Chapter 4 BGP Session Lifetime Modeling in Congested Networks
6.6 Simulation Results
6.6.2 Optimality and Routing Message Overhead
In order to show the advantages of using our proposed statistical metrics, we present the simulation results of LCR, ABR, and ABIR to study the relationship between the routing optimality and the message overhead. In the route weight calculation of ABI, η = 1.
Performance Overview
The routing optimality and routing message overhead are shown in Fig.6.6(a) and Fig.6.6(b) with respect to different network topologies and values of Ts. normal distribution is used to model the link available bandwidth.
101 102 103 50 100 150 200 250 3000.4 0.5 0.6 0.7 0.8 0.9 1 Ts
Routing Optimality Comparison
n (Number of Nodes) ξ (Routing Optimality) ABR ABIR LCR
(a) Routing optimality compari- son. 101 102 103 50 100 150 200 250 300 0 2 4 6 8 x 105 Ts
Routing Message Overhead Comparison
n (Number of Nodes)
C
Routing Message Overhead
ABR
ABIR
LCR
(b) Message overhead comparison.
Figure 6.6: Performance comparisons of ABIR, LCR and ABR.
In term of finding the path with the maximum available bandwidth, ABR protocol has the best performance among the three. If the thresholds (Tl andTr) in ABR are zero and we assume that the routing protocol converges fast enough in one time unit, ABR can achieve 100% optimality. The ABR curves, shown in Fig.6.6, have non-zero thresholds: Tl = 20 and Tr = 80. Its optimality ξ is about 85%. However, message overhead of ABR is still very
large and it increases substantially as the network size increases. Therefore, ABR is not a practical protocol.
On the contrary, LCR only selects path by the static QoS metric – link capacity. Thus, there is no route change due to QoS in LCR after the network is set up, i.e. C = 0. However, because LCR does not adapt to the real available bandwidth, its optimality ξ is only about 50%.
ABIR makes a good compromise between the routing message overhead and the routing optimality. Its routing optimality ξ is about 75%. Its routing message overhead is far less
than the ABR protocol. In the worst case of our simulations, where Ts = 20 time units and the number of node is 300, the routing message overhead incurred in ABIR is only 6.8% of that in ABR. When the Tsis larger, ABIR has even less message overhead. The advantage of ABIR comes from the routing based on the statistical properties of the available bandwidth instead of using instantaneous values. In summary, ABIR achieves higher routing optimality than LCR with much lower routing message overhead than ABR.
Comparison between ABIR and ABR with Large Threshold
ABIR can substantially reduce routing message overhead by decreasing only slightly the routing optimality. Although ABR can also control the routing message overhead to a low level by using sufficiently large thresholds, Tl and Tr, simulation results show that the optimality of ABR degrades quickly as the thresholds increase. If the same amount of message overhead is incurred, ABIR performs much better than ABR in terms of routing optimality.
Fig. 6.7(a) presents the simulation results of ABR and ABIR in a network of 100 nodes and the link available bandwidth follows normal distribution. The upper three curves show the message overhead C and optimality ξ of ABR with respect to Ts. When the C is reduced (by increasingTlorTr), ξ decreases, e.g., when C 2000, ξ = 67%. On the contrary, ABIR, which is shown as the lowest curve, can achieve 74% optimality with much lower message overhead.
In Fig. 6.7(b), the relationship between the routing optimality and the routing message overhead is shown in one curve directly. Higher routing optimality is obtained at the price of larger message overhead. In the range of the optimality which can be achieved by ABIR, the routing message overhead incurred by ABIR increases much more slowly than that of ABR.
0 100 200 300 400 500 600 700 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000
ABR and ABIR Message Overhead Comparision ( n =100)
Ts
C
(Routing Message Overhead)
ABIR ξ=74%
ABR ξ=78%
ABR ξ=72%
ABR ξ=67%
(a) Routing message overhead of ABR and ABIR.
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0 1000 2000 3000 4000 5000 6000 7000
ABR and ABIR Performance Comparision ( n =100 T
s=200)
ξ (Routing Optimality)
C
(Routing Message Overhead)
ABIR ABR
(b) Performance comparison of ABR and ABIR.
Figure 6.7: ABIR demonstrates better optimality than ABR when incurring the same amount of routing message overhead.
ABIR in Different Traffic Distributions
In section 6.4.2, we use normal distribution to derive an ABI normalization method as an approximation for any general distribution. The simulation results below support that this approximate method also works well for other distributions. Two bandwidth distributions are tested: Pareto and uniform. D is the link capacity. For Pareto distribution F (x) = 1−(k/x)a, k is a random number in [0.1D, 0.9D], and γ is the average value of the shape parameters a on all links. The uniform distribution is set to the interval [s, s + d], where d = θD and s is a random value in [0, D− d]. θ stands for the range of the bandwidth in the uniform distribution.
The simulation results are shown in Fig. 6.8. If the available bandwidth follows Pareto or uniform(θ = 0.4) distribution, ABIR has similar optimality and message overhead in all three distributions. However, in the uniform distribution of θ = 0.8, the optimality of ABIR is almost the same as LCR (shown in Fig.6.6(a)). This can be explained as follows. If θ is close to 1, ABI of each link tends to have = [0, D], because ρ is chosen to be around 0.9. Thus, in this scenario, the ABIs of links actually only reflect link capacities. We conclude that ABIR performs better than LCR, if the available bandwidth is mainly distributed in an
0 100 200 300 400 500 600 700 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9
Optimality of ABIR in Different Bandwidth Distributions ( n =100)
Ts ξ (Routing Optimality) Normal Pareto γ=0.5 Uniform θ=40% Uniform θ=80%
(a) Optimality comparison in dif- ferent bandwidth distributions.
0 100 200 300 400 500 600 700 0 500 1000 1500 2000 2500 3000 3500 4000
Message Overhead of ABIR in Different Bandwidth Distributions ( n =100)
Ts
C
(Routing Message Overhead)
Normal
Pareto γ=0.5
Uniform θ=40%
Uniform θ=80%
(b) Message overhead comparison in different bandwidth distribu- tions.
Figure 6.8: The performance of ABIR in different bandwidth distributions.
interval whose length is smaller than D. For example, if θ = 0.4, as shown in the simulation, the optimality of ABIR is about 80%, much higher than the optimality of LCR.