## 6 Fuzzy Based Adaptive Resource Allocation
### FRB Enhanced Class-based Policy-Driven Resource Control  
Let the service classes in the CNQF managed domain be denoted by C\({}_{1}\), C\({}_{2}\) and C\({}_{3}\) with corresponding per class bandwidth allocations B\({}_{1}\), B\({}_{2}\) and B\({}_{3}\) respectively from a maximum available bandwidth B\({}_{\mathrm{T}}\). B\({}_{1}\), B\({}_{2}\) and B\({}_{3}\) are parameters stipulated within the high level policies in the policy management tool and can be altered to suit operator policies without affecting the operation of the underlying CNQF RMS admission control functionality. A dynamic resource allocation strategy is implemented within the RB whereby:  
\[B_{th}^{j}=\{\max(B_{j},B_{ELS}^{j})\}\,|\,\forall\,j\in[1,2,3] \tag{3}\]  
Figure 7: FRB component implemented within CNQF Resource Management Subsystem. \(\mathrm{B_{FLS}}\) represents the output of the fuzzy logic system which varies with the traffic load per class within the network and \(B_{ih}^{j}\) is current bandwidth allocation for the \(j^{\mathrm{th}}\) service class. The fuzzy logic system, \(F\) is characterized by a membership function \(\mu_{F}(x)\) where \(x\in X\). The system is expressed as: \(F=\{(x,\mu_{F}(x))\,|\,\forall x\in X\}\) where the membership grade of \(x\), \(\mu_{F}(x)\), is a crisp value in [0, 1]. The fuzzy logic system is represented by fuzzy IF-THEN rules. These rules map the _input space_ to the _output space_ in a linguistic manner that can also allow the designer to incorporate initial knowledge of the operational domain, as well as depict intuitively the relationship between the input and output variables within the system. The \(z^{\mathrm{th}}\) rule of the fuzzy logic system having \(q\) inputs \(x_{1}\in X_{1}\),..., \(x_{q}\in X_{q}\) and one output \(y\in Y\) is expressed as:  
\[Rule\]  
: IF  
\[x_{1}\]  
is  
\[F_{1}^{\mathrm{\pi}}\]  
and/or  
\[x_{2}\]  
is  
\[F_{2}^{\mathrm{\pi}}\]  
and/or  
\[x_{2}\]  
is  
\[F_{q}^{\mathrm{\pi}}\]  
THEN  
\[y^{\mathrm{\pi}}\]  
(4)  
where \(F_{i}^{\mathrm{\pi}}\) (\(i=1\), \(2\),..., \(q\)) are _fuzzy antecedent sets_ represented by their membership functions \(\mu_{F_{i}}^{\mathrm{\pi}}\), and C\({}^{\mathrm{\pi}}\) is a fuzzy _consequent set_ represented by the membership function \(\mu_{C}^{\mathrm{\pi}}\). The output is obtained by combining the outputs from the \(M\) rules in the following form:  
Figure 7:0  
where \(T\) is a \(t\)-_norm_ operation (_i.e._, min or max operation) and \(x\) is the input vector. Finally, the centroid defuzzification method is then used to compute from (5), a corresponding crisp output for the given input vector. The FRB system implemented within the CNQF RB has the following characteristics. The inputs to the fuzzy system are the Class 1, Class 2 and Class 3 network loads. Class 1 network load is expressed by min\(\{\mathrm{b_{1}}/\mathrm{B_{T}},\,\mathrm{B_{1}}/\mathrm{B_{T}}\}\) where \(\mathrm{b_{1}}\) is the current measured aggregate bandwidth consumption by Class 1 flows, while \(\mathrm{B_{1}}\) is set by the high level policy as mentioned earlier. \(\mathrm{B_{T}}\) is the total available bandwidth for all traffic. The input is modeled by three fuzzy sets with the universe of discourse given by [0, \(\mathrm{B_{1}}/\mathrm{B_{T}}\)]:  
1. _Light Load (LL)_, modeled by a Gaussian membership function with parameters mean \(\beta=0\), and variance \(\sigma=(0.17\)\(\mathrm{B_{1}}/\mathrm{B_{T}})\). 2. _Medium Load (ML)_, modeled by a Gaussian membership function with parameters mean \(\beta=(0.5\)\(\mathrm{B_{1}}/\mathrm{B_{T}})\) and \(\sigma=(0.13\)\(\mathrm{B_{1}}/\mathrm{B_{T}})\). 3. _Heavy Load (HL)_, also modeled by a Gaussian membership function with parameters \(\beta=\mathrm{B_{1}}\), and \(\sigma=(0.17\)\(\mathrm{B_{1}}/\mathrm{B_{T}})\).