Ensemble relations for resource allocation tasks

In general resource allocation problems there are usually different notions of optimality. While these usually refer to extreme elements of a binary relation, there are no further means to prefer the choice of one relation over the other. Here we consider a combined approach, called ensemble relations, where for a number of relations the larger count of domain element x being in relation to y than vice versa gives another specification of a binary relation. Extreme values of that relation are considered as combined solutions to the allocation problem at hand. While ensemble relations will not be cycle-free in the general case, in practical circumstances cycles are either rare or absent. The approach is demonstrated on the wireless channel allocation problem with an ensemble relation composed of maximal minimum, maximal product and maximal sum. As a result of simulations it can be seen that the selection of the ensemble relations is strongly specified and tends to equal the selection by product maximization.