Ann. Telecommun. (2012) 67:181–189DOI 10.1007/s12243-012-0291-1

Traffic-based topology control algorithm for energy savingsin multi-hop wireless networks

Steven Martin · Khaldoun Al Agha · Guy Pujolle

Received: 21 July 2011 / Accepted: 27 January 2012 / Published online: 1 March 2012© Institut Télécom and Springer-Verlag 2012

Abstract This paper presents a traffic-based topologycontrol algorithm for multi-hop wireless networks, inorder to optimize the global energy consumption whilemaximizing the aggregate throughput. Contrary to ma-jor related works, we do not consider that reducingtransmission powers implies reducing interferences andthat the traffic is uniformly distributed among the links.Thus, we propose to dynamically calculate the trans-mission power of nodes depending on the traffic. First,we redefine the N-hop interference model for varyingtransmission powers. Then, we define a function givingthe minimum interference according to the transmis-sion powers. We propose several algorithms minimizingthis function: global optimization, local optimization,and distributed optimization for a limited computationcost. Our first algorithm is used as a reference forlimited cases. We show by simulation that our heuristicsare relevant compared to existing works.

Keywords Green networking · Ad hoc · Power ·Interference

1 Introduction

In multi-hop wireless networks, two distant nodes can-not communicate directly and use intermediate nodes

S. Martin · K. Al Agha (B)LRI—University Paris 11, 91405 Orsay, Francee-mail: alagha@lri.fr

S. Martine-mail: steven.martin@lri.fr

G. PujolleLiP6—University Paris 6, 75005 Paris, Francee-mail: guy.pujolle@lip6.fr

to relay messages. The neighbors of a node are deter-mined by the ability to understand the transmission ofthe information which means that they are in the cov-erage area. This area is more or less wide and dependson the transmission power and also the received inter-ference, itself corresponds to the transmission power ofinterfering nodes located somewhere in the network.Hence, a variation of the transmission power will playan important role on the topology of the network andits capacity.

Obviously, maximizing the spatial reuse of resources(simultaneous communications on the same frequency)enables to increase the aggregate throughput of flowsin a network. Moreover, this technique also leads tothe minimization of the global energy consumptionsince it minimizes interferences. Therefore, our strategyconsists in varying dynamically the transmission powersof the nodes to optimize the energy saving and increasethe global throughput. Thus, some nodes can reducetheir transmission power in order to reduce their inter-ferences while other nodes may have to increase theirpower to reach the destination by minimal number ofhops, for example.

Many works on power control were done to increasethe global bitrates in cellular networks or in wirelessnetworks. For wireless multi-hop networks, this prob-lem has mainly been studied in order to reduce theenergy node consumption. The objective was to assignpre-calculated values for the transmission powers of thenodes, with the following constraint: reduce as much aspossible the transmission powers while maintaining theconnectivity of the network topology.

Those works were realized under the assumptionwhere the minimization of the transmission powers willreduce interferences and hence maximize the spatial

182 Ann. Telecommun. (2012) 67:181–189

reuse and increase the bitrates of the flows. However,other works have shown that this assumption was notrealistic, but they affirm the fact that varying the trans-mission powers increases the amount of traffic [1].

In this paper, we propose to dynamically computethe transmission powers of nodes depending on thenetwork. We consider that the best allocation vectorfor the transmission powers varies according to theamount of á enlever traffic: For a given set of flows, wecould choose an optimal allocation while it representsthe worst case for another set of flows. To addressthis issue, we propose several algorithms according todifferent contexts:

• Global optimization. The objective is to calculateor approximate the optimal solution considering aglobal knowledge of the network.

• Local optimization. Considering also a globalknowledge of the network, the objective is to calcu-late a near-optimal solution close to an initial givenone.

• Distributed optimization. The objective is the sameas for the local optimization in a distributed mannerwhere only a local knowledge of the network isconsidered.

This paper is organized as follows. Related work isdiscussed in Section 2. Section 3 is used to describeour traffic-based topology control solution. Simulationresults are presented in Section 4, before we concludethe paper.

2 Related work

The control of the emitting power of nodes in a multi-hop wireless network has a direct impact on the topol-ogy and interferences. Therefore, power control hasbeen widely studied in the literature in different con-texts. For instance, in cellular networks, power controlaims at adapting dynamically the emitting power of astation so that the channel quality remains the same,regardless of the distance and interferences. Then,other criteria have been studied, such as the lifetimeof a sensor network or still the overall throughput ina multi-hop wireless network. The common term forthis second generation of related work is “power man-agement.” As for “topology control,” it refers to theproblem of determining the best topology consideringa given criterion, thus defining the emitting power ofnodes.

