Simulation Results

This section evaluates the performance of hierarchical routing with different aggregation schemes and cost functions via simulations. Figure 3.8 shows the network topology of the simulations. The capacity of each link is 155 Mbps, except for link(A.3.2-B.1.3) and link(B.1.3-A.3.2), which are 622 Mbps. Each link has a delay of 1ms.

In the simulations, the network supports two classes of traffic. The class 1 traffic has a bandwidth requirement of b₁= 1 Mbps, and an end-to-end delay bound of d₁= 15 ms. Class 1 traffic is assumed to arrive at any O-D pair with the same arrival rate λ^ω1 =λ , while the class 2 traffic is assumed to have a bandwidth requirement of b₂= 5 Mbps, an end-to-end delay bound of d₂= 15 ms, and an arrival rate of λ^ω₂ =λ / b₂ between each O-D pair. The average holding times of these two classes of traffic are normalized to unity.

The 95% confidence intervals of the simulation results shown in the following figures are

A.1.1

Figure 3.9 shows the fractional reward loss of calls under different arrival rates, when two aggregation schemes are used for the WP and the MDP and the COL link cost functions.

The figure shows that the fractional reward loss increases as the arrival rate increases.

Meanwhile, the fractional reward loss of the Asymmetric Simple scheme of the COL link cost is slightly higher than for the Full Mesh scheme. The fractional reward loss of Asymmetric Simple scheme of MDP link cost is almost the same as Full Mesh scheme. Meanwhile, the MDP approach yields a better performance than the COL in both the Asymmetric Simple and Full Mesh schemes. This superiority is because the MDP approach considers the arrival rate, and so can provide more accurate cost information and call admission function. However, the MDP and COL cost-based approaches significantly outperform the WP approach. The main reason is that the bandwidth-based approach only considers the maximum residual bandwidth

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

19 21 23 25 27

Arrival rate of O-D pair

Fractional Reward Loss

WP_Asimple WP_Mesh COL_Asimple COL_Mesh MDP_Asimple MDP_Mesh

Figure 3.9 Fractional reward loss.

of bottleneck link among all candidate paths. However, the cost-based approaches first transfer the residual bandwidth of link into a reasonable cost and then route the minimum path cost.

Figure 3.10 shows the average number of crankbacks per connection request under different arrival rates, when two aggregation schemes are used. The figure shows that the average number of crankbacks increases as the arrival rate increases. The average number of crankbacks of the Asymmetric Simple of the COL link cost function is higher than for the Full Mesh scheme. Meanwhile, the average number of crankbacks of the Asymmetric Simple of MDP link cost function is almost the same as that of the Full Mesh scheme. The COL approach of all schemes requires less crankbacks than the MDP. The reasons for this phenomenon are that the cost function is less accurate and the call admission of COL approach is less conscientious than that of the MDP approach. Consequently, a call may be routed to non-optimal path that requires more network resources and thus increases call

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

19 21 23 25 27

Arrival rate of O-D pair

Crankback per requested calls

WP_Asimple WP_Mesh COL_Asimple COL_Mesh MDP_Asimple MDP_Mesh

Figure 3.10 Crankback per requested calls.

higher call blocking probability. However, the MDP approach provides more accurate aggregated cost and precise call admission policy because the link cost is computed based on Markov decision theory. This approach results in less calls being blocked due to call admission at the hierarchical routing procedure, but more blocking due to the call admission at the physical network level. Hence, the MDP approach results in more crankbacks.

Additionally, the number of crankbacks of the WP approach is more than that of the COL and MDP approaches. Clearly, the reason is that the WP approach is not a good approach for hierarchical routing.

Figure 3.11 shows the fractional reward loss yielded by the five update policies under different arrival rates. As figure 3.11 illustrates, the FU policy yields the lowest fractional reward loss, because it provides the most accurate routing updates. However, the LRBU, DCU, and DCUH policies all yield very competitive fractional reward loss as compared to the FU policy. Figure 3.11 shows that the DCUH policy yields slightly lower fractional reward loss than the LRBU and DCU policies. Meanwhile, figure 3.11 also illustrates that PNNIU policies yield worse performance than the other four policies. The performance of PNNIU

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

19 21 23 25 27

A rrival rate of O -D pair

Fractional Reward Loss

FU PNNIU_1 PNNIU_4 LRBU DCU DCUH

Figure 3.11 Fractional reward loss of five update policies.

policy can be improved if the update interval reduces. For example, the PNNIU_1 policy outperforms the PNNIU_4 policy.

