Joint Optimization of Data Routing and Energy Routing in Energy-cooperative WSNs

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1 Jont Optmzaton of Data Routng and Energy Routng n Energy-cooperatve WSNs Dongha Da, Hu Feng, Yuedong Xu, Janqu Zhang,BoHu Key Laboratory of EMW Informaton, Fudan Unversty Electronc Engneerng Department, Fudan Unversty No., Handan Rd., Shangha 0433, Chna. Emal: {dda1, hfeng, ydxu, jqzhang01, bohu}@fudan.edu.cn Abstract In today WSNs, sensor nodes are able to obtan energy from ambent wth energy-harvestng components. However, the energy consumpton are dverse across these nodes due to functonal or geographcal varaton, whch may lead to potental energy mbalance n network. In vrtue of recent wreless power transfer WPT) technology, the mbalance can be allevated f all sensor nodes share energy wth each other. In order to acheve the maxmum energetcally sustanable workload, we desgn an energy cooperaton strategy n network by WPT, named energy routng, whch should be jontly optmzed wth data routng smultaneously. An teratve dstrbuted algorthm s developed to acheve the optmal data routng and energy routng solutons, where all sensors only need to exchange local nformaton wth neghbors. Smulaton results show that the proposed algorthm can acheve hgher workload than algorthms wthout energy cooperaton. I. INTRODUCTION Wreless Sensor Networks WSNs) are composed of groups of sensor nodes over a target regon, used for sensng, transmsson and processng data 1]. It has ganed wde attentons n many applcatons, such as envronmental montorng, dsaster survellance, vehcular trackng. In a general applcaton scenaro, sensor nodes collect and transmt data packets to the snk node by multple-hop routng. Therefore, routng polcy has a great nfluence on the energy consumpton dstrbuton among the network, as the energy spent for communcaton s usually much more than that for computng n WSNs ]. Battery-powered sensors may be prohbtvely expensve or even mpossble to replace the batteres, especally n remote locatons. To extend the lfetme of WSN, Chang and Tassulas 3] frst calculate the maxmum lfetme routng network flow) under certan ntal battery level. A mathematcal model ntegratng sensor places, actvty schedules, data routes and trajectory of the moble snk s studed n 4] for maxmzng network lfetme. Wth the rapd development of the energy-harvestng EH) technology 5], energy-harvestng WSN EH-WSN) s proposed to overcome battery lmtatons by extractng energy from ambent renewable sources such as lght, wnd or heat. When a sensor node s energy consumng rate s lower than the energy supplyng rate, t wll keep functonng and have unlmted lfetme, known as energetc sustanablty 6] or energy neutralty 5]. Instead of maxmzng the lfetme, Ambent energy Energyharvestng devce Rechargeable battery Wreless energy transfer unt Energy transmttng Energy recevng Fg. 1. The energy unt of a sensor n EC-EH-WSN energy-aware routng polces for EH-WSN focus on how to maxmze the workload under gven energy-harvestng rate 7], where workload s a metrc on the amount of data gathered n unt tme, or total samplng rate. Related works nclude the energy-opportunstc weghted mnmum energy E-WME) algorthm 8], the randomzed maxflow R-MF) algorthm and the randomzed mnmum path recovery tme R-MPRT) algorthm 6], and so on. However, the energy-harvestng rates among nodes vary across nodes accordng to locaton or envronment deployed, whch leads to the bottleneck effect lmtng the network workload. To allevate ths problem, the concept of energy cooperaton s ntroduced by Gurakan 9] n a relay mode, whch enables a node to share a porton of ts harvested energy wth another one. Energy cooperaton n a network s feasble by wreless power transfer WPT) technques ] of three categores, nductve couplng, EM radaton and recent developed magnetc resonance couplng MRC) 11]. It s notable that MRC can acheve rather hgh effcency for pont-to-pont and pont-to-multpont