Related work in multi-hop wireless networks hasmainly focused on the energy consumption reduction.Two visions can be explored, depending on the follow-

ing assumption: Interferences are reduced with loweremitting powers. Under this assumption, it can be de-duced that algorithms aiming at reducing the emittingpower of nodes as much as the network stay connectedare, in the same time, reducing the interferences andincreasing the network lifetime. Without this assump-tion, the objective is directly to minimize interferences.But in both cases, a specific problem is that the en-ergy consumption reduction leads to a lower capacity,already critical in multi-hop wireless networks. Beforedescribing our solution minimizing the global energyconsumption while maximizing the overall throughput,we first present existing work aiming at reducing emit-ting power of nodes and then those aiming at reducinginterferences.

2.1 Minimizing transmission power

The network can be represented by a directed graphG = (V, E), with V the set of nodes and E the setof links. The objective is to compute a subgraph G′ =(V ′, E′) with the following properties: |V ′| = |V|, E′ ⊆E, and if it exists a path between two given nodes in G,it is also the case in G′. Other constraints can possiblybe added.

In [2], the authors consider that nodes have a com-mon emitting power and they compute a subgraph whosethe probability of connectivity tends to one for randomnetworks. If each node can have a varying emittingpower, apart from those of other nodes, the problemcan be seen as an optimization problem. Then, the goalis to minimize the emitting power of the node havingthe highest one while keeping the network connectedor two-connected [3]. Several algorithms are proposed,for distributed and centralized networks. The heuristicdoes not guarantee the subgraph connectivity.

A network one- or two-connected, even if it success-fully reduces the emitting powers, could easily lose itsconnectivity in practice. So, it can be more interestingto reduce emitting powers while keeping the network k-connected [4]. Parameter k is determined from severalcriteria such as robustness, capacity, or energy con-sumption. This work has been extended by consideringthe use of directional antennas [5].

Previous solutions provide good results, but theyneed complex computations, which is not always trac-table in dynamic networks where the nodes have lim-ited memory and computation resources. A good andfast approximation is to let nodes reduce their emit-ting power until they reach a degree equal to six [6].Another pragmatic solution consists in reducing theemitting power of each node such that two of its neigh-bors are not separated by more than a given angle

Ann. Telecommun. (2012) 67:181–189 183

[7]. This algorithm, called cone-based topology control(cbtc), requires that each node knows the direction ofits neighbors. The authors show that an angle equalto 5π/6 is a necessary and sufficient condition to en-sure the network connectivity. The algorithm smallminimum-energy communication network (smecn) im-proves the previous work by increasing the networklifetime [8].

2.2 Minimizing interferences

It has been shown that reducing the transmission pow-ers does not imply reducing interferences [9]. So re-searchers have focused their work on the interferencesthemselves. A first interesting result is that using vary-ing emitting power can increase the network capacity[1]. This capacity can be even more increased if weconsider a grid topology instead of a random one [10].

To be able to reduce interferences, it is first ap-propriate to quantify them. Several works propose toevaluate the interference of a link by computing thenumber of links which cannot be used at the same time[9, 11]. Based on this definition, the interference ofa topology is deduced from the link with the highestinterference.

The algorithm low interference forest establisher(life) computes a set of trees sufficient to ensure that thegraph is connected and the interference is minimized[9]. The principle is based on the Kruskal algorithm[12]. More precisely, the topology graph G = (V, E) isreplaced by G = (V, Elife) as follows. Elife = ∅ initially.Let l = ((s, d), p) ∈ E be the link between s and d withthe transmission power p. Recursively, link l which hasthe lowest interference is added to Elife (and removefrom E) if it does not exist a path between s and d.

The previous work can be extended considering abounded path length. The algorithm low interferencespanner establisher (lise) [9] minimizes interferencesunder the constraint that the path length does not ex-ceed the length of the shortest path times a parameter.Thus, instead of aiming at reducing the interference ofthe link with the highest one, it reduces the averageinterference of links [11].

