Continuity of Link Scheduling Rate Region for Wireless Networks with Propagation Delays

We study the link scheduling problem of wireless networks with signal propagation delays into consideration. Recently, when the propagation delays are integers, the rate region using slotted scheduling with a proper timeslot size has been characterized explicitly. We study the general case that the propagation delays can be real values and the scheduling can be unslotted. As a practical communication device cannot transmit signals in arbitrarily short time intervals, we focus on scheduling where an active interval’s length is bounded below by a given value. We first reveal some properties of continuity of the scheduling rate region concerning the propagation delays. We then show that for a network with rational propagation delays, the continuous (unslotted) scheduling rate region is the same as that of slotted scheduling with a proper timeslot size when the bound on the active interval length is sufficiently small. Moreover, for a network with possibly irrational propagation delays, we provide an approximation of the network by Dirichlet’s theorem so that the continuous scheduling rate region of the original network can be approximated by the slotted scheduling rate region for a network with integer delays.