Figure 3.12 shows the average number of crankbacks per connection request under different arrival rates. Intuitively, the more accurate the aggregated routing information, the less the average number of crankbacks. Hence, the average number of crankbacks per connection request is an important performance metric for update policies. Figure 3.12 illustrates that FU, LRBU, DCU, and DCUH have almost the same number of crankbacks per connection while the PNNIU policies have a much higher number of crankbacks.

Figures 3.13 and 3.14 show the number of information re-aggregations and distributions per unit of time under different arrival rates. Intuitively, the FU policy should have the highest re-aggregation frequency, and the two figures confirm this. On the other hand, adjusting the update interval gives the PNNU policy the least update frequency. Comparing the LRBU, DCU, and DCUH policies reveals that the DCU and DCUH policies yield less overhead

re-0

Average number of crankback per connection request

FU

Figure 3.12 Average number of crankback per connection request.

0

Average number of re-aggregation per unit of time

F U

Figure 3.13 Average number of re-aggregation per unit of time.

DCU policy does not suffer much from oscillation. The effect of hysteresis requires further investigation.

0 500 1000 1500 2000 2500

19 21 23 25 27

Arrival rate of O -D pair

Average number of re-aggregation per unit of time

LRBU D C U D C U H

Figure 3.14 Average number of re-aggregation per unit of time yielded by DCU, DCUH, and LRBU policies.

The above figures reveal that the Asymmetric Simple and Full Mesh aggregation scheme of hierarchical routing perform very competitively under different simulation parameters.

However, the complexity of advertised information of Asymmetric Simple is O(n) while that of Full Mesh is O(n²). The MDP link cost function outperforms the COL link cost function due to more accurate cost information and more systematic call admission function. We also observe that FU, LRBU, DCU, and DCUH perform competitively in fractional reward loss and average number of crankbacks per connection request. However, the DCU and DCUH policies require the least re-aggregation frequency. Furthermore, the time-based PNNIU policies yield the highest fractional reward loss and number of crankbacks, but require significantly less update frequency. Meanwhile, the LRBU performs very competitively performance compared to the cost-based update policies, and thus can be considered a simple but efficient policy. Finally, DCU appears not to suffer from the oscillation problem, while

Finally, the performance of PNNI routing with the proposed crankback schemes, CIS and CT, is evaluated via simulations and compared with two baseline crankback schemes, NAIVE and ABL. When crankback procedure is initiated, the NAIVE scheme tries to route the call setup message on alternate paths one by one. ABL(Avoids Block Link) is similar to NAIVE but will avoid routing on alternate paths with blocked link. Both schemes crank back the blocked setup message to the ingress node within a PG or the first PG of the same level. The blocked link information is required in the ABL scheme. Figure 3.15 shows the network topology for our simulations. The detail capacity of each link is shown in Table 3.11 and each link has 1 ms delay.

Table 3.1: Link capacity assignments

Link id Cap. Link id Cap. Link id Cap.

e(A11,A12) 250 e(A42,A47) 400 e(B21,B22) 155 e(A11,A13) 250 e(A43,A44) 350 e(B21,B24) 155 e(A12,A21) 350 e(A43,A46) 350 e(B22,B23) 155 e(A13,A51) 350 e(A44,A45) 350 e(B22,B24) 155 e(A21,A22) 155 e(A46,A47) 400 e(B23,B24) 155 e(A21,A24) 155 e(A47,B41) 622 e(B23,B34) 350 e(A22,A23) 155 e(A51,A52) 155 e(B31,B32) 350 e(A22,A24) 155 e(A51,A56) 155 e(B32,B33) 155 e(A23,A34) 350 e(A52,A53) 155 e(B32,B36) 155 e(A23,A24) 155 e(A52,A54) 155 e(B33,B34) 350 e(A31,A32) 350 e(A53,A54) 155 e(B33,B35) 155 e(A31,A53) 350 e(A54,A56) 155 e(B35,B36) 155 e(A32,A33) 155 e(A55,A56) 350 e(B36,B37) 350 e(A32,A36) 155 e(B11,B12) 155 e(B37,B45) 350 e(A33,A34) 350 e(B11,B17) 155 e(B41,B42) 400 e(A33,A35) 155 e(B12,B13) 155 e(B41,B46) 400 e(A35,A36) 155 e(B12,B15) 155 e(B42,B43) 350 e(A36,A37) 350 e(B13,B14) 350 e(B42,B47) 350 e(A37,A45) 350 e(B14,B21) 350 e(B43,B44) 350 e(A41,A42) 400 e(B15,B17) 155 e(B44,B46) 400 e(A41,A55) 350 e(B16,B17) 350 e(B44,B47) 350 e(A42,A43) 350 e(B16,B31) 350 e(B45,B46) 400