However, the definition of interference in previouswork is not always pertinent. Indeed, in practice, theinterference of a given link depends not only to thenumber of links interfering with it but also to the traffictransmitted by these other links. Hence, the problemmust be studied from a general point of view whereroutes and emitting powers are determined by an op-timization algorithm. The size of the formulation beingexponential with the network size, the resolution needsimportant computing resources.

3 Solution

In this paper, we present a traffic-based topology con-trol solution in order to minimize the global energyconsumption while increasing the aggregate throughputof flows. For this, we consider that the traffic is notuniformly distributed among the links and that the min-imization of transmission powers does not reduce inter-ferences. The problem consists of determining the besttopology, that is to say the best allocation vector for thetransmission powers satisfying the flows requirements.We first present the network and interferences modelswe consider. Then, we define the objective function tominimize. Finally, we propose several algorithms fordifferent contexts.

3.1 Network and interferences models

As defined in Section 2, the classical representationof a network topology is a directed graph G = (V, E)

where vertexes are nodes and edges are transmissionlinks. We assume that each node has at its disposal a setof transmission powers, denoted P. When there existtwo links between the same two nodes with differenttransmission powers, we only consider this with thelowest one.

The whole network interferences can be representedby a conflict graph CG = (V ′, E′) which is an undi-rected graph where V ′ = E and where edges belongingto E′ join interfering links. A clique C of CG is a set oflinks interfering with each other. A maximal clique isa clique where it is impossible to add another link. Wedenote C the set of the maximal cliques. Determiningthe cliques of a graph is NP-complete, but polynomialheuristics exist [13].

The classical model used to compute the conflictgraph is the N-hop interference model. For instance,when N = 2, a node interferes with its neighbors andthe neighbors of its neighbors. This model is commonlyused by considering constant transmission powers andundirected links.

We redefine the N-hop interference model in orderto remove these assumptions. Indeed, we consider thattwo vertexes of the conflict graph, which are two linksl = ((s, d), p) and l′ = ((s′, d′), p′), are connected in CGif and only if there exists a route of at most N hops withtransmission powers lower than (a) max(p, p′) betweens and s′, (b) p between s and d′, or (c) p′ between s′and d.

Moreover, we adopt the following additional nota-tions in the rest of this paper. Let F be the set of flowscoexisting in the network, R a set of routes for theseflows, and R the set of all the sets of feasible routes.

184 Ann. Telecommun. (2012) 67:181–189

Then, ul,R represents the bandwidth proportion con-sumed on link l by the flows belonging to F and follow-ing the routes of R. Likewise r f,R is the route defined inR for flow f ∈ F.

3.2 Maximization of the flow acceptance rate

These last years, researchers have focused on the ad-mission control in multi-hop wireless networks, andthe following constraint has been established: ∀C ∈C,

∑l∈C ul,R ≤ β, with β = 1 or 0.46 for a necessary or

a sufficient constraint respectively [14]. We have shownin [15] how to improve these results by considering amore accurate model.

Maximizing the number of accepted flows comes todetermine the set of routes R such that the previousconstraint is satisfied. In other words, the clique whosethe cumulative load on its links is maximal has tomaintain a utilization ratio less than or equal to β, thatis: maxC∈C{∑l∈C ul,R} ≤ β.

This leads to determine R minimizing the utilizationof the clique having the maximum load:

arg minR∈R

{

maxC∈C

{∑

l∈C

ul,R

}}

. (1)

For instance, when the links interfere with eachothers, we have C = V ′. Thus, function (1) becomes:arg minR∈R{∑l∈V ′ ul,R}. It means that the overall trans-missions have to be minimized, so that the shortest pathfirst algorithms are the most pertinent. Obviously, thegeneral problem is more complex, since the allocationvector for the transmission powers depends on the flowreservations. For example, Fig. 1 represents a topologyof five nodes and the associated conflict graph. Eachnode has two levels of transmission power, p1 and p2.When only one flow f1 exists in the network from node3 to node 5, the use of the maximal power enables

to reach a throughput equal to the capacity of thechannel, denoted W. With another flow f2 from 1 to2, the use of the minimal power for f1 leads to the bestoverall throughput (W/2 for f1 and W for f2) due tointerferences, though the route from 3 to 5 is not theshortest one.

To determine the set of routes maximizing the flowacceptance rate, we first propose to compute the op-timal solution considering a global knowledge of thenetwork. Then, we propose a local optimization, in acentralized and a distributed manner.

