Resource-Considerate Data Routing Through Satellite Networks

C = network connectivity C = total journey cost D = matrix of maximum communication range between nodes (Rn×n) E = set of edges in G EG = subset of edges in G G = graph containing all nodes and edges G = evolving graph H = number of hops in a journey J = set of feasible journeys J = journey between nodes J = highest-value journey M = total number of edges in G m = number of edges in G N = total number of nodes in G n = number of nodes in G P = set of packets P = path taken in a journey Q = set of nominal resources Q 0 = set of virtual resources R = matrix of bandwidth (data rate) between nodes (Rn×n) rij = entry in R (ith row, jth column) SG = sequence of subgraphs St = sequence of times at which subgraphs occur S = storage cost matrix (R1×n) Si = entry in S (ith column) T = time horizon for G T = transmission cost matrix (Rn×n) T ij = entry in T (ith row, jth column) t0 σ = start time of a journey V = set of nodes in G VG = subset of nodes in G α = time of packet generation Γ = node availability matrix (Rn×n) γij = entry in Γ (ith row, jth column) δij = entry in D (ith row, jth column) ρ = volume of a packet σ = times of edges in a journey τ = number of subgraphs φ = time to live of a packet χ = journey feasibility (0, 1)