Abstract
In this paper, we study the optimisation problem of transmission power and delay in a multi-hop wireless network consisting of multiple nodes. The goal is to determine the optimal policy of transmission rates at various buffer and channel states in order to minimise the power consumption and the queueing delay of the whole network. With the assumptions of interference-free links and independently and identically distributed (i.i.d.) channel states, we formulate this problem using a semi-open Jackson network model for data transmission and a Markov model for channel states transition. We derive a difference equation of the system performance under any two different policies. The necessary and sufficient condition of optimal policy is obtained. We also prove that the system performance is monotonic with respect to (w.r.t.) the transmission rate and the optimal transmission rate can be either maximal or minimal. That is, the 'bang-bang' control is an optimal control. This optimality structure greatly reduces the problem complexity. Furthermore, we develop an iterative algorithm to find the optimal solution. Finally, we conduct the simulation experiments to demonstrate the effectiveness of our approach. We hope our work can shed some insights on solving this complicated optimisation problem.