added. Structure of Ethernet frame used in the IP station model. Using this model, the applications' protocol does not impact the generated traffic. The model is suitable for the simulation cases, when we want to statistically model the network traffic, which can be caused by many arbitrary communications' applications. Using this approach, we can model such network traffic by single traffic source.