PG(A)

Default link : 155 Mbps

PG(B)

In this simulations, the network supports two classes of traffic. The class 1 traffic has a bandwidth requirement of b₁= 1 Mbps, and an end-to-end delay of d₁= 30 ms, with arrival rate

λ

λ₁^w= . The class 2 traffic has a bandwidth requirement of b₂=5 Mbps, and an end-to-end

delay of d₂= 30 ms, with arrival rate λ^w₂ =λ / b₂. The average holding time of these two classes of traffic is normalized to unity. The PNNI protocol adopts time-based PTSE update policy, referred to as the PNNIU policy. We assume that the PTSE update interval is 0.2 times of mean call holding time. Each simulation result is observed over 10 independent runs. The

samples were discarded. Crankback overhead is measured by the average number of nodes that a call setup message traversed during the crankback procedure.

Note that, NAIVE, ABL, and CIS, use the same call admission control policy. The difference of these schemes is where to crank back, referred as crankback destination node.

Therefore, these three schemes have the same fractional reward loss. The CT scheme predicts that an alternate path will be blocked if its aggregated path cost is larger than a cost threshold.

In our simulations, the threshold is set such that crankback overhead can be reduced as much as possible without increasing the fractional reward loss. According to our experiments, the best cost threshold parameter is set to 1.25∗D_k,min. Figure 3.16 shows that these schemes have the same fractional reward loss. The vertical lines about each point in the figure indicate 95 percent confidence interval. Figure 3.17 shows that both of CIS and CT schemes yield much lower crankback overhead than the NAIVE and ABL schemes. Furthermore, when we combine CIS with CT, referred to as the CIS_CT scheme, the crankback overhead can be reduced further. The reduction on crankback overhead becomes more significant as traffic load goes higher.

0.000 0.030 0.060 0.090 0.120 0.150 0.180 0.210

27 29 31 33 35

Arrival rate of O-D pair

Fractional reward loss

NAIVE ABL CIS CT CIS_CT

Figure 3.16 Fractional reward loss of different crankback schemes under PNNIU update policy.

0.0 3.0 6.0 9.0 12.0 15.0 18.0 21.0

27 29 31 33 35

Arrival rate of O-D pair

Average hop count of crankback

NAIVE ABL CIS CT CIS_CT

Figure 3.17 Average hops count of crankback of different crankback schemes under PNNIU update policy.

Chang et al. show that PTSE update interval will affect the accuracy of routing information. Therefore, in following simulations, we adopt LRBU (logarithm of residual bandwidth update), as the PTSE update policy. In LRBU, the bandwidth of linkλ, is divided into



^log2Cap(λ)



⁺¹ states. For example, a link with capacity Cap(λ)=8 has four states with residual bandwidth of [0,1),[1,2), [2,4), [4,8], respectively. The routing information will be re-aggregated and distributed when the link state changes. Figure 3.18 shows that CT yields the same fractional reward loss as compared to the NAIVE, ABL, and CIS schemes under the LRBU update policy. The CT scheme yields much lower crankback overhead than those schemes, as shown in figure 3.19. The crankback overhead yielded by the CT scheme is only half of that of the CIS scheme.

From the above figures, we observe that CIS and CT schemes reduce the crankback overhead significantly. Furthermore, combining CIS and CT schemes can further reduce the

0.000

Figure 3.18 Fractional reward loss of different crankback schemes under LRBU update policy.

Average hop count of crankback

NA IVE

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