Practical implications of continuity properties of resource allocation strategies in wireless systems

Abstract

We utilize axiomatic bargaining theory to depict certain implications of continuity properties of resource allocation strategies in wireless systems. Feasible utility sets are characterized as sub-level sets of interference functions. The collective choice function is used to represent resource allocation strategies. We use an axiomatic framework to emulate certain desirable properties of resource allocation strategies. We focus on the axiom of feasible set continuity, to emulate robustness of the resource allocation strategy to channel estimation and prediction errors. The connection between the axiom of feasible set continuity, lower semi-continuity and upper semi-continuity is elucidated. We investigate continuity properties, which allow a resource allocation strategy to be a strict monotone path collective choice function (MPCCF). We provide a result, which displays the practical importance of the axiom of feasible set continuity to develop bounds on the uncertainty region, resulting from channel estimation and prediction errors. We provide examples to show that the strict MPCCF is a useful tool to characterize solution outcomes of resource allocation strategies, e.g. egalitarian solution and dictatorial solution.