On Minimum-Time Scheduling Problem in a Class of Wireless Networks

We consider a set of transmitter-receiver pairs, or links, that share a wireless medium, and address the problem of emptying backlogged queues with given initial size at the transmitters in minimum time. The minimum-time scheduling problem (MTSP) amounts to determining activation subsets of links, and their time durations, to form a minimum-time schedule. This scheduling problem has been studied a great deal in the past, either through the classical protocol model, or through the current physical model, which enables a crosslayered view that combines rate and power control with overall network resource allocation. Assume a wireless network with N links, each link i has a finite amount of bits di to be transmitted. Let H denote the union of all subsets of N , excluding the empty set. Clearly, |H| = 2 − 1. We use the term group to refer to a member c ∈ H. Scheduling a group c of the N links means that all links in c are concurrently activated, with a given fixed power, for some positive amount of time tc . For any group c , the effective transmit rate ric of any link i ∈ c directly depends on the composition of the activation group. If all the link rates for all 2 − 1 groups c ∈ H are known, the MTSP accepts the following linear programming (LP) formulation: