Joint scheduling and routing with power control for centralized wireless sensor networks

Abstract

We consider a TDMA-based multi-hop wireless sensor network, where nodes send data to a sink, which is aware of received powers at all receivers; the sink is responsible for creating the network topology and assigning time slots to links. Under this centralized approach, we propose two algorithms that jointly define the tree topology connecting nodes to the sink, and assign time slots, avoiding any packet loss. In contrast with previous works, the proposed algorithms accurately account for interference effects; when evaluating the signal-to-interference ratio to establish the tree and schedule transmissions, we consider the sum of all actual interfering signals, a fact of relevance for networks with increasing number of nodes. Optimal selection of transmit powers, minimizing energy consumption, is also applied. Our algorithms are compared to a benchmark solution and other proposals from the literature; it is shown that they bring to better radio resource utilization, higher throughput and lower energy consumption, while keeping the average delay limited.

Appendices

Appendix 1: Power control optimization problem

Once the paths and the set of resources to be used by links are defined, power control can be applied, in order to minimize the energy consumption. In particular, with the aim of reducing as much as possible the transmit powers to be used in the selected links, we apply the SIR-based power control optimization problem presented in Eq. (1). To compute an optimal solution to (1), Algorithm 3, proposed in [12], is used in this paper.

Intuitively, each user i increases its power when its SIR is below $\alpha$ and decreases it otherwise. The optimal power allocation in (1) is achieved in the limit, that is when $t_{limit}\rightarrow \infty$. This algorithm has been extensively studied, with results on existence of feasible solution and convergence to optimal solution characterized through several approaches. Theorem 2.2 in [46] demonstrates the convergence and optimality of the algorithm.

Appendix 2: Time slots re-ordering algorithm

In general, the delay of a packet will be affected by: (i) the number of hops, (ii) the number of resources used, s, and (iii) the ordering of allocated slots [28]. In order to ensure that all algorithms compared are treated fairly from this viewpoint, a re-ordering of the s time slots assigned by the Scheduling phase is performed (without any impact on packet losses and throughput, since the s sets of vertices $V_1, V_2, \ldots ,V_s$ are not modified) to minimize the average delay; this is easily achieved by assigning the last time slots in the frame to those nodes having more children. The implemented approach is reported below in Algorithm 4, where we use the notation $\underline{c}'[v]$, to indicate the v-th element of the vector $\underline{c}'$. At each iteration we search for the node having the largest number of children (e.g., node j using color $c_j$) and we assign to this node the largest available color, $c_{max}$ (i.e., color s at the first iteration). Then we assign the same color to all nodes using the old color of j (i.e., we assign color s to all nodes in $V_{c_j}$, being $c_j$ the old color used by node j). The above steps are repeated until all nodes have a new color assigned.