International audienceLes réseaux de capteurs sont utilisés afin de collecter un grand nombre de données de l'environnement. Ces données sont délivrées au travers de l'interface de communication sans fil des capteurs par des communications multi-sauts jusqu'au puits traitant l'information. Le placement de ce puits influe sur les performances des réseaux de capteurs en ce qui concerne le délai et la consommation énergétique, en particulier celle des capteurs intermédiaires servant de relais. L'optimisation de la collecte des données est donc un aspect important dans l'étude des réseaux de capteurs sans fil. Notre article s'intéresse à la collecte de données utilisant des puits mobiles. Nous proposons un modèle permettant d'étudier le compromis entre la consommation énergétique du réseau et le délai de collecte des données

Caillouet, Christelle

Razafindralambo, Tahiry

INRIA a CCSD electronic archive server

HAL Id: inria-00586681https://hal.inria.fr/inria-00586681Submitted on 18 Apr 2011HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Compromis énergie-délai pour la collecte de donnéesdans les réseaux de capteursChristelle Caillouet, Tahiry RazafindralamboTo cite this version:Christelle Caillouet, Tahiry Razafindralambo. Compromis énergie-délai pour la collecte de donnéesdans les réseaux de capteurs. 13es Rencontres Francophones sur les Aspects Algorithmiques de Télé-communications (AlgoTel), 2011, Cap Estérel, France. ￿inria-00586681￿Compromis énergie-délai pour la collecte dedonnées dans les réseaux de capteursChristelle Caillouet2 †and Tahiry Razafindralambo11INRIA Lille - Nord Europe, France2RWTH Aachen University, AllemagneLes réseaux de capteurs sont utilisés afin de collecter un grand nombre de données de l’environnement. Ces donnéessont délivrées au travers de l’interface de communication sans fil des capteurs par des communications multi-sautsjusqu’au puits traitant l’information. Le placement de ce puits influe sur les performances des réseaux de capteurs ence qui concerne le délai et la consommation énergétique, en particulier celle des capteurs intermédiaires servant derelais. L’optimisation de la collecte des données est donc un aspect important dans l’étude des réseaux de capteurs sansfil. Notre article s’interesse à la collecte de données utilisant des puits mobiles. Nous proposons un modèle permettantd’étudier le compromis entre la consommation énergétique du réseau et le délai de collecte des données.Keywords: optimisation multi-objectif, programmation linéaire, réseaux de capteurs, placement1 IntroductionWireless sensor networks (WSNs) have received a lot of attention in recent years due to their potentialapplications in various areas such as environment monitoring or tracking [BISV08]. In order to get usefuland up-to-date information from the environment, the WSN is composed of a large number of low-capacity(processor, memories, battery) sensors. Unfortunately, the amount of data in the network increases with thenumber of sensors. The data has to be sent to a central entity, called sink, for storage and processing. Thanksto the wireless communication capabilities and the protocols developed, multi-hop transmissions can beused to route data from a sensor to the sink if no direct connection is available. However, this classical N to1 communication paradigm rapidly consumes the energy of intermediate sensors and provides unfair delaydistribution depending on the distance to the sink [KR09]. Data collection is therefore a key issue in WSNs.Various solutions have been proposed to extend the network lifetime and reduce delay for data collection.In [CCDF09], authors present an integer linear program for placing a minimum number of gateways andensure connectivity among them and the sink to form a wireless mesh network to deliver the data. The useof mobile sinks instead of static sinks to collect the data is more efficient and significantly increases thelifetime of the WSN [LH05]. In their work, the location of the mobile sinks is periodically computed sothat the network