3.3 Global optimization

Due to the exponential size of the solution space, theglobal optimization is particularly complex. The ideais to obtain reference values in order to evaluate theother algorithms. In Section 4, we will compute allthe solutions when the network is small, thanks to thefollowing exhaustive algorithm. When the number ofnodes and the number of flows increase, we will apply ameta-heuristic widely used in practice, that is, simulatedannealing.

To perform the global optimization, we save datain a three-dimensional array, denoted A. The first di-mension corresponds to the flows (F). The second onecontains all the feasible routes for each flow (R). Thelast one is for the maximal cliques of the conflict graph(C). The array value A f,r,C is the bandwidth utilizationof flow f on route r in clique C: A f,r,C = ∑

l∈C∩rb f

W ,with b f the requested bandwidth of f .

The algorithm aims at finding a combination ofroutes minimizing the load of the clique the most used:

arg minR∈R

⎧⎨

⎩maxC∈C

⎧⎨

⎩

∑

f∈F

A f,r f,R,C

⎫⎬

⎭

⎫⎬

⎭. (2)

Fig. 1 Topology of five nodeswith its conflict graph

interference area of node 3 with p2

with p1

3 4 51 2p2

p1 p1 p1

((3,4), p1)

((1,2), p1)((3,5), p2)Conflict graph:

((4,5), p1)

Clique C2Clique C1

Ann. Telecommun. (2012) 67:181–189 185

This is equivalent to the objective defined in Section 3.2(function (1)), as

∑f∈F A f,r f,R,C=

∑l∈C ul,R.

3.4 Local optimization

The previous algorithm is interesting since it gives oneof the optimal solutions concerning the allocation vec-tor for the transmission powers. But in practice, fastand simple algorithms are required in order to takeinto account the network changes (topology, traffic,interferences, etc.) and the nodes constraints (energy,processor, memory, etc.). Moreover, a new event mustnot generate a large succession of changes into thenetwork. Hence, we propose to perform a local opti-mization based on an initial solution given by a shortestpath first algorithm. The local optimization does notrequire cooperation between nodes, each one having toreach the objective within its neighborhood, apart fromthe other nodes.

Our algorithm considers a set of initial routes Ri andapplies the four following steps:

1. Compute all the sets of feasible routes whose thelengths are shorter than or equal to these of initialroutes times a parameter β. Let Rl be the set ofthese sets.

2. Compute all the array values (A f,r,C), that is, foreach flow in F, each set of routes in Rl and eachclique in C.

3. Compute Rv , the set of the next possible solutions:Rv = {R|R ∈ Rl ∧ ∃! f ∈ F, r f,R �= r f,Ri}.

4. Let Cmax =arg maxC∈C{∑ f∈F A f,r f,Ri ,C} be the clique

the most used with the set of routes Ri. If thereexists a set R ∈ Rv such that the most used clique’sload is lower than the load of Cmax, that is,maxC∈C{∑ f∈F A f,r f,R,C} <

∑f∈F A f,r f,Ri ,Cmax , then

replace Ri with R and repeat from step 3.Otherwise, Ri leads to the local minimum.

3.5 Distributed optimization

The local optimization enables to reduce the complex-ity compared to the global one. Now, we focus on thelocal minimum computation in a distributed manner.Hence, contrary to the previous subsection, we considerthat a node only knows some of the cliques and flowswithin its neighborhood.

As defined in [16], the set of cliques known by noden is Cn. This set contains the cliques of C where thelinks for which the source emissions have no impact onthe channel of n are removed. Moreover, the networkcontains |F | flows for which the routing algorithm hascomputed the initial routes, denoted Ri. Let Fn be the

set of flows known by node n, which are those beingtransferred within its interference area. If Ln denotesthe set of links whose emissions possibly interfere withthe channel of node n, that is Ln = ⋃

C∈CnC, then we

get: Fn = { f | f ∈ F ∧ r f,Ri ∩ Ln �= ∅}.Each node has the responsibility of its transmission

power, that is to say the next hop for flows transmittedor relayed. Therefore, it can only act on these flows.We denote F I

n the set of invariant flows for n and FVn

this of flows whose the route can be modified by n.These two sets are disjoined and their union gives Fn.Hence, we have: F I

n = Fn \ FVn and FV

n = { f | f ∈ Fn ∧∃l = ((s, d), p) ∈ r f,Ri , s = n}.

