Knaster Procedure for Proportional Fair Wireless Channel Allocation

For the allocation of indivisible goods to a number of agents, appearing in many wireless infrastructure problems, common characteristics of fairness like proportionality, envy-freeness, or equity are hard to achieve or even impossible. As one of the few feasible allocation approaches, the Knaster procedure for item allocation is based on user bidding for items and adds an additional settlement step where users with higher benefit compensate users with lower benefit by payments. Here, the Knaster procedure is extended to a general allocation procedure, where the payments are considered as a measure for unfairness of a certain allocation. By minimizing the maximal payment, a fair state is uniquely specified. The approach is studied within the domain of wireless channel allocation and it is demonstrated that by following the proposed approach, deviations from proportional fairness can be kept small.