On the minimum latency transmission scheduling in wireless networks with power control under SINR constraints

In order to alleviate interference and contention in a wireless network, we may exploit the existence of multiple orthogonal channels or time slots, thus achieving a substantial improvement in performance. In this paper, we study a joint transmission scheduling and power control problem that arises in wireless networks. The goal is to assign channels (or time slots) and transmitting powers to communication links such that all communication requests are processed correctly, specified quality-of-service requirements are met, and the number of required time slots is minimised. First, we formulate the problem as a mixed-integer linear programming. Then, we show that the problem considered is non-deterministic polynomial-time hard, and subsequently, we propose non-trivial bounding techniques to solve it. Optimisation methods are also discussed, including a column generation approach, specifically designed to find bounds for the transmission scheduling problem. Moreover, we develop optimisation techniques in which the bounding techniques are integrated in order to derive the optimal solution to the problem faster. We close with an extensive computational study, which shows that despite the complexity of the problem, the proposed methodology scales to problems of non-trivial size. Our algorithms can therefore be used for static wireless networks where propagation conditions are almost constant and a centralised agent is available (e.g. cellular networks where the base station can act as a centralised agent or wireless mesh networks), and they can also serve as a benchmark for the performance evaluation of heuristic, approximation or distributed algorithms that aim to find near-optimal solutions without information about the whole network.