# Towards an Efficient Method for Large-Scale Wi-SUN-Enabled AMI Network Planning
## 3 Related Work
### Approaches for Key Devices Positioning
Then, the algorithm assembles an additional set with the candidate centroid and its neighbor nodes and analyzes whether the cluster is viable. A cluster is considered viable if a spanning tree, rooted in \(v\) and covering all cluster nodes, satisfies the cluster size and relay load constraints. It continues the iteration (recursion) as long as there are nodes to be clustered. The recursive algorithm's stopping condition occurs when the next iteration's cluster radius exceeds a specific maximum radius \(R\). The authors in [15] highlight that, although many studies address the problem of the optimization of device placement in wireless networks, few specifically address the location of concentrators in AMI networks. Compared to the work by [13], they also consider existing poles as candidate positions for installing concentrators. They aim to establish the concentrator position that minimizes the number of hops, maximizes throughput, and keeps delay within certain limits. To analyze the average throughput and delay, they use an M/M/1/K queue model and present a set of formulas for calculating throughput. This includes packet loss probability, service rate, time-of-service with no errors, the packet error rate at the physical layer, and traffic at a given node. For the delay analysis, they consider the queue size, the waiting time, the end-to-end delay, and the end-to-end average delay. A similar study is presented by [16], proposing a channel-aware optimal location approach for the data concentrator unit placement in smart grids. For the positioning of concentrators in problems of smart grid networks expansion, the authors in [17] used mixed-integer non-linear programming (MINLP) and mixed-integer linear programming approaches (MILP) to minimize network congestion by optimizing residual buffer capacity by positioning data concentrators and network routing. They pro posed an approach for adding new devices to AMI networks that are already in operation, maximizing the quality of service (QoS) performance for customers, providing redundant connectivity in cases of security threat or interruption in power supply, and assisting in network expansion. They suggest using the path loss propagation model to identify the communication radius around data concentrators and analyze different restrictions to establish the best position for this type of equipment. The authors in [18] proposed using clustering techniques for the problem of data aggregation points (DAPs) positioning in NAN to minimize the distance between DAPs and SMs, dividing the neighborhoods into subnetworks. With this, they also seek to reduce the number of hops to up to 3 hops. Furthermore, they introduced a new metric called coverage density, which defines whether the planning done for a given zone ensures the necessary coverage. The authors cite that the problem of positioning DAPs is an underexplored topic in the domain of smart grids. The methods used by the authors include Haversine distance, Floyd-Warshall (FW) algorithm to find the (shortest path) route between a given node and another node in the network, and the k-Medoids clustering algorithm, which takes into account the distance between smart meters and the transmission range of the meters. Minimizing the distance between data aggregation points (DAPs) and smart meters served by them can be the requirement of a device placement problem. About this, the authors in [19] used a network partitioning approach, using a clustering algorithm clustering-based DAP placement algorithm (CDPA) that performs the clustering aiming to minimize distance. The authors also used the Floyd-Warshall algorithm for the shortest path search and the distance between nodes as information considered by the method. In [20], the authors discussed the positioning of access points (APs) in smart grids with a communication network implemented with a power-line communication (PLC) network.