Network models with fixed parameters at the communication nodes. I
In this part of the paper non-oriented networks without loops are considered. A network \(S\) consists of a set \(U(n)\) of \(n\) communication nodes and a set \(H\) of nonoriented arcs \((u_i, u_j)\). For \(U(n)\) the vector \(A = (a_1, \dots, a_n)\) of nonnegative parameters \(a_i\) is specified representing the information exchanged per time unit between the node \(u_i\) and the other nodes of \(U(n)\). For the arcs of \(S\) a weight function is defined by \(C(A) = \{c_{ij}\}\), where \(c_{ii} = 0\) for all \(i\). The set of all weight functions \(C(A)\) is denoted by \(\Gamma (A)\). The function \(C(A)\) is called a \(c\)-realization of \(A\) if \(c_{ij} \leq c\) for any \(\text{arc} \in H\). A vector \(A\) is said to be informational if \(\Gamma (A) \neq \emptyset\) and it is called \(c\)-informational if there exists a \(c\)-realization \(C(A) \in \Gamma (A)\). For the network \(S\) the following results and properties are presented: necessary and sufficient conditions for \(A\) to be informational (respectively-\(c\)-informational), an algorithm for constructing the \(c\)-realization \(C(A)\), the minimum \(c\) for which \(A\) is \(c\)-informational and the general properties of all the \(c\)-realizations for a fixed \(c\).
scientific article; zbMATH DE number 821820