Today, whether in industry, research, or civil applications, there are many incentives to reduce the energy footprint of automated systems. In multihop wireless networks, the main objective in that regard is usually to maximize the lifetime of the network by distributing the load over all nodes. In this paper, we improve a solution that aggregates flows to optimize the number of nodes that can be turned off. We introduce interference awareness in a routing metric designed to aggregate flows to avoid overloading the network and to preserve the quality of service required by the flows. This way, it becomes possible to integrate this metric into classical shortest path routing algorithms that do not consider interference. We also show that flow aggregation and overall energy consumption are equivalent problems.

For a long time, web services, social networking, mail, and online shopping contributed to develop a kind of network centralization. It is now common to see the application layer of the network running on large data centers that aggregate tons of data and provide services to users. Moreover, the adoption of cellular phones, followed by smartphones, has led to the deployment of wireless network architectures based on wireless access points, creating fully centralized services from the user’s perspective at the application and network layers. Although this type of architecture can achieve high performance, its deployment and maintenance can be very costly both financially and in terms of energy. Indeed, if a network provider wishes to cover a new area, for example, a large number of antennas must be deployed. For each of them, it must buy or rent a place, build the infrastructure to support the antenna, wire it up to its backbone network, and finally supply it. In addition, achieving full and effective coverage requires addressing spatial constraints that can lead to many logistical, financial, or political problems. Furthermore, we have seen an increasing demand in terms of network capacity in recent years. Mainly caused by HD video and audio streaming as well as social networking applications that create a lot of data, it has highlighted the limitations of such centralized architectures. Thus, recent work on edge computing [

Developed in parallel, multihop wireless (or ad hoc) networks were mainly dedicated to specific applications such as satellite systems, sensor networks, device-to-device communications, or areas without infrastructure (e.g., military field, disaster recovery, and last mile) covering. The low popularity of these networks is due to the extreme difficulty in optimizing these distributed systems, which leads to lower performance than centralized wireless networks. Nevertheless, multihop wireless networks have an advantage in terms of flexibility that allows them to be deployed almost anywhere, as long as there is a way to power the nodes. Moreover, interest in these networks will certainly increase in the coming years with the expansion of the Internet of Things.

In addition, since multihop wireless networks represent an increasingly important part of our society’s total energy consumption, a lot of work must be done to minimize it. In the past, most of the work on energy efficiency in ad hoc networks focused on wireless sensor networks and aimed at maximizing their lifespan. Although perfectly legitimized by energy constraints (e.g., battery-powered nodes), the proposed solutions are based on the basic principle of uniformly distributing the load over the entire network. In this context, nodes reduce their energy supply at the same location. However, this approach becomes less relevant when the network is composed of more traditional nodes (or things) that are not necessarily battery powered, such as in MESH networks, and where radio components are not the most consuming.

In the case of more complex wireless nodes (such as Wi-Fi routers, connected vehicles, and urban equipment), a static amount of energy is consumed by turning them on. Hence, we proposed the use of flow aggregation, which consists of routing flows along common paths to maximize the number of nodes that can be turned off to minimize overall energy consumption. This paradigm is based on the observation that the energy cost of data transmission is lower than the static energy cost required to have a node turned on. It then becomes more interesting to make nodes process more data and turn off others that can be unloaded.

In this paper, we confirm this observation by comparing our flow aggregation routing with a routing solution that minimizes the overall energy consumption of the network. We also extend our Flow Aggregation MEtric [

We show that the maximization of flow aggregation and the minimization of overall energy consumption are equivalent in the assumption that most of the energy consumption is induced by the powering up of the nodes. In the following, this part will be called the static energy consumption of a node.

We extend our Flow Aggregation MEtric by taking into account interference to avoid network overload.

These contributions are evaluated by simulation using CPLEX [

The remainder of this paper is organized as follows. In Section

The state of the art defines two types of routing protocols: reactive and proactive. In the former, a node calculates a route to reach the destination when it has data to send. The most common protocols in this family are Dynamic Source Routing (DSR) [

In proactive protocols, the Optimized Link State Routing (OLSR) protocol [

Most of the work dealing with energy savings in multihop wireless networks tends to focus on wireless sensor networks. Thus, considering that nodes are powered by batteries, the problem is to improve the lifetime of the network. However, multihop wireless networks can be composed of other types of nodes. These nodes can have generators to draw power from the environment or may be powered by a renewable energy source. This is the case for mesh networks that have different energy constraints. Since the nodes can be switched on continuously, the objective of energy saving in mesh networks is to reduce the energy footprint of the network globally. A solution based on integer linear programming to route flows in order to maximize the number of nodes that can be turned off is proposed in [

In [

Usually, multihop wireless networks are represented with a directed graph noted

Interference can be modeled using two different methods [

Then, we use the conflicts between the links to build a conflict graph [

To estimate the energy consumption of the network, we use a state energy model [

We present in Figure

Notations used throughout this paper.

Integer Linear programming (ILP) is a powerful mathematical tool used to study optimality in many areas of research. In networking, it is typically used to solve network provisioning, performance improvement, and routing problems [

Shortest path routing algorithm using integer linear programming formulation.

This formulation models a shortest path routing algorithm. Here, the objective function minimizes the sum of the paths’ lengths, which is calculated as the sum of the weight of nodes that make the path, used to route a set of flows. The first eight constraints are state-of-the-art constraints used to model a routing algorithm and will be common to all the solutions we will present later in this paper.

Constraint (1) is the capacity constraint and is based on the interference model described in Section

In this paper, we aim at minimizing the overall energy consumption of the network by allowing unused nodes to be turned off (or put into sleep mode) instead of remaining in idle mode. We model this behavior by a set of linear constraints that we integrate into the previous ILP. Figure

ILP formulation for minimal energy consumption routing.