lifetime is maximized. Some research efforts have focused on approaches either minimi-zing the energy consumed by the sensors [GDPV03], or maximizing the global network lifetime [BST09].Considering the route of the mobile sinks in WSNs instead of its periodical relocation has not been addres-sed in previous work to the best of our knowledge. Our purpose is to determine where to place a set ofgateways to collect the data of a region in the WSN field, and compute the route of a mobile sink movingalong the gateways to gather data from the sensors. To answer these questions, we propose a Multiobjec-tive Linear Program (MLP) that allows to study the trade-offs between the length of the route of a mobilesink associated with a computed gateway placement, and the overall energy consumption in a WSN. Themain contribution is to give a multi-criteria vision of the data collection problem in WSNs. As far as weknow there is no multiobjective analysis in this subject. Unlike the works proposed in the literature, theresults of this paper are twofold. First, we tackle the problem of optimal placement of data gateways in anenergy-efficient WSN. Second, we optimize the data collection tour by the sink to minimize the delay.†Financée par une bourse Post-doctorale de la Fondation allemande Alexander von Humboldt.Christelle Caillouet and Tahiry Razafindralambo2 Problem definitionGiven a WSN represented by a set of sensor nodes S , we define a set of candidate sites CS for thegateway locations. We want each sensor to be associated with its closest gateway : Oi is the vector ofordered reachable gateways for sensor i. If j < k, then dist(i, j)≤ dist(i,k) and Oi( j) is before Oi(k) in thevector, where dist(i, j) is the euclidean distance between i and j. Sets Ji are index sets of vector Oi.We assume the routing in the WSN (from sensors to gateways) given so that our model is independentof a specific routing strategy. P is the set of paths between the sensors and the candidate sites. O(p) (resp.D(p)) denotes the source node (resp. the destination) of path p ∈ P. From P, we introduce the binary matrixC to indicate the sensor-gateway connectivity : Cic is 1 if it exists a route between sensor i and gateway c.The energy model considered for the sensors is based on the first order radio model described in [HCB00].A sensor consumes εelec = 50 nJ/bit to run the transmitter or receiver circuitry, εamp = 100 pJ/bit/m2for the transmitter amplifier. Thus, to receive a k-bit message, sensor i consumes Er = εeleck, and Et =εeleck+ εampdist2(i, j)k to transmit this message to a neighbor j.Emax is a decision variable of our MLP corresponding to the amount of energy spent by a sensor. We thenhave the binary variables xi j, y j, χi j indicating respectively if sensor i is assigned to gateway j, if a gatewayis installed at candidate site j, and if two gateways are installed at candidate sites i and j and so that link(i, j) is selected for the route of the mobile sink.To evaluate the overall quality of our solutions, we use the following metrics :– MinMaxE ( f 1) : Balancing the energy spent by the sensors, i.e. WSN lifetime maximization. From theenergy model presented above, we seek to minimize the maximum energy spent by each sensor node.– MinRoute ( f 2) : Minimizing the route of the mobile sink between the different installed gateways.The optimization problem of placing the gateways such that we jointly minimize the length of the mobilesink route, and the energy spent by the sensor nodes is the following :(i) min f 1 = Emax(ii) min f 2 = ∑i∈CS∑j∈CSdist(i, j)χi j (1)∑j∈CSxi j = 1 ∀i ∈ S (2)xi j ≤Ci jy j ∀i ∈ S , j ∈ CS (3)yOi(k)+ ∑h∈Ji,h>kxiOi(h) ≤ 1 ∀i ∈ S (4)∑p ∈ P, i ∈ p | i 6= O(p)(Er +Et) xO(p)D(p)+ ∑p ∈ P | i = O(p)Et xiD(p) ≤ Emax ∀i ∈ S (5)∑i∈CSχi j = y j, ∑j∈CSχi j = yi ∀i, j ∈ CS (6)Obj. (1) minimizes (i) the maximum energy consumed by the sensors, and (ii) the length of the route ofa mobile sink along the placed gateways. Constraints (2) and (3) ensure that each sensor must be associatedwith an installed gateway. Constraints (4) force each sensor to be assigned to its closest gateway. Constraints(5) minimize the maximum amount of energy spent by the sensors, i.e. the sum of the forwarded trafficfrom other sensors and its own traffic. Equalities (6) force the mobile sink to visit all the chosen gatewaysto collect data generated by the sensors.3 Performance evaluationWe present results obtained with our MLP on networks of size between 50 and 250 sensors in whichthe sensor’s position is randomly chosen in a unitary square area. We use two policies of candidate sitelocations. First, we divide the area into equal squares and place one candidate site in the center of eachsquare. In this way, the candidate sites form a regular grid. Second, we choose randomly the location of thecandidate sites in the area. We solved the proposed MLP with these instances using IBM Cplex solver onan INTEL Core 2 2.4 GHz with 2 Gb of memory. Each result has been averaged on 10 instances.MinRoute0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4MinMaxE (mJ)00.40.81.21.622.42.83.23.6250 sensors200 sensors150 sensors100 sensors(a) Different size and |CS |= 9.MinRoute0 0.3 0.6 0.9 1.2 1.5 1.8MinMaxE (mJ)00.20.40.60.811.21.41.61.822.236 gateways25 gateways16 gateways9 gateways(b) Different number of candidate sites and |S |= 50.FIGURE 1: Pareto fronts obtained for the random networks tested.Combining the two metrics of our MLP is not relevant. Indeed, there exists confliction between routelength and energy consumption, i.e., pursuing the optimization of the route length of the mobile sink inex-tricably damages the performance of energy spent by the sensors. Saving energy enforces to deploy moregateways in the network, thus increasing the length of the route for the mobile sinks. The main idea to studythe trade-offs between MinMaxE and MinRoute is to find out the possible non-dominated solutions of themulti-objective optimization problem. A solution is non-dominated if it is not possible to improve one of themetrics without worsening at least one another. The set of non-dominated solutions is the Pareto front, thatprovides a set of solutions that can be chosen depending on the application requirements. In order to gene-rate solutions on the Pareto front, we use the ε-constraint method that transforms the multiobjective probleminto a sequence of parameterized single-objective problems such that the optimum of each single-objectiveproblem corresponds to a Pareto-optimal solution.3.1 Effect of candidate sites and network densityLimiting the energy spent by each sensor increases the length of the mobile sink route (see Fig. 1(b)and 1(a)). Moreover, the number of installed gateways strongly depends on the limit of the energy spent. Inparticular, when we focus on energy (optimizing only MinMaxE, without any constraints on the number ofdeployed gateways) the optimal solution minimizes the energy spent by each sensor essentially by limitingits forwarding traffic. The gateway placement thus verifies that each sensor is a neighbor of its associatedgateway (when possible). When the size of the network increases, then the energy consumption of the sensornodes also increases (see Fig. 1(a)). The total traffic is more important, so the sensors have more forwardingtraffic to relay which increases their load. When the energy is limited to Emax = 2 mJ for each sensor, thelength of the mobile sink route also increases with the network size. The average route length of the mobilesink equals respectively 0.33, 0.47, 0.6, and 0.65 for a WSN of 100, 150, 200, and 250 nodes. However,the maximum amount of energy spent by the sensor nodes decreases when the number of candidate sitesin the network increases as depicted in Fig. 3. On one hand, placing a gateway reduces the relaying trafficand the energy spent. On the other hand, the route length of the mobile sink increases, especially when theenergy consumed by each sensor is low. This assertion is confirmed by Fig. 4 that depicts the number ofdeployed gateways depending on the maximum energy spent by the