On the Fundamental Limits of Multi-user Scheduling under Short-term Fairness Constraints

Abstract: In the conventional information theoretic analysis of multiterminal communication scenarios, it is often assumed that all of the distributed terminals use the communication channel simultaneously. However, in practical wireless communication systems - due to restricted computation complexity at network terminals - a limited number of users can be activated either in uplink or downlink simultaneously. This necessitates the design of a scheduler which determines the set of active users at each time-slot. A well designed scheduler maximizes the average system utility subject to a set of fairness criteria, which must be met in a limited window-length to avoid long starvation periods. In this work, scheduling under short-term temporal fairness constraints is considered. The objective is to maximize the average system utility such that the fraction of the time-slots that each user is activated is within desired upper and lower bounds in the fairness window-length. The set of feasible window-lengths is characterized as a function of system parameters. It is shown that the optimal system utility is non-monotonic and super-additive in window-length. Furthermore, a scheduling strategy is proposed which satisfies short-term fairness constraints for arbitrary window-lengths, and achieves optimal average system utility as the window-length is increased asymptotically. Numerical simulations are provided to verify the results.