# Distributed Management Systems for Infocommunication Networks: A Model Based on TM Forum Framework
## 3 Methods
### Model of Distributed Management System for Next-Generation Networks  
A distributed management system (DMS) for infocommunication networks can be expressed as a set of modules or program components (PCs) executed by processor modules (PMs). Each PC implements a corresponding business component (BC) as a microservice described within Framework. PMs can be implemented in the form of physical devices or virtual resources. PCs interact with each other through the network adapters of PMs using the capabilities of real or virtual networks. Any service in this management system is implemented by assigning a certain set of PCs located on separate PMs for the execution of a given BP. All services are created by uniting heterogeneous PCs that are formed using the virtual resources of several virtual networks. Instead of a local assignment to a specific PC, each service is implemented with a global distribution over the whole network. Clearly, the performance of a distributed management system (DMS) depends on the quality of solving several tasks as follows:  
* the distribution of PCs among PMs (note that (a) the number of PCs sets is often much greater than the number of PMs and (b) the real sequence of control transfers between PCs is approximated by an absorbing Markov chain);
* the prioritization of BPs with parallel execution as well as the elimination of dead states and interlocks during execution;  
Figure 4: Flowchart for BP 1.4.6.3 (Correct and Resolve Service Problem) [9]. * the reduction of system cost to unite separate components of BPs, achieved via a rational integration of PCs. A successful solution of these tasks yields an optimal DMS in terms of the TM Forum criterion (1)  
\[\Phi=\min\!\sum_{k=1}^{L}P_{k}\times t_{k}(\theta,\ S,\ Q), \tag{1}\]  
with the following notations: \(t_{k}\) as the execution time of the \(k\)th BP; \(\theta\) as a distribution method of PCs among PMs; \(S\) as a service schedule of requests; \(Q\) as an integration method for the separate solutions of PMs; \(L\) as the number of BPs served by the system; finally, \(P_{k}\) as the execution priority of the \(k\)th BP. To distribute PCs over PMs, consider \(n\) PCs \(f_{1}\),..., \(f_{n}\) and also \(d\) PMs. Assume each two PCs, \(f_{i}\) and \(f_{j}\), are exchanging joint requests with a known frequency \(P(i,j)\). The mean number of control transfers between the \(i\)th and \(j\)th PCs can be obtained using the measurements of a program monitor of the system. Find an analytical expression of the mean number of control transfers between PCs in the course of service implementation. To this end, decompose the set of PCs into \(d\) groups \(\Phi=\{F_{1},\ F_{2},\ldots,\ F_{d}\}\) so that  
\[\mathop{\cup}\limits_{i=1}^{n}f_{i}=\mathop{\cup}\limits_{i=1}^{d}F_{i}\quad \text{and}\quad F_{k}\cap F_{l}=\varnothing,\quad k\
eq l. \tag{2}\]  
The frequency of conflicts on the \(k\)th PM is given by  
\[C_{k}=\sum_{i,\ j}p(i,\ j). \tag{3}\]  
Then the total frequency of conflicts can be calculated as  
\[C=\sum_{k=1}^{d}C_{k}=\sum_{k=1}^{d}\sum_{i,\ j}p(i,\ j). \tag{4}\]  
If \(\text{PC}_{i}\) performs a transition between groups \(F_{s}\) and \(F_{t}\), then the optimality criterion has the variation (5)  
\[\Delta C=\sum_{i\in\text{PM}_{i}}(P(i,\ j)+P(j,\ i))-\sum_{i\in\text{PM}_{i}}( P(i,\ j)+P(j,\ i)). \tag{5}\]  
All \(\text{PC}_{i}\), \(i=1,\ldots,\ n\), are decomposed into \(d\) groups using a system of operators \(R=\{R_{i\,t},\ i=1,\ldots,\ n;\ t=1,\ldots,\ d\}\) that formalizes the transition of \(\text{PC}_{i}\) to another class \(t\), i.e., the operation \(R_{i\,t}(\Phi)\). As a result, the optimal decomposition criterion has the increment \(\Delta_{i\,t}(\Phi)=C(\Phi)-C(R_{i\,t}(\Phi))\), where \(C(R_{i\,t}(\Phi))\) is the frequency of conflicts for the operation \(R_{i\,t}(\Phi)\) and \(C(\Phi)\) is the preceding frequency of conflicts.