Table 1 Notation, variables, and parameters used in the DDIP model
From: Robust communication network formation: a decentralized approach
Variable | Definition |
|---|---|
\(V=\{1,2,\ldots,n\}\) | Set of actors in the network |
\(|V|=n\) | The number of actors in the network |
\(P_i\) | Set of actors in the proximity of actor i |
t | Time period |
\(t_{{\text{max}}}\) | The maximum number of periods to run the DDIP model |
\(O_{i}^{t}\) | The set of actor i’s out-directed neighbors at period t |
\(I_{i}^{t}\) | The set of actor i’s in-directed neighbors at period t |
\(g_{i}^{t}\) | The local network structure of actor i at period t |
m | The number of messages each actor sends per period t |
\(p_{ijk}^{t}\) | The fraction of messages actor i receives from source j through neighbor k during period t |
\(\alpha\) | The probability of a message being terminated |
\(\beta _{ij}^{{\text{own}},t}\) | Actor i’s own (personal) preference for messages from actor j, during period t |
\(\beta _{ij}^{{\text{neigh}},t}\) | The average preference of actor i’s out-directed neighbors for messages from actor j during period t |
\(\beta _{ij}^{{\text{total}},t}\) | The overall preference that actor i has for messages from actor j at time t |
\(\rho\) | Preference parameter: The weight of an actor’s own preferences against it’s neighbors preferences |
\(\gamma\), w | Cost parameters: the weights in the objective |