power tranfer 1] n a few meters dstance, whch presents huge potental for energy cooperaton n md-range network transmsson. Fg.1 llustrates the energy-cooperatve EH-WSN EC-EH-WSN) consdered n ths paper, where all nodes are enabled wth energy harvestng and energy cooperaton functons. Current researches on energy cooperaton manly come from the communcaton feld, such as transmttng power controllng n two-hop relay channels 9], network capacty theory n smultaneous wreless nformaton-and-power transfer scenaro 13] and base staton deployment n cellular network 14], whle there s lttle related research n network contexts. Dfferent from communcaton scenaros, each node

2 n the network can both transfer and receve energy, whch leads to mult-hop energy sharng. Thus, ths paper focuses on the modelng and optmzaton of data flow, energy cooperaton and workload n energetcally sustanable WSNs. The contrbutons of ths paper are summarzed as follows: 1) We ntroduce energy cooperaton nto EH-WSNs to allevate energy mbalance among nodes, so that the network acheves a hgher workload. We nterpret the amount of energy cooperaton as energy routng, and ntegrate t wth data routng n a network workload optmzaton model. ) We propose a dstrbuted algorthm so that each node can compute both routngs only wth local nformaton. Smulaton results show that our jont optmzaton algorthm wll acqure a hgher workload wth the ad of energy cooperaton than conventonal networks wthout energy cooperaton. The rest of ths paper s organzed as follows. In Secton II, we descrbe the system model and establsh the optmzaton problem. We propose the dstrbuted jont optmzaton algorthm n Secton III. The smulaton results are presented n Secton IV. Fnally, some concludng remarks are gven n Secton V. II. MODELING A. System Model We consder an EC-EH-WSN consstng of N sensor nodes and one snk node. Denote V = {1,,..., N} as the set of all sensor nodes. Sensor node collects data perodcally and generates data packets at sample rate r. Two nodes and j can communcate drectly f ther dstance d j s shorter than the maxmum transmsson radus d max. The nodes connected to node wthn one hop are called neghbors, whose set s denoted as N, ncludng the snk node. We assume that there always exsts a path between sensor node and snk node. All the data packets generated at each sensor node should be delvered to the snk node by multple-hop routng. The routng can be seen as a network flow matrx F on average, whose element f j denotes the flow rate from node to node j. Assume that all data sampled by source nodes wll be routed to the snk node wthout data loss. Based on the flow conservaton law, f j = f j r V) 1) The energy consumpton for per unt data transmsson from node to node j s c j, whch s a nonlnear functon of d j, whle the energy consumpton for per unt data recepton s ρ, whch s ndependent of dstance. Let p denote the energy consumpton rate of node, accordng to the power consumpton model n 3], p = ρ f j c j f j V) ) All sensor nodes are equpped wth energy-harvestng devces, whch can harvest energy from the envronment and store t n rechargeable batteres. Because of the random postons, nodes n dfferent envronments have dfferent energy-harvestng rates. The energy-harvestng rate of node s denoted as h. Actually the nstantaneous energy-harvestng rate s dynamc and stochastc, but the rechargeable batteres are used as energy buffers to compensate those varatons 15]. We assume these buffers have suffcent capactes, so we wll only consder the average energy-harvestng rate nstead of the nstantaneous rate. In order to ncrease the total sample rate, nodes can transmt and receve energy wrelessly wth others n EC-EH-WSN. Naturally, a polcy s mportant to gude the best energy flow n a network, whch s called energy routng, analogous to the conventonal data routng. Smlar to the data routng, energy routng can also be seen as a network flow matrx Δ, whose entry δ j s the energy transfer