The system model considers an upper bound ϕ on the time a process takes to execute a step and eventually timely links, i.e. an upper bound δ on the transmission delay. However, both bounds ϕ and δ are unknown and hold after an unknown Global Stabilization Time (GST), so the system is partially synchronous, as described in Section 2.2 and Section 2.4.
There exists one process per node. Therefore, the words node and process are interchangeable.
Every node always follows the specification of the algorithm, until a potential fail. It is considered correct if it never fails and never leaves the system during the whole execution. Otherwise, it is considered faulty, until it comes back to the system.
A node can fail by crashing and a failed node can recover, joining the system again with the same unique identifier, i.e. two nodes cannot have the same identifier, as detailed in Section 2.3. Therefore, a node keeps its identifier regardless of its state. However, the node does not recover its state neither the knowledge of the network membership and, thus, is initialized again.
The system is modeled as an undirected graph, as presented in Section 2.6. Two nodes can communicate directly if they are in the transmission range of each other, i.e. a receiver node is located inside the emission range of a sender node. The system assumes that the emission range is the same as the reception range. Therefore, if node i can communicate with node j, node j can also communicate with node i (bidirectional links).
A given node belongs to a connected graph formed by its neighbors, neighbors of its neighbors, and so on, which is called a connected component. Due to the movement, failure, and disconnection of nodes, the system can be divided into two (or more) different connected components. Each of them is considered to be a fully-fledged network in itself, and therefore, eventually elects one leader. Both partial synchrony and algorithm ensure that, regardless of topology changes, if the changes cease, each connected component will eventually elect a single leader.
Nodes only communicate by broadcast on a fixed Wi-Fi channel selected beforehand. All neighbors of the sender node receive the broadcast message. Reliable communication channels are assumed, possible in a wireless network where the MAC layer reliably delivers broadcast messages, even in the presence of signal attenuation, collision, and interference. Otherwise, the transmitter is faulty or out of the neighborhood. There is no assumption about message order, so messages can be delivered out of order.
The number of nodes is unknown. Each node initially knows its own identifier which is unique in the system. A probe system is used which allows detection of neighbor nodes. By receiving messages from its neighbors, a node gets knowledge of the membership of the network.