sensors. The location of the gatewaysamong the WSN is also important regarding the network lifetime and the delay of data collection.3.2 Sensor’s loadWe define the sensor’s load as the number of paths going through a sensor : Load(i) =∑p∈P |i∈p xO(p)D(p),∀i ∈ S . The most loaded sensor is therefore the one that has the maximum number paths going through it :Load(S) = maxi∈S Load(i). Fig.4 presents the value of Load(S) in function of the number of deployedgateways. This confirms that deploying more gateways allows to limit the amount of forwarding traffic ateach sensor. Another way of limiting the sensor’s load is to fairly deploy the gateways among the WSN.When the candidate sites are regularly placed in the area (i.e. the regular policy), then the load is reducedin comparison to a random placement (see Table 1). Load(S) is the mean value Load(S) over the ParetoChristelle Caillouet and Tahiry RazafindralamboTopology Grid placement Random placement|S | |CS | f1∗ (mJ) f 2∗ Dpl. Gtw Load(S) f 1∗ (mJ) f 2∗ Dpl. Gtw Load(S)50 9 0.45 0.5 3.5 8.93 0.45 0.21 2.96 13.2450 16 0.15 0.4 4.25 8 0.35 0.22 4.63 9.83100 9 0.45 0.5 3.33 10.2 0.65 0.28 3.71 21.26100 16 0.35 0.4 4.81 9.87 0.65 0.21 4 21150 9 0.75 0.5 2.85 17 0.95 0.08 3.05 27.88150 16 0.45 0.4 4.24 12.76 0.75 0.01 4.41 20.53200 9 0.85 0.5 3.9 16.3 0.95 0.22 3.17 20.79200 16 0.25 0.4 4.77 13.5 1.05 0.11 3.53 27.4TABLE 1: Comparison between regular and random placement for the candidate sites.MinMaxE (mJ)0 0.5 1 1.5 2 2.5 3 3.5Nb of installed gateways123456789101112131415250 nodes200 nodes150 nodes100 nodes50 nodes(a) Deployed gateways vs. Emax.Nb of installed gateways1 3 5 7 9 11 13 15Nb paths on most loaded sensor051015202530 250 nodes200 nodes150 nodes100 nodes50 nodes(b) Sensors load vs. gateways.FIGURE 2: Results for random networks with 25 candidate sites.optimum. This value is always greater when the gateway placement is performed among candidate siteschosen randomly, leading to more loaded sensors.4 ConclusionIn this paper, we present a framework for efficient data collection in WSNs. We develop a multi-objectivelinear program with two functions to evaluate the trade-off between the energy spent by the sensors, andthe length of the route of mobile sinks collecting data at gateways that we jointly deploy. We show that thesensors’ load decreases with the number of gateways until a given threshold when it remains stable. Thisallows to save energy in the WSN, but, when the number of deployed gateways is important, the mobilesink has a longer route to perform, therefore increasing the delay of data collection until processing. Thistrade-off must be taken into consideration for an optimal WSN design. Our work provides solutions thatallow decision makers to optimally design the data collection plan in WSN with mobile sinks.Références[BISV08] G. Barrenetxea, F. Ingelrest, G. Schaefer, and M. Vetterli. The hitchhiker’s guide to successful wirelesssensor network deployments. In ACM SenSys, pages 43–56, 2008.[BST09] L. Ben Saad and B. Tourancheau. Multiple mobile sinks positioning in wireless sensor networks for buil-dings. In SENSORCOMM, pages 264–270, 2009.[CCDF09] A. Capone, M. Cesana, D. Donno, and I. Filippini. Optimal placement of multiple interconnected gatewaysin heterogeneous wireless sensor networks. In IFIP-TC 6 Networking Conference, pages 442–455, 2009.[GDPV03] S.R. Gandham, M. Dawande, R. Prakash, and S. Venkatesan. Energy efficient schemes for wireless sensornetworks with multiple mobile base stations. In IEEE GlobeCom, pages 377–381, 2003.[HCB00] W.R. Heinzelman, A. Chandrakasan, and H. Balakrishnan. Energy-efficient communication protocol forwireless micro sensor networks. In HICSS, pages 3005–3010, 2000.[KR09] F. Khadar and T. Razafindralambo. Performance evaluation of gradient routing strategies for wirelesssensor networks. In IFIP-TC6 Networking Conference, pages 535–547, 2009.[LH05] J. Luo and J.-P. Hubaux. Joint mobility and routing for lifetime elongation in wireless sensor networks. InIEEE INFOCOM, pages 1735 – 1746, 2005.

Compromis énergie-délai pour la collecte de données dans les réseaux de capteurs

HAL - Lille 3

Compromis e´nergie-de´lai pour la collecte de donne´esdans les re´seaux de capteursChristelle Caillouet, Tahiry RazafindralamboTo cite this version:Christelle Caillouet, Tahiry Razafindralambo. Compromis e´nergie-de´lai pour la collecte dedonne´es dans les re´seaux de capteurs. Ducourthial, Bertrand et Felber, Pascal. 13es RencontresFrancophones sur les Aspects Algorithmiques de Te´le´communications (AlgoTel), 2011, CapEste´rel, France. 2011. <inria-00586681>HAL Id: inria-00586681https://hal.inria.fr/inria-00586681Submitted on 18 Apr 2011HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Compromis e´nergie-de´lai pour la collecte dedonne´es dans les re´seaux de capteursChristelle Caillouet2 †and Tahiry Razafindralambo11INRIA Lille - Nord Europe, France2RWTH Aachen University, AllemagneLes re´seaux de capteurs sont utilise´s afin de collecter un grand nombre de donne´es de l’environnement. Ces donne´essont de´livre´es au travers de l’interface de communication sans fil des capteurs par des communications multi-sautsjusqu’au puits traitant l’information. Le placement de ce puits influe sur les performances des re´seaux de capteurs ence qui concerne le de´lai et la consommation e´nerge´tique, en particulier celle des capteurs interme´diaires servant derelais. L’optimisation de la collecte des donne´es est donc un aspect important dans l’e´tude des re´seaux de capteurs sansfil. Notre article s’interesse a` la collecte de donne´es utilisant des puits mobiles. Nous proposons un mode`le permettantd’e´tudier le compromis entre la consommation e´nerge´tique du re´seau et le de´lai de collecte des donne´es.Keywords: optimisation multi-objectif, programmation line´aire, re´seaux de capteurs, placement1 IntroductionWireless sensor networks (WSNs) have received a lot of attention in recent years due to their potentialapplications in various areas such as environment monitoring or tracking [BISV08]. In order to get usefuland up-to-date information from the environment, the WSN is composed of a large number of low-capacity(processor, memories, battery) sensors. Unfortunately, the amount of data in the network increases with thenumber of sensors. The data has to be sent to a central entity, called sink, for storage and processing. Thanksto the wireless communication capabilities and the protocols developed, multi-hop transmissions can beused to route data from a sensor to the sink if no direct connection is available. However, this classical N to1 communication paradigm rapidly consumes the energy of intermediate sensors and provides unfair delaydistribution depending on the distance to the sink [KR09]. Data collection is therefore a key issue in WSNs.Various solutions have been proposed to extend the network lifetime and reduce delay for data collection.In [CCDF09], authors present an integer linear program for placing a minimum number of gateways andensure connectivity among them and the sink to form a wireless mesh network to deliver the data. The useof mobile sinks instead of static sinks to collect the data is more efficient and significantly increases thelifetime of the WSN [LH05]. In their work, the location of the mobile sinks is periodically computed sothat the network lifetime is maximized. Some research efforts have focused on approaches either minimi-zing the energy consumed by the sensors [GDPV03], or maximizing the global network lifetime [BST09].Considering the route of the mobile sinks in WSNs instead of its periodical relocation has not been addres-sed in previous work to the best of our knowledge. Our purpose is to determine where to place a set ofgateways to collect the data of a region in the WSN field, and compute the route of a mobile sink movingalong the gateways to gather data from the sensors. To answer these questions, we propose a