## 2 Data Transmission in IoT Networks  
A wireless ad hoc network and MANET are important concepts of smart city communication. It is widely used for ensuring self-configuring and dynamic connectivity between sensors, humans, and devices that send and receive information. [PERSON] et al. [10] study the Quality of Service of MANET in smart city networks with an emphasis on healthcare. Several frameworks were considered that improve the transmission quality of MANET, as well as individual elements, such as video signal transmission. [PERSON] et al. [11] discuss the MANET and WSN hybrid network for fast data collection in the smart city. The authors provide a transmission protocol based on modern data transmission standards considering IPv6. [PERSON] et al. [12] study methods to improve the reliability of MANET networks and propose a method of self-healing nodes. In this work, our goal is to increase the speed and reliability of MANET communication to ensure security. To achieve this goal, we propose the use of RRNS in MANET. In the original version, MANET solves the minimax optimization problem of finding the shortest path in the network. The smart city network can be represented as a directed graph, where the vertices are the communication nodes (devices in the network), and the arcs are the data transmission between the nodes. Let us establish that \(G(V,E)\) is a network graph with a flow \(v_{0}\in V\) and path cost function \(c:E\to R\). We assume that the set of vertices \(V\) split into two non-overlapping subsets \(V_{A}\) and \(V_{B}\) (\(V_{A}\cup V_{B}=V,V_{A}\cap V_{B}=\varnothing\)). Now, we fix a pair of mappings:  
\[s_{A}:v\to V_{G}(v)\ for\ v\in V_{A}\backslash\{v_{0}\};\ s_{B}:v\to V_{G}(v)\ for\ v\in V_{B}\backslash\{v_{0}\}; \tag{1}\]  
where \(V_{G}(v)\) is the set of ends of all arcs outgoing from a vertex \(v\). We define the following subgraph \(T_{s}=(V,E_{s})\), generated by a set of arcs of the form \((v,s_{A}(v))\) and \((v,s_{B}(V))\). This subgraph has the property that for some given vertex \(w\in V\), or there is a way \(P_{T},(w,v_{0})\) from \(w\) to \(v_{0}\). For an arbitrary vertex, \(w\in V\) defines the value \(\widetilde{c}(s_{A},s_{B},w)\) as the sum of the costs of the arcs of the path \(P_{T},(w,v_{0})\), if such a path exists in \(T_{s}\). If the path \(P_{T},(w,v_{0})\) does not exist in \(T_{s}\), we assume the value \(\widetilde{c}(s_{A},s_{B},w)\) equals to \(\infty\) or \(-\infty\) depending on the positivity and negativity of the sum of the costs of the arcs of the oriented cycle \(C_{w}\). If the sum of the costs of the arcs of an oriented cycle \(C_{w}\) is zero, then \(\widetilde{c}(s_{A},s_{B},w)\) equals the sum of the costs of the arcs of the path connecting the vertex \(w\) with the cycle \(C_{w}\). That is, a problem is formulated as \(F(w)=\underset{s_{A}}{\text{minmax}}\widetilde{c}(s_{A},s_{B},w)\). Let us consider the data transmission model presented in Figures 1 and 2. It is known that MANET transmits data using devices located on the infrastructure-less, distributed wireless networks without static-located transmission stations. It is an interesting and promising solution providing communication of a big variety of devices, from mobile devices to personal cars, from smart devices to public transport, etc. In addition, a smart city infrastructure also contains static nodes, such as data centers, storage, decision centers, etc. For such a dynamic heterogeneous network, we propose the concept of parallel data transmission based on RRNS that divides data into smaller shares and transmits them in parallel. The self-correcting properties of RRNS can improve the reliability and fault tolerance of the entire system [13; 14; 15; 16]. Figure 1 shows a conceptual model described above. We group the elements of a smart city according to common features. They can be separated from each other by large distances and distributed like data management modules. This model gives a general idea of the transmission network complexity.