rate from node to node j. However, node j wll only receve energy η j δ j per second from node because of the lnk loss. Let η j denote the transfer effcency n -j lnk. The power transfer effcency η j depends on dstance. The dstance correspondng to η j = 90% s the effectve dstance d 0, whch s nfluenced by hardware realzaton and power supply. The WPT effcency wll decrease rapdly as d j exceeds d 0, only remans % wthn dstance 4d 0. Each sensor node should satsfy the energetc sustanablty condton, p δ j h η j δ j V) 3) whch ensures the energy supplyng rate of each node should not be lower than the energy consumng rate. The left two tems of 3) ndcate the energy consumng rate n communcaton and n energy transference, respectvely. The rght two tems are the energy harvestng rate and energy recevng rate n energy cooperaton, respectvely. B. Problem Formulaton The objectve s to maxmze the energetcally sustanable workload, whch s equal to maxmzng the total samplng rate of the whole network V r, wthout volatng the energetc sustanablty constrants. However, maxmzng the total rate leads to a loss of farness, some of the nodes may have a rate close to zero and have lttle contrbuton, whch goes aganst the goal of deployng them. Therefore, we add a quadratc regularzaton term to the objectve that ensures the farness, then the objectve T r) becomes T r) = r μ r 4) V V where μ s a postve punshment coeffcent. A large μ makes the regularzaton term domnate, and thus the rates of nodes would have small varety. The energetc sustanablty condton n 5) combnes energy harvestng and energy cooperaton together, and determnes the pattern of energy routng Δ as well as data routng F. In vrtue of collaboraton of the two types of routngs, the workload of network wll outperform those

3 algorthms wthout energy cooperaton. The jont optmzaton problem s as follows max T r) s.t. 1), ), 3) r 0 V) f j 0 V,j N ) δ j 0 V,j N ) where the optmzaton varables are r, f j, and δ j. The three constrants are the flow conservaton law, the energy consumpton model, and the energetc sustanablty condton, respectvely. All nodes are randomly deployed n the target feld, whch wll connect wth each other automatcally at ntalzaton. Durng the ntalzaton, node can acqure the followng nformaton: ) the neghbor set N ; ) energy consumpton n transmttng data to neghbors E j,j N ; ) lnk effcency whle recevng energy from neghbors η j,j N ; v) ts energy-harvestng rate h. Problem 5) s a typcal lnear programmng problem, whch can be solved by well-understood methods such as smplex method and nteror pont method, or by exstng solvers such as CVX?]. In centralzed optmzaton, a central computer n the network s necessary, whch can acqure other nodes local nformaton to solve 5), and then route the results to each node. The number of both optmzaton varables and constrants n 5) s ON ). When the network scale becomes larger, the scale of 5) ncreases rapdly, leadng to hgher computatonal costs of computng center. However, the network may not have such qualfed computng center n Ad-Hoc or non-nfrastructure modes. Therefore, t s requred to adopt dstrbuted optmzaton rather than centralzed optmzaton under that condton. In dstrbuted optmzaton scenaros, each sensor node calculates the optmal routngs by exchangng data wth neghbors, usually accompaned by teratons n networks. Besdes, the computaton complexty for each node wll not vary wth network scale. In the next secton, we wll dscuss how to desgn the optmzaton algorthm n a dstrbuted manner. III. DISTRIBUTED OPTIMIZATION In ths secton, we wll propose our dstrbuted jont optmzaton algorthm DJOA). We wll transform the problem 5), decouple the optmzaton varables, and then solve the routngs dstrbutedly usng the projected subgradent algorthm 16]. A. Problem Transformaton In dstrbuted optmzaton, each node performs calculaton only wth nformaton from ts neghbours, nstead of sendng ts nformaton to the snk for centralzed computaton. Note