Multiobjec-tive Linear Program (MLP) that allows to study the trade-offs between the length of the route of a mobilesink associated with a computed gateway placement, and the overall energy consumption in a WSN. Themain contribution is to give a multi-criteria vision of the data collection problem in WSNs. As far as weknow there is no multiobjective analysis in this subject. Unlike the works proposed in the literature, theresults of this paper are twofold. First, we tackle the problem of optimal placement of data gateways in anenergy-efficient WSN. Second, we optimize the data collection tour by the sink to minimize the delay.†Finance´e par une bourse Post-doctorale de la Fondation allemande Alexander von Humboldt.Christelle Caillouet and Tahiry Razafindralambo2 Problem definitionGiven a WSN represented by a set of sensor nodes S , we define a set of candidate sites CS for thegateway locations. We want each sensor to be associated with its closest gateway : Oi is the vector ofordered reachable gateways for sensor i. If j < k, then dist(i, j)≤ dist(i,k) and Oi( j) is before Oi(k) in thevector, where dist(i, j) is the euclidean distance between i and j. Sets Ji are index sets of vector Oi.We assume the routing in the WSN (from sensors to gateways) given so that our model is independentof a specific routing strategy. P is the set of paths between the sensors and the candidate sites. O(p) (resp.D(p)) denotes the source node (resp. the destination) of path p∈ P. From P, we introduce the binary matrixC to indicate the sensor-gateway connectivity :Cic is 1 if it exists a route between sensor i and gateway c.The energy model considered for the sensors is based on the first order radio model described in [HCB00].A sensor consumes εelec = 50 nJ/bit to run the transmitter or receiver circuitry, εamp = 100 pJ/bit/m2for the transmitter amplifier. Thus, to receive a k-bit message, sensor i consumes Er = εeleck, and Et =εeleck+ εampdist2(i, j)k to transmit this message to a neighbor j.Emax is a decision variable of our MLP corresponding to the amount of energy spent by a sensor. We thenhave the binary variables xi j, y j, χi j indicating respectively if sensor i is assigned to gateway j, if a gatewayis installed at candidate site j, and if two gateways are installed at candidate sites i and j and so that link(i, j) is selected for the route of the mobile sink.To evaluate the overall quality of our solutions, we use the following metrics :– MinMaxE ( f 1) : Balancing the energy spent by the sensors, i.e. WSN lifetime maximization. From theenergy model presented above, we seek to minimize the maximum energy spent by each sensor node.– MinRoute ( f 2) : Minimizing the route of the mobile sink between the different installed gateways.The optimization problem of placing the gateways such that we jointly minimize the length of the mobilesink route, and the energy spent by the sensor nodes is the following :(i) min f 1 = Emax(ii) min f 2 = ∑i∈CS∑j∈CSdist(i, j)χi j (1)∑j∈CSxi j = 1 ∀i ∈ S (2)xi j ≤Ci jy j ∀i ∈ S , j ∈ CS (3)yOi(k)+ ∑h∈Ji,h>kxiOi(h) ≤ 1 ∀i ∈ S (4)∑p ∈ P, i ∈ p | i 6= O(p)(Er+Et) xO(p)D(p)+ ∑p ∈ P | i= O(p)Et xiD(p) ≤ Emax ∀i ∈ S (5)∑i∈CSχi j = y j, ∑j∈CSχi j = yi ∀i, j ∈ CS (6)Obj. (1) minimizes (i) the maximum energy consumed by the sensors, and (ii) the length of the route ofa mobile sink along the placed gateways. Constraints (2) and (3) ensure that each sensor must be associatedwith an installed gateway. Constraints (4) force each sensor to be assigned to its closest gateway. Constraints(5) minimize the maximum amount of energy spent by the sensors, i.e. the sum of the forwarded trafficfrom other sensors and its own traffic. Equalities (6) force the mobile sink to visit all the chosen gatewaysto collect data generated by the sensors.3 Performance evaluationWe present results obtained with our MLP on networks of size between 50 and 250 sensors