# A Palm-Jacobaeus Loss Formula for Multi-Service Systems with Separated Resources
## 4 Results and Discussion
### Accuracy of the Model
Figure 7: Probability of the non-availability of \(x\) strictly determined resources for class 1 calls (\(t_{1}=1\)) in System 3, where \(x\) is the set of strictly determined resources in the limited-availability group. Figure 9: Probability of the non-availability of \(x\) strictly determined resources for class 3 calls (\(t_{3}=7\)) in System 3, where \(x\) is the set of strictly determined resources in the limited-availability group. The comparative analysis of the obtained analytical and simulation results verifies that the developed analytical model, which allows us to determine the non-availability probability for strictly determined resources, is an approximate model. The main reasons for the inaccuracies, inherited from the basic model of the limited-availability group (which allows the probability to be determined in whole the system regardless of the occupancy distribution in individual resources), are the following:  
* The analysis of the considered system is carried out from the microstate level (multi-dimensional Markov process) to the macrostate level (one-dimensional Markov process)--a detailed analysis of this problem is presented in [55]. * The conditional transition coefficients are determined in an approximate way (Equation (4)): in the process of determining the conditional transition probability (Equation (4)) in the occupancy distribution (Equation (2)) the division of \(n\) busy AUs between individual call classes is omitted. On the basis of a large number of simulation experiments, it has been proven [48] that the influence of these two criteria on the inaccuracies in the obtained results stabilizes if the following condition is satisfied: \(f>5t_{\text{max}}\), where \(t_{\text{max}}\) is the number of AUs required for a call with the maximum demands to be set up. In such cases, the basic LAG model offers the accuracy that is adequate for engineering applications. The analysis of the results of the accuracy of the model proposed here shows that the accuracy of the model is not influenced by changes in the parameter \(\mu_{i}\), the proportions of the offered traffic, or the number of traffic classes. In addition, the influence of the number of demanded allocation units and the number of resources and their capacities is only slight. The results of the study, presented in Figures 1-9, allow us to evaluate the influence of any change in the value of these parameters. Any further increase in the number of resources, their capacity, and the demands of the individual traffic classes did not cause any increase in the inaccuracy of the systems under investigation. The main influence on the inaccuracy of the model is exerted by the number of resources \(x\), whose non-availability is determined. The highest accuracy was obtained for a case in which we determined the non-availability of a large part of the resources, whereas the lowest accuracy was obtained when we determined the non-availability of only one resource. However, these dependencies are not critical for engineering applications related to the dimensioning of telecommunication networks, for which the possibility of servicing a given demand is critical. From the point of view of network operators, essential is also that the proposed method for the majority of traffic classes leads to overdimensioning of the system (i.e., the value of the non-availability probability is overestimated)--Figures 2, 3, 5, 6, 8 and 9--regardless of the number of unavailable resources. It is only for the traffic class with the lowest number of resources (Figures 1, 4 and 7) that the value of the non-availability probability is slightly underestimated. It is worthwhile to stress, though, that the classes with a larger number of required resources are mainly responsible for blocking. To sum up, in the typical range of applications, i.e., for a traffic intensity per single AU between 0.7-1.0 Erlangs (Figures 1-9), the method ensures high accuracy and can be used in teletraffic engineering of multi-service communication systems.