# A Palm-Jacobaeus Loss Formula for Multi-Service Systems with Separated Resources
## 4 Results and Discussion  
### General Assumptions  
In the model that allows us to determine the probability of the non-availability of strictly determined resources for requests/calls (flows/streams) of particular traffic, we used the approach, generally accepted in the literature on the subject, according to which variable bitrates of real packet streams are replaced with constant bitrates [19; 46; 50; 51]. Such an approach much simplifies the process of modeling, since it allows multi-rate (multi-service) systems to be analyzed in a Markovian way at the flow/stream/session level (call level). There are two approaches to the replacement of variable bitrates of packet streams with their equivalents with constant bitrates: They can be chosen on the basis of the maximum bitrates [42; 51] of particular packet streams or, alternatively, on the basis of the so-called equivalent bandwidth determined for each packet stream [45; 52]. An analysis at the flow level is the only approach to dimensioning, designing, and optimizing whole networks, which is much appreciated by network operators [19; 46].  
After the determination of constant bitrates (volume of required resources) for calls of individual classes serviced in the system, it is possible to determine the allocation unit (AU) for a given system. The AU is defined as the highest common divisor of the capacity of the system and all bitrates (equivalent bandwidths, volume of required resources) allocated to calls of individual classes. Subsequently, both the capacity of the system and the amount of resources required for a call of a given class to be serviced, are expressed in the number of AUs.  
The value of a single AU can also depend on the applied technological solutions. Besides the convention of expressing AUs in bits per second, dominant in the literature, commonly used expressions include the so-called interference (noise) unit, used in WCDMA systems (wideband code division multiplexing) [19; 53]. To maintain the maximum versatility of the developed model and taking the constant development of 5G systems for granted, we assume in our further research that it will be possible to express the volume of demands and the capacity of the system in the multiplicity of a certain AU, without specifying precisely the method for their determination. A suitable example of the determination of demands of individual traffic classes in 5G systems with OFDMA multiplying can be found in [42].  
The proposed method for the determination of the non-availability probability of strictly determined resources is an approximate method, since the LAG model it uses is an approximate model for any analysis at the call level. It is possible to develop more accurate models, although an accurate and precise solution for the service process in the considered system would, however, involve its analysis at the level of the so-called microstates (a microstate is defined by the number of serviced calls of individual classes) whose sheer number would almost entirely prevent its solution. Such an approach is impractical and totally ineffective from an engineering point of view. Therefore, an approximation of real service processes with the LAG model (an analysis at the macrostate level, where the macrostate is determined by the number of occupied AUs) requires the validity of the adopted assumptions to be verified by simulation experiments.