# Performance Analysis of Latency-Aware Data Management in Industrial IoT Networks +
## 3 System Modeling  
The network: We consider networks of industrial IoT devices that usually consist of sensor motes, actuators and controller devices. We model those devices as a set of \(S=\{s_{1},s_{2},...,s_{n}\}\) nodes, with a total number of \(|S|=n\) nodes, deployed in an area of interest \(\mathcal{A}\). The central network controller \(C\) is set as the first device in the network, \(C=s_{1}\). The communication range \(r_{u}\) of a node \(u\) varies according to the requirements of the underlying routing protocol and the constraints of the technological implementation. Nodes \(u,v\in S\) are able to communicate with each other if \(r_{u},r_{v}\geq e(u,v)\), where \(e(u,v)\) is the Euclidean distance between \(u\) and \(v\). We assume that the controller \(C\) is able to maintain centralized network knowledge. This is usual in industrial applications, in which the locations of the nodes are known, traffic flows are deterministic and communication patterns are established a priori. We assume that \(C\) knows all the shortest paths in the network and comes with an \(n\times n\) matrix \(\mathbf{D}\), where \(\mathbf{D}_{u,v}\) is the length of the shortest path between nodes \(u\) and \(v\) (the offline shortest path computation between two nodes is a classic problem in graph theory and can be solved polynomially, using [PERSON]'s algorithm [PERSON] (1996)). Note that only the control of the data management plane is centralized, while, when using the DML, the data plane itself can be distributed and cooperative, by storing the data in proxies. A proxy \(p\) is a node that is able to store data that can be accessed in a timely manner from the consumer nodes of the network. The set of all proxies is denoted as \(P\), with \(p\in P\subset S\). The DML ensures the effective proxy cooperation so as to achieve the optimal performance of the network according to the objective function defined next. The network controller \(C\) is also serving as a proxy, and thus, we have that \(|P|\geq 1\) in all cases. Data production and consumption: In typical industrial applications, like condition monitoring, sensor nodes perform monitoring tasks (producers), and in some cases, their sensor data are needed either by other sensor nodes, which could need additional data to complement their own local measurement, or by actuator nodes, which use the sensor data so as to perform an actuation (consumers). When needed, a consumer \(u\) can ask for data of interest using the primitives defined by the underlying routing protocol from a sensor node \(v\) (ideally from a proxy \(p\), when using the DML). We define the set of consumers as \(S_{c}\subset S\), with \(|S_{c}|=m<n\). When a consumer \(u\) needs data, it requests the data via a multi-hop routing path, from the corresponding proxy \(p\). When \(p\) receives the data request from \(u\), it sends the requested data along the same routing path, starting at \(p\) and finishing at the consumer \(u\). Note that the length of this individual data delivery path is twice the length of the path between \(u\) and \(p\). We assume that the data generation and access processes are not synchronized. Specifically, we assume that data consumers request data at an unspecified point in time after data have been generated by data producers and transferred to the proxies. The latency constraint: Let \(l_{u,v}\) be the single-hop data transmission latency from a node \(u\in S\) to another node \(v\in S\). We define as access latency \(L_{u,p}\) the amount of time required for the data to reach consumer \(u\), after \(u\)'s request, when the data follow a multi-hop propagation between \(u\) and \(p\). We denote access latency as \(L_{u,p}=l_{u,v_{1}}+...+l_{v_{i},p}+l_{p,v_{i}}+...+l_{v_{1},u}\). An example of the access latency composition is depicted in Figure 2. We denote as \(\overline{L}\) the average access latency across all consumers as the mean value of all the latencies \(L_{u,p}\).