# A Palm-Jacobaeus Loss Formula for Multi-Service Systems with Separated Resources
## 4 Results and Discussion
### Accuracy of the Model  
In line with the information given in Section 4.1, the process of determining the non-availability probability in the system is based on an approximation of the Markov process in the system. The simulator developed for the purpose of this article (presented in Section 4.2) was used to evaluate the influence of this approximation on the accuracy of the proposed analytical model. The study carried out by us included a wide range of systems. The influence of the number of resources (\(k\)), their capacity (\(f\)), the number of classes of offered traffic streams (\(M\)), the volume of demanded resources (\(t_{i}\)), the proportion of offered traffic \(A_{1}t_{1}:A_{2}t_{2}:\ldots:A_{M}t_{M}\), and the intensity of service streams (\(\mu_{i}\)) were all investigated. A result of this study, three representative systems (from the perspective of the differences in the results) were chosen. The systems had the following parameters:  
1. System 1: \(k=3\), \(f=20\) AUs, \(V=60\) AUs, \(M=3\), \(t_{1}=1\) AU, \(t_{2}=2\) AUs, \(t_{3}=3\) AUs, \(A_{1}t_{1}:A_{2}:t_{2}:A_{3}t_{3}=1:1:1\), \(\forall_{1\leq i\leq M}\,\mu_{i}=1\);
2. System 2: \(k=5\), \(f=20\) AUs, \(V=100\) AUs, \(M=3\), \(t_{1}=1\) AU, \(t_{2}=2\) AUs, \(t_{3}=5\) AUs, \(A_{1}t_{1}:A_{2}:t_{2}:A_{3}t_{3}=1:1\); \(\forall_{1\leq i\leq M}\,\mu_{i}=1\);
3. System 3: \(k=5\), \(f=50\) AUs, \(V=250\) AUs, \(M=3\), \(t_{1}=1\) AU, \(t_{2}=3\) AUs, \(t_{3}=7\) AUs, \(A_{1}t_{1}:A_{2}:t_{2}:A_{3}t_{3}=1:1:1\), \(\forall_{1\leq i\leq M}\,\mu_{i}=1\). The obtained results of the non-availability for the strictly determined resources in the systems under investigation are presented in Figures 1-9. The determined confidence intervals for the simulation results are far lower than the markers used to indicate the results of the simulation experiments. For this reason they are not visible in the figures. In the specification of the examined systems, both the resources and the demands of the offered traffic streams are expressed in AUs. As a result, the notion of a small or large system is rather relative. If a system services call classes for which the AU is equal to 100 Mbps, then such a system can be considered to be large. If, however, the AU is 100 kbps, then the system can be regarded as small even though the number of demanded AUs is the same in both systems. Figure 1: Probability of the non-availability of \(x\) strictly determined resources for class 1 calls (\(t_{1}=1\)) in System 1, where \(x\) is the set of strictly determined resources in the limited-availability group. Figure 3: Probability of the non-availability of \(x\) strictly determined resources for class 3 calls (\(t_{3}=3\)) in System 1, where \(x\) is the set of strictly determined resources in the limited-availability group. Figure 2: Probability of the non-availability of \(x\) strictly determined resources for class 2 calls (\(t_{2}=2\)) in System 1, where \(x\) is the set of strictly determined resources in the limited-availability group. Figure 4: Probability of the non-availability of \(x\) strictly determined resources for class 1 calls (\(t_{1}=1\)) in System 2, where \(x\) is the set of strictly determined resources in the limited-availability group. Figure 5: Probability of the non-availability of \(x\) strictly determined resources for class 2 calls (\(t_{2}=2\)) in System 2, where \(x\) is the set of strictly determined resources in the limited-availability group. Figure 6: Probability of the non-availability of \(x\) strictly determined resources for class 3 calls (\(t_{3}=5\)) in System 2, where \(x\) is the set of strictly determined resources in the limited-availability group. Figure 8: Probability of the non-availability of \(x\) strictly determined resources for class 2 calls (\(t_{2}=3\)) in System 3, where \(x\) is the set of strictly determined resources in the limited-availability group.