3.5 Solution Methods
3.5.5 One-dimensional Implementation
Implementation of the placement problem can consider the computing resources and elim- inates the communication overhead, which converts the problem to a one-dimensional re- sources allocation problem. To eliminate the communication overhead and be able to satisfy the traffic constraint, the stateful class modules will be allocated to switches where they can capture all traffic destined to the requested tenant such as single ingress allocation or egress allocation. Of course, this implementation is limited to architectures where at least one al- location available for every user where are all terrific is passing through one point the same as in egress allocation in Section 3.3. For-short, we reference the two implementations as a one-dimensional model and two-dimensional model.
The same as the two-dimensional model, the one-dimensional model is optimising the place- ment problem to achieve efficient management of resources. Therefore, the objective is to maximise the residual resources of the framework which represent the spare resources after the placement has been completed. While the allocation resources cost is represented by the sum of the computing resources consumption of VNFs allocated to satisfy tenants requests
and will be increased with duplicated instances of modules deployed in higher layers of the hierarchy of the architecture to cover traffic distribution.
The formulation of problem is as follows: Let the overall framework include a set of q > 0
requests Q= {r1, r2, ....rq} with each request r representing a function requested by a tenant,
a set of k > 0 locations P = {p1, p2, ....pk}, each with attribute p.c as the resources’ capacity
at location p which represent the sum of switches capacity in the location. A matrix w of size
k x q representing the validation of allocating request to locations where wp,requal 1 if the
location p valid for satisfy request r or zero otherwise. For instance, for the stateful class, only the ToR level will be valid for allocation. While, for the stateless class, there are three parent locations that are valid. A matrix u of size k x q representing the locations resource
cost of allocation where up,r is the required resources to be allocated in location p to satisfy
request r; or zero if location p can not accommodate request r due to function type or does not require any resources to be allocated. The allocation is represented as a binary variable x
of size qxk where xr,p=1 when request r is allocated to location p; 0 otherwise. The problem
variable x is represented as xr,p ∈ 1, 0 ∀r ∈ Q, ∀p ∈ P (3.15)
The formulation is as follows: , i.e.:
max .h X ∀p∈P p.c − X ∀r∈Q X ∀p∈P xr,p· up,r i (3.16) s.t. X ∀r∈Q xr,p· up,r ≤ p.c ∀p ∈ P (3.17) xr,p = 0, ∀r ∈ Q, ∀p ∈ P if wp,r= 0 (3.18)
X
∀p∈P
xr,p = 1, ∀r ∈ Q (3.19)
The objective function of the one-dimensional formulation is represented in (3.16) as max- imising the residual resources after the placement. The constraint in (3.17) represents the location’s capacity constraints which are enforced by the resources requirements of the prob- lem. The constraint in (3.18) represents the location-validity for requests which enforce the traffic constraint of the problem and the stateful allocation constraint. The constraint in (3.19) ensures that each request is allocated to only one location.
While the one-dimensional consider computing resources of the architecture, previous meth- ods can be adopted to solve the implementation by adding the placement of stateful class modules in single switch locations as a constraint.
3.6
Summary
In this chapter, The framework proposed has used the SDN and VNF technology to address the limitation of legacy deployment of network function. It has tackled the specific con- straints of security modules that previous virtualised network management systems failed to address. It has exploited features like on-path deployment and non-shared models to save re- sources and reduce management complexity. The framework allocation strategies are based on the classification of security modules that depends on the granularity of traffic process- ing in the module. These strategies have combined the efficient management of network resources and satisfying the traffic granularity required by the security module.
The resource-aware placement is responsible for selecting the final allocation of the secu- rity functions requests by satisfying the constraints of the placement presented by traffic, resources and security constraints and maintaining efficient management of resources by op- timising the placement based on optimising the computing and communication resources objectives. Furthermore, we propose a one-dimensional implementation to the placement
problem that will eliminate the communication cost of the problem; however, it will restrict the stateful class module to locations where all traffic flows are passing through.
Chapter 4
Implementation
4.1
Overview
The placement of security modules is a resource allocation problem, where modules re- quested by tenants in virtualised data centers are allocated in a set of distributed locations each with limited capacity. We focus on the initial placement of security equivalence classes introduced in Chapter3. The following sections present the implementation of the proposed framework on fat-tree as the most common virtualised data centers architecture. Moreover, the implementation of the allocation strategy and the placement solutions on fat-tree will be demonstrated.
The fat-tree architecture and its characteristics are presented in Section 4.2. Then the imple- mentation of the allocation strategies will be discussed. Then, we represent the constraint programming solution of the placement problem in Section 4.3. In Section 4.4, the imple- mentation of the heuristic solution algorithm will be demonstrated. In Section 4.5, the imple- mentation of a Meta-heuristic Tabu algorithm is presented. Then, a subset-sum Near-optimal solution is discussed in Section 4.6. In Section 4.7, the LP solution of the one-dimensional model of the placement problem is introduced. Finally, we conclude the chapter in Sec- tion 4.8.