3.3 C LAIM 2.3: H EURISTIC RWA FOR THE ADAPTIVE CONFIGURATION SCHEME
3.3.4 Results
allowed to tune the signal powers of the channels. The second method is the adaptive routing where a globally optimal solution is given for the adaptive routing scheme. The third one is the heuristic. Here the results are given for the case where the maximum deviation is zero i.e.
shortest path routing is done. Obviously if the maximum deviation parameter is infinite we get the same complexity as in case of adaptive routing.
Wavelength Demands Method Row Columns Nonzero
8 15
Fix 83605 82992 343096 Adaptive 83605 83007 343141 Heuristic 5413 4143 16973
8 40
Fix 300821 305656 1257909 Adaptive 300821 305711 1257909 Heuristic 23446 18768 78440
4 15
Fix 41881 41496 171548 Adaptive 41881 41511 171593 Heuristic 2769 2079 8509 Table 3-3: Complexity of different methods.
The absence of solution can have two reasons: the RWA does not succeed, or the distance between the source and destination node is too long, i.e. the signal quality will be inadequate.
The bandwidths of the demands were equal to the capacity of one channel.
I have compared the proposed algorithm with the traditional RWA algorithm (Figure 3-24-Figure 3-25). Here in this case the maximum deviation parameter was infinite, i.e. the ILP is solved which gives the globally optimal solution. On the y-axis the maximum number of routed demands is depicted, while on the x-axis the used routing schemes. RWA means that the traditional routing scheme is used where each channel has the same signal power. It has to be mentioned that the n-factor parameter gives the maximum possible deviation between the channel powers, see equation 5-7 in chapter 5, appendix. The n = 1 routing scheme is similar to the RWA routing scheme. The only difference is that in case of n = 1 the channel powers can be lower than the average of the powers. In RWA case this variation is not allowed. In n >
1 cases I used the proposed routing algorithm with n equal to the depicted numbers. The result marked as “MAX” is the number of maximum routed demands in case when physical effects are neglected. The scale parameters mean that I changed the lengths of the used network link by multiplying the original lengths with the scale parameter. In Figure 3-24 the scale is 1, i.e., the original link lengths are used. In Figure 3-25 the scale parameter is 1.25. (The geographical distances are decreased to 25%)
In Figure 3-24 and Figure 3-25 it can be seen that the traditional RWA algorithm can route 19 and 1 demands, respectively. While by increasing the n-factor more and more demands can be routed until we reach a limit, where the RWA problem is infeasible in itself (without considering physical effects). These results show that using the proposed RWA scheme it is possible to reach the same number of routed demands as in case of neglecting the physical impairments.
RWA 1 1,1 1,2 1,3 1,4 MAX 0
10 20 30 40 50 60
70 Scale parameter = 1
n-factor
maximum routed demands
Figure 3-24: Maximum number of routed demands versus n-factor parameter in case of COST 266 topology
RWA 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 MAX 0
10 20 30 40 50 60 70
maximum routed demands
n-factor Scale
parameter = 1,25
Figure 3-25: Maximum number of routed demands versus n-factor parameter in case of COST 266 topology, scale 1.25
The results lead to a conclusion that just a small amount of n-factor increase, highly increases the number of maximally routed demands.
To investigate the dependency of the proposed method on the number of wavelengths I made simulations using the COST266 network topology and different wavelength numbers (see Figure 3-26). Here also the maximum deviation parameter was infinite. The figure shows that while increasing the number of channels the maximum number of routed demands is increasing. This behavior is what it is expected when solving the RWA problem. The interesting property is that, if we double the number of wavelengths and the n-factor is high enough, the maximum number of routed demands is more than double in each case. This behavior is due to the way how the proposed algorithm works. If we have more wavelengths,
there are more possible variations how the signal power can be allocated. Consequently, if the number of wavelengths is increased, the performance of the proposed algorithm will improve.
RWA 1 1,1 1,2 1,3 1,4 2
10 20 30 40 50 60 70
13 26 31 54 70 2 wavelengths
3 wavelengths 4 wavelengths 6 wavelengths 8 wavelengths
maximum routed demands
n-factor
Figure 3-26: Maximum number of routed demands versus n-factor parameter in case of COST 266 topology, for different wavelength numbers
In the previous figures the performance of the algorithm was presented in case of globally optimal solution. As it was mentioned the proposed scheme is able to scale while changing the maximum allowable distance. In Figure 3-27 the performance of the method is presented in case of eight wavelength network. Two extreme cases are compared when the maximum allowable distance is zero, i.e. all demands are routed in shortest path, and when the maximum allowable distance is infinite, i.e. the globally optimal solution. As it is to be seen in case of low n-factor values the two methods give the same result but while increasing the tune-ability of the signal powers, as it was expected, the globally optimal solution performs better than the shortest path routing. The emphasis is on, that even for the simplest shortest path routing, if it is allowed to tune the signal power much more demands can be routed in all-optical domain than in case when this is not allowed. In Figure 3-28 the results for sixteen wavelength network topology is shown in case of shortest path routing. As it is to be seen the number of routed demands is highly increasing while increasing the n-factor.
RWA 1 1,1 1,2 1,3 1,4 MAX 0
10 20 30 40 50 60 70
m a x im u m r o u te d d e m a n d s
n-factor Heuristic method Global optimum
Figure 3-27: The performance of heuristic method in case of globally optimal solution and shortest path routing
RWA 1 1,1 1,2 1,3 1,4 MAX
0 10 20 30 40 50 60 70 80
Scale parameter = 1
n-factor
maximum routed demands
Figure 3-28: Shortest path results in case of 16 wavelengths