Total Control Traffic

In the distributed setting, messages generated by hosts and those generated by controllers contribute to the total control traffic as compared to those generated only by hosts in the centralized approach. So, even though the distributed pub/sub may perform better in terms of scalability, it clearly generates more control traffic due to the additional controller requests used for communication between controllers. So, with increased partitioning, the total control traffic would also increase. The total generated control traffic(TCT ) can be represented with equations simply by using the above equations for average controller overhead. The best case and worst case values for each request type have also been presented.

Advertisement Overhead

Using the same argument as in average controller overhead analysis (6.2), TCT generated by an advertisement request can be represented as follows :

T CT = P (C) ∗ 1 + (1 − P (C)) ∗ n

= n − P (C)(n − 1) (6.6)

Here, event C bears the same meaning as above. Best case : P(C) = 1

ACO = n − 1 ∗ (n − 1) = 1

Worst case : P(C) = 0

ACO = n − 0 ∗ (n − 1) = n

Fig. 6.8 depicts generated traffic with varying values of P(C) when 1, 2 and 4 controllers control the network. The best case and worst case values are clear from the figure. The figure also indicates that increased partitioning increases control traffic.

6.2 Control Overhead

Figure 6.8: Total Control Traffic (Advertisement)

6 Analysis and Results

Un-advertisement Overhead

The equation relevant to an un-advertisement can be derived from equation (6.3) and can be presented as follows :

T CT = P (C) ∗ 1 + (1 − P (C))[n + E(D) ∗ (n − 1)]

= n + (n − 1)[E(D)(1 − P (C)) − P (C)] (6.7) Here, along with event C, event D also bears the same meaning as above.

Best case : P(C) = 1

T CT = n + (n − 1)[E(D) ∗ (1 − 1) − 1] = 1

Worst case : P(C) = 0

T CT = n + (n − 1)[E(D)(1 − 0) − 0] = n + E(D) ∗ (n − 1)

Fig. 6.9 portrays TCT with varying values of P(C) when 1, 2 and 4 controllers control the network and E(D) has a constant value of 1. The best case and worst case values for the 3 scenarios and the selected constant value of E(D) are clear from the graphs. The plots show that for E(D) = 1 un-advertisement increases control traffic further as compared to the control traffic generated for an advertisement. Also, the worst case is unbounded as it depends on the value of E(D).

Subscription Overhead

Figure 6.10: Total Control Traffic (Subscription)

6.2 Control Overhead

The following equation formulates the total control traffic generated by a subscription request and can be derived from (6.4).

T CT = P (C) ∗ 1 + (1 − P (C))[P (A) ∗ n + (1 − P (A)) ∗ 1]

= 1 + P (A)(1 − P (C))(n − 1) (6.8)

Again, events C and A mean the same as above. Best case : P(C) = 1, P(A) = {x : x ∈ [0 to 1]}

T CT = 1 + x ∗ (1 − 1)(n − 1) = 1

Worst case : P(C) = 0 , P(A) = 1

T CT = 1 + 1 ∗ (1 − 0)(n − 1) = n

Fig. 6.10 plots TCT along P(C) when the network is divided into 1, 2 and 4 partitions and a constant value of P(A) = 1. The best and worst case scenarios can be determined from the figure as well. It is visible from the graphs that increased partitioning increases control traffic except for the best case.

Un-Subscription Overhead

Figure 6.11: Total Control Traffic (Un-subscription)

Finally, the equation relevant to un-subscription may be derived from (6.5) as follows :

T CT = P (C) ∗ 1 + (1 − P (C))[P (A)(n + E(D) ∗ (n − 1)) + (1 − P (A)) ∗ 1]

6 Analysis and Results

Events C, A and D have the same meaning as before. Best case : P(C) = 1, P(A) = {x : x ∈ [0 to 1]}

T CT = 1 + (n − 1)(1 − 1)[x ∗ (1 + E(D))] = 1

Worst case : P(C) = 0 , P(A) = 1

T CT = 1 + (n − 1)(1 − 0)[1 ∗ (1 + m ∗ 1)] = n + E(D) ∗ (n − 1)

In an un-subscription, even TCT depends on four parameters. So, Fig. 6.11 keeps the value of P(A) constant at 1, the value of E(D) constant at 1 and plots TCT along P(C) when the network is divided into 1, 2 and 4 partitions. Again, the best case and worst case scenarios for such a setting are clear from the figure as is the fact that except for the best case, in all other scenarios increased partitioning increases control traffic. Also, un-subscription may contribute to the total control traffic more than a subscription does.

Experimental Results

Figure 6.12: Total Control Traffic (uniform distribution)

It is quite clear from the equations above that except for the best case, in each type of request, control traffic increases with increasing number of controllers. The experiments performed confirm this fact where again the same test environment is used. In the following graphs the total control traffic is plotted on the y axis with the number of controllers along x-axis.

6.2 Control Overhead

Figure 6.13: Total Control Traffic (zipfian distribution)

Fig. 6.12 plots the total control traffic for 100, 200 and 400 subscriptions generated using uniform distribution. In each case, the traffic increases with increasing number of controllers. The graphs are again normalized to compare the behavior of the system in all three cases. As expected, the comparative increase in control traffic for 400 subscriptions is lesser than 200 subscriptions which in turn is lesser than 100 subscriptions. The reason behind this is that with more number of subscriptions, the probability of a match is also more. This results in less number of controller messages being shared between remote controllers.

The graphs for zipfian distribution are depicted in Fig. 6.13. Even for this distribution, for each subscription set depicted in blue, red and green, the total control traffic increases with increasing number of controllers. For the same reasons discussed in uniform distribution, here too the graph for 100 subscriptions grows more rapidly, followed by the graph for 200 subscriptions and finally the one for 400 subscriptions.

So, the results indicate that partitioning of the network should be done according to band- width constraints and performance requirements of the system in question. Increased number of controllers may result in a lower average controller overhead, but it may result in very high control traffic. So, both these parameters should be considered before taking a decision on the total number of controllers to be used in the system. Finally, it can be concluded that addressing the question on the number of controllers to be used in the system is not straight- forward. It cannot be generalized and depends on all the factors influencing it as pointed out in this chapter.

6 Analysis and Results