that 5) s naturally decoupled. In order to apply the projected subgradent algorthm, we transform the maxmzaton operaton n 5) nto mnmzaton operaton, and then combne constrant ) and 3) to elmnate p. Then 5) becomes 5) mn s.t. r μ r V V f j = f j r V) ρ f j c j f j h η j δ j V) r 0 V) f j 0 V,j N ) δ j 0 V,j N ) δ j Before applyng the projected subgradent algorthm, we frst observe the Lagrangan of 6). Note that the optmzaton varables f j and δ j appear only n the lnear constrants but not n the objectve, the Lagrangan wll be lnear wth f j and δ j, whle the projected subgradent algorthm requres the Lagrangan to be strct convex of each varable. We use a smple trck smlar to that n 17], to adjust the objectve. We add a small quadratc regularzaton term of f j and δ j,to make the objectve strctly convex of each varable. Eventually, 6) becomes mn s.t. r μ r V V e 1 fj e V V f j = f j r V) ρ f j c j f j h η j δ j V) r 0 V) f j 0 V,j N ) δ j 0 V,j N ) δ j δ j where the regularzaton coeffcents e 1,e are postve. When the coeffcents e 1 and e approach 0, the optmal soluton of 7) converges to the soluton of 6), whch s also the optmal soluton of the orgnal problem. B. Varable Update After the problem transformaton, we apply the projected subgradent algorthm to update our optmzaton varables n 7). The Lagrangan of 7) s Lr, F, Δ, λ, ν) = r μ r V V e 1 fj e δj V V λ h ν f j ) f j r V V λ ρ f j c j f j V δ j h ) η j δ j 6) 7) 8)

4 where λ and ν are dual varables, λ 0. Ther entres are denoted as λ and ν, respectvely. By symmetry of undrected graph, we have ν f j = a j ν f j V V j V = a j ν j f j 9) V j V = ν j f j V where a j s the entry of adjacency matrx A. Based on 8) and 9), we rewrte the Lagrangan as Lr, F, Δ, λ, ν) = λ h V ] μr 1 ν )r V e1 fj ν ] ) λ c j v j λ j ρ)f j V e δj λ ] λ j η j )δ j V In teraton k, the dual varables are λ k), ν k). Based on dualty theory, the optmal prmal varables r k), F k) and Δ k) are obtaned by seekng the nferor bound of Lagrangan, r k), F k), Δ k)) =argnf Lr, F, Δ,λ k),ν k) ) 11) Apparently, the prmal varables r, F and Δ are decoupled wth each other, and separable for each node. Therefore, each node can optmze ts own r, f j and δ j n parallel. Snce the objectve of each varable s a convex quadratc functon, whose feasble set s all real postve numbers, the closedform soluton can be drectly obtaned by fndng the poston of valley n the curve, as follows r k) 1 = μ 1 f k) j = δ k) j = ] 1 νk) ) ν k) λ k) e 1 1 λ k) λ k) j η j ) e c j ν k) j ] ] λ k) j ρ),j N,j N 1) where ] s the operator of projectng to the real postve axs. After sensor node update ts prmal varables, t wll update dual varable usng subgradent of dual functon. The specfc update formulatons are as follows, ν k1) λ k1) = = ν k) β k f k) j f k) j r k) λ k) β k ρ f k) j δ k) j η j δ k) j ) c j f k) j h )] 13) Accordng to the convergence concluson of the projected subgradent algorthm 16], f the step-sze β k n 13) meets the followng condton, β k > 0,β k 0, β k =. 14) k=1 then the teraton 1) and 13) wll converge, and the optmal soluton of the prmal problem 7) wll be obtaned by r = r k), fj = f k) j and δj = δk) j. C. Remarks on Algorthm Above all, the procedure of DJOA s lsted n Algorthm 1. Algorthm 1 Dstrbuted Jont Optmzaton Algorthm 1: Intalze. Set k =0. Each node chooses the ntal dual varables ν 0),λ 0). : Transmt dual varables. Each node transmts ν k),λ k) to each neghbor j. 3: Update prmal varables. Each node updates ts prme varables by 1). 4: Check the stop crteron. If the step crteron s satsfed, go to Step 8. 5: Transmt prmal varables. Each node transmts r k) f k) j and δ k) j to each neghbor j., 6: Update dual varables. Each node updates ts dual varables by 13). 