## 3 Materials and Methods
### Statement of Research
To conduct simulation and computational experiments to prove the adequacy of the created mathematical model and the effectiveness of available services made on its basis. Mathematical Model of the Process of Operation of E-Commerce Oriented Ecosystem of 5 Ge Base Station, the Information Environment of Which Supports the Functioning of Virtual Network Segments  
We identified the operation of the localized e-commerce-oriented ecosystem of the 5 Ge base station, the information environment that supports the operation of \(S\) virtual network segments, as a stochastic function \(X(t)\ =\ \{m_{s}(t)\}\ s\ =\ \overline{1,S}\), where \(m_{s}\) is the number of active terminal-segment information interaction sessions for the \(s\)-th virtual network segment at the time \(t\): \(m_{s}\ \in\ \left\{0,1,\ldots,\left\lceil\frac{C}{a_{s}}\right\rceil\right\} \forall s\ \in\ S\). Let us define the state space of the stochastic process \(X(t)\): \(X\ =\ \left\{(m_{1},m_{2},\ldots,m_{s}),\ \sum\limits_{s}^{S}m_{s}a_{s}\ \leq\ C\right\}\). Suppose the control mechanism allocated system resources to support one active terminal-segment information interaction session for the \(s\)-th virtual network segment, which is \(r_{s}\) c.u. Then, the intensity of the request service is equal to \(r_{s}\mu_{s}\forall s\ \in\ S\). To localize the \(s\)-th virtual network segment in the information space of the e-commerce-oriented ecosystem of the 5 Ge base station, we make the following assumption: The control mechanism is guaranteed to allocate to its support \(\overline{R}_{s}\) c.u. of the system resources, which, accordingly, guarantees the support of the \(\overline{M}_{s}\ =\ \left\lfloor\overline{R}_{s}/a_{s}\right\rfloor\) active terminal-segment information interaction sessions. A virtual network segment in the information space from which more active terminal-segment information interaction sessions are supported than their guaranteed supported number \(\overline{M}_{s}\), will be denoted as being overloaded. In conditions where there is a shortage of free system resources, the support for guaranteed terminal-segment information interaction sessions in any virtual network segment is conducted due to premature the termination of the required number of active terminal-segment information interaction sessions in the overloaded virtual network segments. If a shortage of free system resources is observed in the absence of crowded virtual network segments, then the incoming request is lost. Let us investigate the dynamics of the stochastic process \(X\) in time: \(X(t)\). Let the e-commerce-oriented ecosystem of the 5 Ge base station be in the state \((m_{1},m_{2},\ldots,m_{s})\in X\). Then, upon receipt of the \(s\)-th virtual network segment of the incoming request, one of the following scenarios is implemented:  
1. \((m_{1},m_{2},\ldots,m_{s}\,+\,1,\ldots,m_{S})\in X\)--in the e-commerce-oriented ecosystem of the 5 Ge base station, where there are enough free system resources; therefore, the input request is accepted, and the stochastic process \(X(t)\) goes to state \((m_{1},m_{2},\ldots,m_{s}\,+\,1,\ldots,m_{S})\);
2. \((m_{1},m_{2},\ldots,m_{s}\,+\,1,\ldots,m_{S})\
eq X\)--in the e-commerce-oriented ecosystem of the 5 Ge base station, where there are not enough free system resources, therefore: 1. If \(m_{s}\,<\,\overline{M}_{s}\) and \(m_{k}\,>\,\overline{M}_{k}\), \(s,k\in\,S\), and \(s\
eq k\), then the system resources are released by forcibly terminating the active terminal-segment information interaction sessions in the \(k\)-th overloaded virtual network segment: \(B_{s}=\{(m_{1},m_{2},\ldots,m_{s})\}:[(m_{1},m_{2},\ldots,m_{s}\,+\,1,\ldots,m _{S})\
eq X]\cap\), where \(B_{s}\) is the state space with forced termination of the active terminal-segment information interaction session. The functional realization algorithm from step 2.1 will be formulated further in Section 3.3; 2.