Therefore, a set of feasible routes seen by n for allthe flows is limited, since a first part of the routes isnot modifiable by n and on the other part, node ncannot influence the portion of routes leading to it. Wedefine Rn, the set of the sets of feasible routes seen by n,as follows:

Rn =

⎧⎪⎪⎨

⎪⎪⎩

R

∣∣∣∣∣∣∣∣

R ∈ Rl∧∀ f ∈ F I

n, r f,R = r f,Ri \ (E \ Ln)∧∀ f ∈ FV

n , r f,R = r f,R \ (E \ Ln)∧∀ f ∈ FV

n , ∃l = ((s, d), p) ∈ r f,R, s = n

⎫⎪⎪⎬

⎪⎪⎭

The distributed algorithm has to compute the routecombination R ∈ Rn reducing the load of the most usedlocal clique. More precisely, any node n maintains athree dimensions array, denoted An, whose the valuesare An, f,r,C = ∑

l∈C∩rb f

W . By applying our local viewnotations to function (2), the objective is to determine:arg minR∈Rn{maxC∈Cn{

∑f∈Fn

An, f,r f,R,C}}.As for the local optimization presented in the previ-

ous subsection, in every node n, our distributed algo-rithm considers a set of initial routes Ri and applies thefour following steps:

1. Compute all the local sets of feasible routes. Let Rn

be the set of these sets.2. Compute the local array values (An, f,r,C) for each

flow, each set of routes and each clique.3. Compute Rn,v , the set of the next possible solu-

tions:Rn,v = {R|R ∈ Rn ∧ ∃! f ∈ F, r f,R �= r f,Ri}.

4. Let Cn,max = arg maxC∈Cn{∑

f∈FnAn, f,r f,Ri ,C

} be theclique of Cn the most used with the set of routes Ri.If there exists a set R ∈ Rn,v minimizing the mostused clique’s load, then replace Ri with R andrepeat from step 3. Otherwise, the local minimumis reached.

A node starts this distributed algorithm each time acondition’s changing occurs. Hence, each node evalu-ated a change of condition permanently, from routing

186 Ann. Telecommun. (2012) 67:181–189

Table 1 Simulation parameters

Duration 120 sArea From 350 × 350 to 620 × 620 m2

Number of nodes From 10 to 30Number of power levels, |P| From 1 to 8

information and current transmission powers, possibil-ities to improve performances within its area. Then,in the best cases, results obtained with this algo-rithm are as well as those provided by the centralizedoptimization.

4 Simulation results

The proposed algorithms are evaluated by simulations.The simulations use the Mesh WiMAX MAC layer(IEEE 802.16j). We consider that all the nodes re-ceive knowledge on the topology and the reservationrequests made by their neighbors. This is not a hardassumption since many routing protocols could dissem-inate this kind of information.

The simulations are done in ns-2 using the extensionNS2mesh80216 developed in [17, 18]. We add to thisextension the topology and admission control and manyrouting algorithms. For the graph calculation in thesimulations, we use the library Boost to enhance thesimulation performance.

Each simulation uses 800 runs with different seedsand calculate confidence intervals of 95%. Flows arecreated randomly during the simulation and have aninfinite duration. Simulation parameters are given inTable 1.

The admission control algorithm accepts a flow onlyif the requested constraints are satisfied. The flowsgenerate CBR traffic.

In each scenario, we represent five results accordingto five different topology-based algorithms:

• spf. It represents the shortest path algorithm ap-plied with different transmission powers. In a gen-eral case, the algorithm tends to use higher powers.

• cbtc. It minimizes the transmission powers con-sidering a geometric criterion. The algorithm isintroduced in Section 2. We consider in the simu-lation an angle of 5π/2 to guarantee the networkconnectivity.

• life. It consists in minimizing the interferences byeliminating the links that add a maximum of in-terferences while maintaining a connected networkgraph. The algorithm is also introduced in the re-lated work section.

• max-far. It finds the global minimum of the func-tion maximizing the flows’ acceptation rate (idealsolution).

• max-far-approx. It calculates a local minimum ofthe function maximizing the flows’ acceptance rate.The algorithm works centrally and starting from theinitial solution given by spf.

• max-far-approx-dis. A distributed approach ofmax-far-approx.

