A Decomposition Method for Transmission Scheduling in Multi-Channel Wireless Sensor Networks

We consider wireless sensor networks with multiple frequency channels, multiple gateways and multiple classes of traffic carrying data generated by different sensory inputs. The objective is to devise joint routing and transmission scheduling policies in order to gather data in the most efficient manner while respecting the needs of different sensing tasks (fairness). We formulate the problem as maximizing the utility of transmissions subject to explicit fairness constraints and propose a decomposition algorithm drawing upon large-scale decomposition ideas in mathematical programming. We show that our algorithm terminates in a finite number of iterations. Every iteration requires the solution of a subproblem which is NP-hard. To solve the subproblem we (i) devise a particular relaxation that is solvable in polynomial time and (ii) leverage polynomial time approximation schemes. A combination of both approaches enables an improved decomposition algorithm which is much more efficient for solving large problem instances.