in whichthe sensor’s position is randomly chosen in a unitary square area. We use two policies of candidate sitelocations. First, we divide the area into equal squares and place one candidate site in the center of eachsquare. In this way, the candidate sites form a regular grid. Second, we choose randomly the location of thecandidate sites in the area. We solved the proposed MLP with these instances using IBM Cplex solver onan INTEL Core 2 2.4 GHz with 2 Gb of memory. Each result has been averaged on 10 instances.MinRoute0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4MinMaxE (mJ)00.40.81.21.622.42.83.23.6 250 sensors200 sensors150 sensors100 sensors(a) Different size and |CS |= 9.MinRoute0 0.3 0.6 0.9 1.2 1.5 1.8MinMaxE (mJ)00.20.40.60.811.21.41.61.822.236 gateways25 gateways16 gateways9 gateways(b) Different number of candidate sites and |S |= 50.FIGURE 1: Pareto fronts obtained for the random networks tested.Combining the two metrics of our MLP is not relevant. Indeed, there exists confliction between routelength and energy consumption, i.e., pursuing the optimization of the route length of the mobile sink inex-tricably damages the performance of energy spent by the sensors. Saving energy enforces to deploy moregateways in the network, thus increasing the length of the route for the mobile sinks. The main idea to studythe trade-offs between MinMaxE and MinRoute is to find out the possible non-dominated solutions of themulti-objective optimization problem. A solution is non-dominated if it is not possible to improve one of themetrics without worsening at least one another. The set of non-dominated solutions is the Pareto front, thatprovides a set of solutions that can be chosen depending on the application requirements. In order to gene-rate solutions on the Pareto front, we use the ε-constraint method that transforms the multiobjective probleminto a sequence of parameterized single-objective problems such that the optimum of each single-objectiveproblem corresponds to a Pareto-optimal solution.3.1 Effect of candidate sites and network densityLimiting the energy spent by each sensor increases the length of the mobile sink route (see Fig. 1(b)and 1(a)). Moreover, the number of installed gateways strongly depends on the limit of the energy spent. Inparticular, when we focus on energy (optimizing only MinMaxE, without any constraints on the number ofdeployed gateways) the optimal solution minimizes the energy spent by each sensor essentially by limitingits forwarding traffic. The gateway placement thus verifies that each sensor is a neighbor of its associatedgateway (when possible). When the size of the network increases, then the energy consumption of the sensornodes also increases (see Fig. 1(a)). The total traffic is more important, so the sensors have more forwardingtraffic to relay which increases their load. When the energy is limited to Emax = 2 mJ for each sensor, thelength of the mobile sink route also increases with the network size. The average route length of the mobilesink equals respectively 0.33, 0.47, 0.6, and 0.65 for a WSN of 100, 150, 200, and 250 nodes. However,the maximum amount of energy spent by the sensor nodes decreases when the number of candidate sitesin the network increases as depicted in Fig. 3. On one hand, placing a gateway reduces the relaying trafficand the energy spent. On the other hand, the route length of the mobile sink increases, especially when theenergy consumed by each sensor is low. This assertion is confirmed by Fig. 4 that depicts the number ofdeployed gateways depending on the maximum energy spent by the sensors. The location of the gatewaysamong the WSN is also important regarding the network lifetime and the delay of data collection.3.2 Sensor’s loadWe define the sensor’s load as the number of paths going through a sensor : Load(i) =∑p∈P |i∈p xO(p)D(p),∀i ∈ S . The most loaded sensor is