TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES Trans. Emerging Tel. Tech. (2013) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/ett.2616 RESEARCH ARTICLE On the minimum latency transmission scheduling in wireless networks with power control under SINR constraints † T. Charalambous*, E. Klerides, W. Wiesemann, A. Vassiliou, S. Hadjitheophanous and K. M. Deliparaschos Automatic Control Lab, School of Electrical Engineering, Royal Institute of Technology (KTH), Osquldas väg 10, 100-44 Stockholm, Sweden ABSTRACT 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. Copyright © 2013 John Wiley & Sons, Ltd. *Correspondence T. Charalambous, Automatic Control Lab, School of Electrical Engineering,Royal Institute of Technology (KTH), Osquldas väg 10, 100-44 Stockholm, Sweden. E-mail: themisc@kth.se † Preliminary results of this work have been published as a Technical Report in [1]. Received 17 October 2012; Revised 27 November 2012; Accepted 14 December 2012 1. INTRODUCTION Wireless technology standards provide a radio-frequency spectrum with a set of many non-overlapping channels, and a node has the option to choose on which channel to transmit. Likewise, in cases where only a single channel is available, it is possible to divide time into frames, and then, frames can be divided into time slots, such that at each frame a node has the option to choose on which time slot to transmit. In the latter case, synchronisation of the wireless nodes in the network is necessary. If synchroni- sation is not considered, however, choosing a channel or a time slot in the network becomes the same problem. It is important to schedule channel/time slot access in such a way that spatial reuse is fully exploited, and hence, the number of channels required to successfully complete all requests is minimised. Power control has been a prominent research area with increased interest (e.g. [2–9]). Increased power ensures longer transmission distance and higher data transfer rate. However, power minimisation increases not only battery lifetime but also the effective interference mitigation that increases the overall network capacity by allowing higher frequency reuse. Power control has been exten- sively employed for medium access control in multi-hop wireless networks (e.g. [10–15]). Some of them aimed Copyright © 2013 John Wiley & Sons, Ltd.