The scalability of the BFD, BFD SINGLE INSTANCE, NEAR OPTIMAL and RANDOM algorithms are shown by increasing the number of requests until the algorithms could not find a complete solution to the problem. Moreover, the experiment will test the performance results of the partial solution found. The experiment shows the effect of request rate workload on the performance metrics as the first experiment in Section Section 5.4 and in case of module size (required resources) parameters are µ=70% and σ=10% of the maximum value of module size and the request rates are ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The results of PR, RS and CO metrics for a k=6 fat-tree are shown Figure 5.19. It is worth mentioning that the experiment does not guarantee the system capacity constraint and that we omit the constraint programming where it could not obtain a partial solution.
2 4 6 8 10 Request rate 0.0 0.2 0.4 0.6 0.8 1.0
Placement Ratio (PR) BFDBFD_SINGLE_INSTANCE RANDOM NEAR_OPTIMAL
(a) Placement Ratio
2 4 6 8 10 Request rate 0.0 0.2 0.4 0.6 0.8 1.0 Residual Resources (RS) BFD BFD_SINGLE_INSTANCE RANDOM NEAR_OPTIMAL (b) Residual Resources 2 4 6 8 10 Request rate 0.0 0.2 0.4 0.6 0.8 1.0
Communication Overhead (CO)
BFD
BFD_SINGLE_INSTANCE RANDOM NEAR_OPTIMAL
(c) Communication Overhead
Figure 5.19a show the PR objective function after the allocation is complete and, the results show P R=1 below r=6 where all requested resources have been allocated while show de- creasing of PR beyond that. Moreover, results show that NEAR OPTIMAL has less PR then BFD and RANDOM. This can be attributed that NEAR OPTIMAL objective of filling loca- tions with the most resources will prioritise stateless class over stateful class which results in allocating the more consuming resources class type and results in less RS to accommodate requests and subsequently less PR. Furthermore, BFD SINGLE INSTANCE has P R < 1 beyond r=2 which is a result of no available bandwidth to allocate requests with its steering strategy.
Figure 5.19b shows a decrease in residual resources below r=6 while showing steady results beyond that which can be attributed to the increase in the number of requests will result in a reduction in available resources until no more resources can be allocated. Furthermore, the results show that BFD SINGLE INSTANCE has more spare resources than BFD, where it could not allocate most of the requests as shown in Figure 5.19a. While BFD and NEAR - OPTIMAL have more spare resources than the RANDOM algorithm as they utilise allocation to minimise resource consumption.
Figure 5.19c show the CO objective function after the allocation is complete and, the results show a linear increase of CO as more requests will introduce more communication overhead to the allocation while BFD SINGLE INSTANCE has less CO than other algorithms where it could not allocate most of the requests. Moreover, the results show that NEAR OPTIMAL algorithm has a decreasing CO beyond r=6, which can be attributed to less stateful class functions being allocated, and less CO endured.
We conclude that increasing the request rate will result in algorithms failing to find a com- plete solution to the placement problem. However, the BFD algorithm has been able to scale and find a solution that will satisfy more computing resources requests than other algorithms including the near-optimal algorithms which will priorities one of the classes over the other and results in less CO but less requests satisfaction.
5.7
Summary
These chapter sections have presented the most important characteristics of the developed so- lutions to solve the placement of security function problems. It has used simulation results to compare the constraint programming, heuristic, meta-heuristic, near-optimal and LP imple- mentation as well. Furthermore, it has explored the different characteristics of the proposed solutions against different factors, such as network size and the number of available security modules. The main findings of this chapter are the BFD algorithm based on sorting request on computing required resources of the requested modules has shown a balance between utilising computing and communication resources compared to other heuristic algorithms. It shows a near-optimal solution compared to the constraint programming solutions while solutions such as TABU meta-heuristic and near-optimal solutions have reached a slightly more utilisation to resources than the tested BFD. However, BFD has proved optimised time and success rate compared to other algorithms. When testing the legacy single instance al- location against BFD, it has shown better saving to computing resources that reached 50% while it showed more communication overhead up to 70% more than BFD. Moreover, an LP implementation that eliminated the communication overhead of the framework has been evaluated. The results show that an increasing amount of computing resources are required to accommodate requests compared to the CP model. Furthermore, the BFD version of the LP implementation is shown to have a near-optimal solution compared to the LP model solution. Furthermore, BFD shows scalability with increasing the request rate.
Chapter 6
Conclusion and Future Work
6.1
Overview
In this chapter, we summarise and conclude this work. The remainder of this chapter is structured as follows: Section 6.2 details the contributions made throughout this work. A discussion on directions for future work is presented in Section 6.3, including improvements and extensions to the current work. Finally, concluding remarks in Section 6.4.