therefore the one that has the maximum number paths going through it :Load(S) = maxi∈S Load(i). Fig.4 presents the value of Load(S) in function of the number of deployedgateways. This confirms that deploying more gateways allows to limit the amount of forwarding traffic ateach sensor. Another way of limiting the sensor’s load is to fairly deploy the gateways among the WSN.When the candidate sites are regularly placed in the area (i.e. the regular policy), then the load is reducedin comparison to a random placement (see Table 1). Load(S) is the mean value Load(S) over the ParetoChristelle Caillouet and Tahiry RazafindralamboTopology Grid placement Random placement|S | |CS | f1∗ (mJ) f 2∗ Dpl. Gtw Load(S) f 1∗ (mJ) f 2∗ Dpl. Gtw Load(S)50 9 0.45 0.5 3.5 8.93 0.45 0.21 2.96 13.2450 16 0.15 0.4 4.25 8 0.35 0.22 4.63 9.83100 9 0.45 0.5 3.33 10.2 0.65 0.28 3.71 21.26100 16 0.35 0.4 4.81 9.87 0.65 0.21 4 21150 9 0.75 0.5 2.85 17 0.95 0.08 3.05 27.88150 16 0.45 0.4 4.24 12.76 0.75 0.01 4.41 20.53200 9 0.85 0.5 3.9 16.3 0.95 0.22 3.17 20.79200 16 0.25 0.4 4.77 13.5 1.05 0.11 3.53 27.4TABLE 1: Comparison between regular and random placement for the candidate sites.MinMaxE (mJ)0 0.5 1 1.5 2 2.5 3 3.5Nb of installed gateways123456789101112131415250 nodes200 nodes150 nodes100 nodes50 nodes(a) Deployed gateways vs. Emax.Nb of installed gateways1 3 5 7 9 11 13 15Nb paths on most loaded sensor051015202530 250 nodes200 nodes150 nodes100 nodes50 nodes(b) Sensors load vs. gateways.FIGURE 2: Results for random networks with 25 candidate sites.optimum. This value is always greater when the gateway placement is performed among candidate siteschosen randomly, leading to more loaded sensors.4 ConclusionIn this paper, we present a framework for efficient data collection in WSNs. We develop a multi-objectivelinear program with two functions to evaluate the trade-off between the energy spent by the sensors, andthe length of the route of mobile sinks collecting data at gateways that we jointly deploy. We show that thesensors’ load decreases with the number of gateways until a given threshold when it remains stable. Thisallows to save energy in the WSN, but, when the number of deployed gateways is important, the mobilesink has a longer route to perform, therefore increasing the delay of data collection until processing. Thistrade-off must be taken into consideration for an optimal WSN design. Our work provides solutions thatallow decision makers to optimally design the data collection plan in WSN with mobile sinks.Re´fe´rences[BISV08] G. Barrenetxea, F. Ingelrest, G. Schaefer, and M. Vetterli. The hitchhiker’s guide to successful wirelesssensor network deployments. In ACM SenSys, pages 43–56, 2008.[BST09] L. Ben Saad and B. Tourancheau. Multiple mobile sinks positioning in wireless sensor networks for buil-dings. In SENSORCOMM, pages 264–270, 2009.[CCDF09] A. Capone, M. Cesana, D. Donno, and I. Filippini. Optimal placement of multiple interconnected gatewaysin heterogeneous wireless sensor networks. In IFIP-TC 6 Networking Conference, pages 442–455, 2009.[GDPV03] S.R. Gandham, M. Dawande, R. Prakash, and S. Venkatesan. Energy efficient schemes for wireless sensornetworks with multiple mobile base stations. In IEEE GlobeCom, pages 377–381, 2003.[HCB00] W.R. Heinzelman, A. Chandrakasan, and H. Balakrishnan. Energy-efficient communication protocol forwireless micro sensor networks. In HICSS, pages 3005–3010, 2000.[KR09] F. Khadar and T. Razafindralambo. Performance evaluation of gradient routing strategies for wirelesssensor networks. In IFIP-TC6 Networking Conference, pages 535–547, 2009.[LH05] J. Luo and J.-P. Hubaux. Joint mobility and routing for lifetime elongation in wireless sensor networks. InIEEE INFOCOM, pages 1735 – 1746, 2005.

Compromis énergie-délai pour la collecte de données dans les réseaux de capteurs

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