## 2 Materials and Methods  
### Statement of the Research  
As mentioned above, in our research we will focus on the analytical description of the influence of the settings of the Slow Start (SIS) and Additive-Increase/Multiplicative-Decrease (AI/MD) mechanisms integrated in TCP on the value of the TCP Window Size controlled parameter \(S_{w}\) for the target connection between the SNEIoTD environment, which generates massive, mission-critical traffic, and a hub. The parameter \(S_{w}\) defines the size of the data block that the SNEIoTD environment can send to a hub without confirmation of receipt from the latter. The interaction of the SIS and AI/MD mechanisms is determined by a controlled parameter, \(T_{sls}\), known as the Slow Start Threshold [21; 22; 23; 24], and feedback signals \(s=\{s^{+},s^{-},s^{o}\}\) from a hub, which will be mentioned later in the paper. The parameter known as Round-Trip Time [21; 22; 23; 24], which characterizes the time required to send a block of data to the hub and receive confirmation of its receipt, is denoted by \(T_{rt}\). After each confirmation from the hub, the SIS mechanism increases the value of the parameter \(S_{w}\) by one. If such a trend is maintained, the value of the parameter \(S_{w}\) doubles in a time not less than \(T_{rt}\). In turn, after each confirmation from the hub, the AI/MD mechanism increases the value of the parameter \(S_{w}\) by \(1/S_{w}\). The value of such an increase is presented in integer form: \(\lfloor 1/S_{w}\rfloor\), therefore (while maintaining the trend of receiving confirmations from a hub) after each subsequent time interval, not less than \(T_{rt}\), the value \(S_{w}\) will increase by one. The inherent TCP Three-Way Handshake logic [17; 18] assumes the existence of three types of reverse communication signals (confirmation signals from a hub):  
- data block received in full: \(s^{+}\),  
- data block received with skips: \(s^{-}\),  
- reverse signal not received (communication channel overload): \(s^{o}\). The initiation of an information interaction between the SNEIoTD environment and a hub begins with setting the initial value of the parameter \(T_{sls}\). Further, after each SNEIoTD reception of the signal \(!s^{+}\), the value of the parameter \(T_{sls}\) is redefined: \(T_{sls}:=\max(2,\left|S_{w}/2\right|)\). The characteristics of the information interaction between the SNEIoTD and a hub are regulated with the SIS mechanism until the SNEIoTD environment receives the signal \(s^{-}\) or the value of the parameter \(S_{w}\) reaches the value of \(T_{sls}\). The moment of detection of certain facts regulates the transfer of connection control to the AI/MD mechanism. Upon receiving the signal \(s^{-}\), the AI/MD mechanism continues to work: \(S_{w}:=\max(2,\left|S_{w}/2\right|)\). Returning control of the connection to the SIS mechanism is possible only upon receipt of the SNEIoTD signal \(s^{o}\). At the same time, the SIS mechanism resets the value \(S_{w}\) to one: \(S_{w}:=1\), and regulates reattempts to send the data block to a hub after a time equal to \(T_{rt}\) has passed. If the SNEIoTD does not receive a signal \(s^{+}\) in response, the SIS mechanism authorizes another attempt to send the data block to a hub after a time interval equal to \(T_{rt}:=2T_{rt}\). The value \(S_{w}\) remains unchanged: \(S_{w}=1\). These described actions are repeated until the SNEIoTD receives the signal \(s^{+}\). We will choose a theoretical basis for an analytical description of the process of information interactions between the SNEIoTD environment and a hub, taking into account the described logic of control. The authors propose a formalization of the researched process based on the queuing theory [7; 8] with a controlled input flow. To serve the latter, we assume one device with an infinite queue, a reverse connection, and a deterministic service of duration \(t_{m}=1/T_{cc}\), where \(T_{cc}\) is the actual capacity of the route between the SNEIoTD and a hub. The set of data blocks represents a population of incoming requests.