Figure 2 represents the acceptation rate of the flowswhen the size of the network varies from 10 to 30 nodeswith the same density (i.e., the area is varying from354 × 354 to 612 × 612 m2). Each node could selectbetween four different transmission powers. The figure

Fig. 2 Flows’ acceptationrate according to the networksize

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

10 15 20 25 30

Acc

epta

tion

Rat

e

Number of Nodes

spfcbtc

life

max−farmax−far−approx

max−far−approx−dis

Ann. Telecommun. (2012) 67:181–189 187

Fig. 3 Average length of apath (source to destination)

1

1.5

2

2.5

3

3.5

4

10 15 20 25 30

Ave

rage

leng

th o

f flo

ws’

path

s

Number of Nodes

spfcbtc

life

max−farmax−far−approx

max−far−approx−dis

shows that the number of accepted flows decreaseswith the size of the network. Our proposed solutionincreases the number of accepted flows and is very closeto the ideal one. This obtained gain is more pronouncedwhen the number of nodes in the network increases.

Figure 3 depicts the average size of a route betweenthe source and the destination of a flow. From the figure,one can observe that, except life, all the algorithmsprovide small paths. Since life gives priorities for lowpowers, the number of hops in a route becomes high.

In [19], the authors propose an upper bound on theflow bitrates in the network where the positioning ofnodes and traffic in the network is ideal. Consideringthe previous simulation scenario, the number of flows

|(F)| and the capacity of the channel W are constant.As the density is constant, the area is proportional tothe number of nodes. We thus have an increasing flowcapacity of an order of �(

√|V|). However, in randomnetworks, it has been shown that the achievable capac-ity approximates �(W/

√(|V|)) [20], which corresponds

to our results. Indeed, increasing the number of nodesallows a higher overall capacity, but in return, theaverage length of flows increases and the flow thereforeuses a larger part of the overall capacity.

Figure 4 displays the flows’ acceptation rate accord-ing to the transmission powers. The network contains20 nodes in an area of 500 × 500 m2. The figure showsthat increasing the transmission power will increase the

Fig. 4 Average acceptationrate as a function of thetransmission power

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

140 160 180 200 220 240 260

Acc

epta

tion

Rat

e

Coverage area (m)

spfcbtc

life

max−farmax−far−approx

max−far−approx−dis

188 Ann. Telecommun. (2012) 67:181–189

Fig. 5 Flows’ acceptationrate when the density varies

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

10 15 20 25 30

Acc

epta

tion

Rat

e

Number of Nodes

spfcbtc

life

max−farmax−far−approx

max−far−approx−dis

amount of traffic in term of number of flows. life min-imizes the interferences and did not take into accountthe transmission power and thus his acceptation rate isconstant. The same phenomena of the previous figureis reproduced where the number of flows will decreasewhen we augment the length of paths. Having a lowtransmission, power increases the number of links in apath.

On Fig. 5, we plot the flows’ acceptation rate accord-ing to the network density. The surface is 500 × 500 m2

including a variable number of nodes (from 10 to 30).Nodes could use four different transmission powers.We observe that the max algorithms allow more trafficin the network when the density increases. Both cbtcand life provide an opposite performance. This ob-servation is due to the fact that the max algorithmslook always to use the optimal transmission power toincrease the amount of traffic. When the network isdense, the diversity in number of links is higher and theopportunity to find an optimal path is higher.

spf looks always to the shortest path which couldbe found with a certain density, and then increasingthe number of nodes will not modify this calculation.cbtc and life reduce the transmissions power and henceincrease the path’s lengths which converge to the previ-ous simulations where the central links in the networkare overloaded.

5 Conclusion

Multi-hop wireless networks suffer from the problem ofsharing sparse radio resources. Controlling the interfer-

ences is an efficient mean to optimize the global energyconsumption while improving the network capacity.Interferences are generated by simultaneous transmis-sions which are in parallel to increase the amount oftransmissions and the global traffic. Varying the trans-mission powers of the nodes modifies the topology ofthe network and allows to minimize the interferencesand thus the consumed energy while optimizing theresources sharing. In this paper, we proposed a newmodel to consider the interferences when modifying thetransmission powers. We also proposed a distributedalgorithm of the model to reduce its computational costand facilitate its implementation. Simulation resultsshowed the gains that could be obtained by the topol-ogy control and confirm the advantages of a dynamiccontrol of the transmission powers.

Acknowledgments The authors would like to thank SimonOdou for his assistance with this work.

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