In this formulation, we have modified the objective function so that the program is now minimizing the overall energy consumption of the network. The first unnumbered constraints are the same as those seen above and are mandatory to implement the routing algorithm regardless of the objective function. Constraint (1) calculates the total energy consumption of any node

Figure

Comparison of a classical shortest path routing and our optimal solution. (a) Overall energy consumption. (b) Number of unused nodes.

In our preliminary study [

ILP formulation to minimize the number of used nodes when routing a set of flows.

In this formulation, the objective function is changed so that the program now minimizes the number of nodes used. Again, we can see the unnumbered constraints that model the routing algorithm. Constraints (

In Figure

Equivalence between energy consumption and number of nodes used. (a) Overall energy consumption. (b) Number of unused nodes.

Thus, by using flow aggregation, we can minimize the global energy consumption of a multihop wireless network while respecting the QoS, without requiring cross-layer information (energy-related information). The only information we need is the set of flows, which can be determined at the routing layer, and the links’ capacity which is a constant that can be known. However, as optimal as ILP can be, the complexity of the algorithms used to solve this problem makes our solution inapplicable. Nevertheless, it gives an optimal bound to which we can refer when evaluating the innovative solutions that will be described in the next section.

Solving the flow aggregation problem using integer linear programming has two issues. Firstly, the complexity is very high. Secondly, it requires that the routing problem be solved with the same method. Thus, it becomes difficult to distribute this solution and only routes between the sources and their respective destinations can be found. If the set of flows changes, all routes have to be recalculated through integer linear programming. To deal with this, we have proposed the Flow Aggregation MEtric (FAME) [

FAME is a routing metric that can be integrated into a classic shortest path routing algorithm. Its purpose consists in routing flows according to a set of attractive nodes. These nodes can be defined statically when the network is deployed or dynamically when network conditions change. We call them nodes of interest. Let NI be the set of such nodes.

As we are using a shortest path routing algorithm, our goal is to give a weight small enough to the nodes of interest so that they naturally attract flows. In this way, the path they are in is shorter and the routing algorithm can route flows over them and their close neighborhood, leading to aggregation. NI can be determined in several ways using, for example, a connected dominating set or a Steiner tree. However, our results in [

We consider two cases to calculate the weight of a node:

If the node does not belong to NI, its weight is a function of the distance with its nearest node of interest and the number of such nodes at this distance (in terms of hops)

The weights of the nodes in NI are set to the minimal value that the other nodes can theoretically have

Hence, we determine the weight of any node

Figure

Number of unused nodes.

Figure

Load of the network through the cliques’ utilization rates. (a) Average utilization rate of cliques. (b) Utilization rate of the most used clique.

Once again, we can notice from these figures that FAME approximates very well our optimal aggregation solution. However, to avoid that our results are biased by the implementation of routing algorithms, we have introduced our metric into the shortest path ILP formulation. This means we were able to benefit from the centralized interference model defined by the cliques. Thus, we need to go a step further in order to consider a fully distributed algorithm.

Our metric FAME allows shortest path routing algorithms to aggregate flows close to an optimal level. Nevertheless, if this is done without consideration of interference, the network may quickly become overloaded. To overcome this difficulty, we propose the Adaptive Flow Aggregation MEtric (A-FAME). This takes into account the network load. More precisely, when it is low, the metric routes flow almost optimally, in the same way as FAME. When it is high, the weights of nodes are calculated so that flows are routed according to the shortest path, by releasing the attraction of nodes of interest. To achieve this, we first need to simplify our interference model.

We now consider interference between nodes instead of links. This allows us to move from the determination of cliques, which is complex, to neighborhoods. Based on the same principle of the previous model, we calculate the transmission rate of nodes (out rate of nodes divided by the capacity of the wireless transmission medium) to evaluate the utilization rate of a neighborhood. As with cliques, it can be interpreted as the load of a neighborhood and is calculated as the sum of the transmission rates of the nodes that compose it:

To implement A-FAME, two parameters need to be set. The first one is the reduction threshold

The aggregation force of a node, when its neighborhood load is greater than the reduction threshold, is calculated by subtracting the excess from the

Finding the optimal value for these parameters is still an open question and will remain out of the scope of this paper. However, interested readers may investigate multiobjective optimization [

In this paper, we expect that if the reduction threshold is high, we may not be able to detect network overload, resulting in underutilization of the A-FAME. Indeed, the higher the threshold is, the less the impact of the excess is on the aggregation force. On the other hand, a low threshold can activate the A-FAME mechanism more often with a potentially greater excess, resulting in a lower aggregation force. With regard to the initial value of the aggregation force, a high value can limit the range of the force of a node, which can reduce the adaptability of the metric. However, a low value may reduce excessively the aggregation, resulting in an oscillation problem where each metric (FAME and A-FAME) is used in turn.

In Figures

Number of unused nodes with various parameters for the A-FAME.

Impact of A-FAME parameters on the network load. (a) Average utilization rate of cliques (b) Utilization rate of the most used clique.

Figure

Figures

Our work focused on aggregating flows in multihop wireless networks to minimize overall energy consumption, while maintaining the quality of service offered in terms of throughput. In this paper, we have shown that maximizing energy savings and maximizing the number of nodes that can be turned off are equivalent problems. Then, we have improved our previous solution [

Future work should focus on finding an effective way to implement flow aggregation in current applications. To do this, we need to disseminate two pieces of information: the network topology which is necessary to determine the routes and the nature of nodes of interest. Our first studies on the adaptation of the OLSR protocol [

The raw data used to support the findings of this study have not been made available because of the large amount of memory space it takes. The tools’ source code used to generate the raw data used to support the findings of this study is available at

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was funded by a PhD grant from the French Ministry of Education and Research.