# Model for Quantifying the Quality of Secure Service
## 4 The Quality of Secure Service Model
The channel load, \(L\), is the percentage of \(M\) on a particular channel \(j\), such that  
\[L_{(j,M)}=\frac{\sum_{i=1}^{n}|f_{i}|\ for\ f_{i}\in C_{(j,M)}}{|M|} \tag{13}\]  
and the Average Loading (AL) for the set of channels is  
\[AL_{M}=\frac{\sum_{i=1}^{n}L_{(j,M)}}{n}. \tag{14}\]  
For example, \(F_{M}=\{f_{1},f_{2},f_{3},f_{4},f_{5},f_{6},f_{7},f_{8}\}\) is the set of eight fragments of message \(M\) on a network that has \(n=8\) channels, and each channel transmits two fragments. Therefore, \(AL=0.25\). Message fragmentation also allows for duplicating data across channels. The Duplication Factor (DF) measures the average number of times a given fragment is transmitted, indicating the network redundancy. The DF may increase as compensatory tuning for known adversarial interactions. For the previous example, \(DF=2\), since each fragment is sent across two channels and, thus, duplicated twice. For these calculations of DF and AL, the fragment sizes are uniform. The AL and DF directly affect \(P(C)\) and \(P(I)\). Of the constituent parts of \(P(C)\), \(P(int)\) is only affected by DF in aggregation across all channels because the probability of interception of a single channel is not necessarily improved by duplication or fragmentation. However, \(P(int)\) may be increased by the message \(M\) being duplicated across multiple channels, offering an adversary more opportunities to intercept portions of the message. Therefore, DF is only multiplied by \(P(int)\) when averaging all the channels into a composite probability of leakage. For the constituent parts of \(P(I)\), duplication directly affects \(P(s)\) because sending fragments multiple times decreases the probability of lost data through suppression. \(P(n)\) and \(P(inj)\) are not directly influenced by duplication. Thus, \(P(s)\) is divided by \(DF\) for each channel, giving  
\[P(c)=\frac{\left( \begin{matrix}\left(1-P(n)\right)P(inj)+\left(P(n)+\frac{P(c )}{DF}\right)-\left(P(n)\frac{P(c)}{DF}\right)\\ -\left(1-P(n)\right)\left(P(n)+\frac{P(c)}{DF}\right)P(inj)\right)\rho\\ n\end{matrix} \right)\rho}{n}. \tag{15}\]  
Fragmentation does not necessarily increase or decrease \(P(s)\) except that it allows for duplication. However, fragmentation does directly affect \(P(inj)\) since each fragment sent needs to be modified by the adversary in order to have malicious data accepted at the receiver. Thus, \(P(inj)\) is multiplied by AL for each channel, giving  
\[P(c)=\frac{\left( \begin{matrix}\left(1-P(n)\right)P(inj)AL+\left(P(n)+\frac{P (s)}{DF}\right)-\left(P(n)\frac{P(c)}{DF}\right)\\ -\left(1-P(n)\right)\left(P(n)+\frac{P(c)}{DF}\right)P(inj)AL\end{matrix}  \right)\rho}{n}. \tag{16}\]  
Applying the PSMT and decomposing the network into constituent channels yields  
\[QoSS: \begin{bmatrix}P_{1}(C),&P_{1}(I),&QoS_{1}\\ P_{2}(C),&P_{2}(I),&QoS_{2}\\ \vdots&\vdots&\vdots\\ P_{n}(C),&P_{n}(I),&QoS_{n}\end{bmatrix} \to Sec\ Reqs, \tag{17}\]  
which highlights that each channel has its own characteristics. From the end-user perspective, only the aggregated QoSS for the entire network is apparent. With insight into each channel's QoSS, an analyst may suggest a different quantity of channels, different fragmentation or duplication, or a different encoding or encryption algorithm if adversarial actors attempt to influence communications.