On Equitable Approaches to Resource Allocation Problems: The Conditional Minimax Solutions

Resource allocation problems are concerned with the allocation of limited resources among competing activities so as to achieve the best overall performances. In this paper, we focus on approaches that attempt to allocate resources equitably among the competing activities. The problems of efficient and equitable resource allocation arise in various systems which serve many users, like in telecommunication systems. Telecommunication networks are expected to satisfy the increasing demand for traditional services as well as to accommodate multimedia services. Hence, it becomes critical to allocate network resources, such as available bandwidth, so as to provide high level performance of all services at numerous destination nodes. The performance can be measured in terms of expected delays to be equitably minimized for all service demands. In this paper we introduce and analyze a solution concept of the conditional minimax as a generalization of the minimax solution concept extended to take into account the number of services (the portion of demand) related to the worst performances. Namely, for a specified portion of demand we take into account the corresponding portion of the maximum results and we consider their average as the worst conditional mean to be minimized. We show that, similar to the standard minimax approach, the minimization of the worst conditional mean can be defined by a linear objective and a number of auxiliary linear inequalities. We report some results of initial computational experience with the new solution concept.