The simulation is proof of concept and shows the properties of the designed methods. It is done for the three methods using Matlab 7.0. The results are compared to updates at the constant intervals and in between. In this way, the qualities of the new method are verified.
Fair comparison is achieved using the same resources for the methods, thus the same number of updates during the time of simulation. Every method runs with the same number of updates in the same experiment time. The better the method is, the shorter the Disconnection Interval. Statistics of the disconnection intervals are compared, such as mean, max, min, variance etc.
7.5 Simulation and performance evaluation 118
Analysis of the results is provided in 8.6, 9.5, 10.9 and 12.3. There is no best performance or winner algorithm (see 12.3) since the optimal algorithm varies for the different usage scenarios. The algorithms choice depends on the concrete deployments. It is also possible to switch between the algorithms.
7.5.1 Simulation input data
Many simulations were carried out to test the properties of the algorithm. Five of them were chosen to demonstrate the qualities of the new algorithms. They are used to test all suggested algorithms, see chapters 8, 9 and 10. In this way, the results of the algorithms can be compared to each other. The first four input data (movements) are generated with mathematical equation. The last case is simulated with real dialup access statistics.
Representative scenarios are difficult to choose since the scenarios are consequence on the usage. The M-VPN can be deployed, for example in cellular networks in 3GPP, mobile vehicle with WLAN or mobile smart devices in campus building (office). The speed of IP/port changes and the moving patterns are different. Furthermore, the M-VPN can be used in VoIP environment with requirement of minimal disconnection or non real-time application like HTTP information with low requirement on disconnection. The chosen four simulation cases represent the most common cases building the primitive scenarios, which are:
1) In the first scenario, the intervals between the ETPs are white noise with some constant shift. Figure 7.3 presents a practical case where a mobile host is moving with a constant speed in a wireless environment, like a car moving at direct road. The wireless access networks cover similar areas transparently connected to the Internet.
The changes of the PoA are at semi equal intervals because the wireless areas and the host speed cannot be constant in the praxis. For this reason, there is a deviation expressed in white noise. The white noise represents the differences between the PoA changes. No doubt, there could be other representations of this case. The equations are expressed by:
10
) , 200 (
=
= σ
σ N
aEIr ,
where aEIris the rth Event Interval. N() denotes normal distributed random values with a mean value of 200 sec and a standard deviation of 10 sec. The mean of 200 means the host stays mean 200 sec in wireless area. Practical representation of these values is for example: wireless cell (aria) with radius less has 1,4 km and the car (mobile host) moving with 50 km/h. The deviation of 10 gives changing intervals mostly from 170 sec to 230 sec, which represents the variation of the speed and size of the wireless cell.
2) In the second scenario, the intervals of PoA change (ETPs) are generated by two rotating white noise sources. A practical representation could be similar to the
Internet Internet
Server
Mobile Host Movement
PoA 1 PoA 2 PoA 3
Wireless networks
Figure 7.3: Host moving in wireless environment with constant speed
7.5 Simulation and performance evaluation 119
previous case with an additional NAPT as an intermediate devices. The wireless access points typically have an NAPT device, which can lead to PoA change before the host leaves the area. The PoA can be changed due to host movement or an NAPT table reset. This is shown in Figure 7.4. There are two white noise sources, which are rotating. They can be described by:
10 , 10
) , 100 ( ) , 100 (
2 1
2 1
=
=
= σ σ
σ σ orN N
aEIr
The operator or denotes the rotation with 50% probability. Half of the values are generated by the first distribution and half by the second. The mean values of 100 sec gives the mean of PoA change. A practical representation my be a wireless aria (cell) with radius of 0,7 km and car (mobile host) speed of 50 km/h. The deviation of 10 represents the variation of cell size and speed. The values are the values mostly between 70 sec and 130 sec.
3) In the third scenario, sinus based Event Intervals with some white noise are defined.
This occurs by repeating patterns in the Event Intervals, like a day cycle. The intervals are small in morning hours and large at night. The values go smoothly between these states. A sinus-based signal with white noise is defined as:
+
+
+
=
,2 500 2 sin
sin 3 10 4 7
sin π σ π σ
σ N
S c k S k S
aEIk k
The variable S indicates the total number of samples, S=5000. The number of samples is set to 5000 because it is sufficiently large to generate meaningful results, thus the results do not change significantly with increasing the number of samples.
The k is the index of the calculated sample. The σis equal to 10 to and represents minimal changes of the day cycle.
4) In the fourth scenario, recursive non-linear values with added white noise are the intervals between the ETPs. This is very challenging for every prediction method. It can represent a complex movement of the host with out any evident simple logic, shown in Figure 7.5. (The equation is also used in [6]). The equation defined as:
) 20 , 200 ( ) 2 . 1 cos(
1 8 25
2 21
1
1 k N
r r aEI aEI
k k k
k + +
+ +
=
−
−
−
5) The fifth experiment is made with real data gathered from L2TP over IPSec dial up network, thus remote access. The intervals between the ETPs are the user’s remote login in the corporate network. The deployment M-VPN can be very different from cell phone to trains. The remote access expresses the relocation of the mobile phone to some degree. There is a peak in the morning and afternoon. In the night, there is
Internet Internet
Server
Mobile Host Movement
PoA 1 or 2 PoA 3 or 4 PoA 5 or 6
Wireless networks
NAPT
NAPT
Figure 7.4: Host moving in wireless environment with NAPT
7.5 Simulation and performance evaluation 120
less activity. The anonymous data was available to the author and used for the testing.
The constant parameters in the simulation are chosen to represent real cases, where small disconnection is required and the mobile host moves fast. For the first four experiments, the following parameters are used: The application requires 5 sec of Maximum Disconnection Interval (MDI). The simulation is made with 5000 samples, thus there were 5000 prediction cycles. The specific parameter are defined in 8.6, 9.5 and 10.9
7.5.2 Statistics and diagrams by the simulation
There are four diagrams showing the properties of the simulated algorithm. They are presented for each simulation case in 8.6, 9.5 and 10.9. The first diagram shows the Event Intervals and the posterior estimated Event Intervals (see example in Figure 7.6). It can be used for the optical evaluation of signal and the prediction.
A second diagram shows the histogram of the Disconnection Intervals (DIs) and gives qualitative numerical results (see example in Figure 7.7). This is the most important diagram since it compares the current method to the constant Update Intervals in a fair way. The fair way means that the same resources are used in the suggested method and in method with constant intervals. Both methods use the same number of location updates for the same time of simulation. In this way, the DIs can be directly compared between the methods which allows qualification of the better algorithm.
The constant update algorithm is the simplest and mostly used method, see chapter 1. The nodes send updates in constant intervals, thus there is no optimisation. The maximum Disconnection Intervals (DI) is equal to the Update Interval. This is reference method and all suggested methods are compared to it.
The DI corresponds to an error in the filter theory and must be minimised. The distribution of the DI is presented in the histogram on the second diagram. The following vertical lines mark the following values:
• A dotted black line shows the mean Update Interval (UI), thus the mean of maximal disconnection.
• A dashed black line shows the maximal Disconnection Intervals (DIs) by constant Update Interval see Variable const UI.
• A red dashed line marks the maximum Disconnection Interval (error) in this simulation by the method.
• A grey dotted line shows the user defined maximum disconnection (MDI).
Certain very important qualitative values are shown in the bottom-right corner of the histogram. Their definitions are:
Mobile Host
Wireless networks
NAPT
Movement
Figure 7.5: Complex mobile host movement