7: Increase the teraton number. Set k = k 1. Go back to Step. 8: Termnate. Each node acqure the approxmate optmal data routng and energy routng by r k), f k) j and δ k) j. There are two stoppng crteron n Step 4. One s that the number of teraton steps reaches the gven upper threshold. The other s that the fluctuaton range of the prme varables after Step 3 s less than the preset tolerance threshold. In practcal, the thresholds n the stoppng crteron can be specfed by experence or experments. Note that for each node, the update of prmal varables 1) and dual varables 13) only need local nformaton and ts neghbors nformaton. In ths way, DJOA solves the jont optmzaton problem n a fully dstrbuted manner. IV. SIMULATION RESULTS In ths secton, we wll frst gve some numercal results to llustrate the benefts of energy cooperaton n EC-EH-WSN. After that, we wll show the performance of the dstrbuted algorthm. A. Smulatons on Jont Optmzaton We deploy sensor nodes randomly n a 0m 0m target fled. The maxmum transmsson radus d max s m. We assume the energy consumpton model based on the basc model from 18], as n 3]. For data transmsson, c j = d 4 j nj/bt, and for data recepton, ρ =50nJ/bt. All sensor nodes are equpped wth energy-harvestng devces as

5 bt/s 7 90 Node wth Λ =.5mJ/s 39 Node wth Λ =7.5mJ/s Node wth Λ =15mJ/s Snk node a) The data routng Total workloadkbt/s) Maxflow on R MF Maxflow on AODV Proposed routng Effectve energy cooperaton dstance d 0 m) mj/s Node wth Λ =.5mJ/s Node wth Λ =7.5mJ/s Node wth Λ =15mJ/s Snk node b) The energy routng Fg.. The soluton of the jont optmzaton problem well as WPT unts to acheve energy cooperaton. By random selecton, nodes are equally classfed nto three groups, wth energy-harvestng rate of.5 mj/s, 7.5 mj/s, and 15 mj/s cf. 19]), respectvely. In order to maxmze the workload, we jontly optmze the data routng and energy routng va solvng 5). The sze of the node ndcates ts energy-harvestng rate. The data routng and energy routng are llustrated n Fg.a) and Fg.b) respectvely. The effectve dstance of WPT s d 0 = 1.5m, and the punshment coeffcent n the objectve s μ = The thckness of each lne s proportonal to the amount of the flow, and the arrow on the lne ndcates the drecton of the flow. In ths smulaton, the average samplng rate of sensor nodes s bt/s. Then we show the nfluences of energy cooperaton of our algorthm compared wth the max-flow wth energy harvestng but wthout energy cooperaton) n two well-known routng algorthms, R-MF 6] and AODV ]. Fg.3 llustrates Fg. 3. The workload versus energy transfer effcency n three cases the workload versus dfferent effectve WPT dstance whle keepng other condtons nvarant. We smulate 0 dfferent random geometrc graphs to make sure the generalty of the results. In all cases, the workload ncreases monotoncally as the effcency of energy cooperaton gets hgher. In Fg.3, R- MF and AODV algorthms do not beneft from the energy cooperaton, so that ther workloads are constants wth respect to the x-axs. B. Performance of Dstrbuted Algorthm We valdate our dstrbuted algorthm DJOA under the same condton as Fg.. The coeffcents of the regularzaton term n 7) are set as e 1 = e = 8. In DJOA, the ntal dual varables are all set to 0, and the step-sze rule s β k = 0.8/ k 5000), whch satsfes the convergence condton 14). In the smulaton on an teratve optmzaton algorthm, we focus on the convergence of varables and the satsfacton of constrants. In Fg.4, each curve represents the normalzed error between the sample rate of a node and the optmal rate n centralzed optmzaton 4) as the algorthm terates. Fg.5 shows the volaton of the two constrants n 7) at each teraton, where one curve shows the maxmum volaton among the flow conservaton equatons of each node, and the other shows the maxmum volaton among the energetc sustanablty condtons of each node. From the smulaton results above, we can see that durng the teraton of DJOA, all varables wll tend to satsfy constrants, and the fnal optmzaton error s acceptable. The results show that DJOA s an effectve dstrbuted optmzaton algorthm jontly solvng data routng and energy routng. V. CONCLUSION In ths paper, we ntroduce the energy cooperaton nto the EH-WSN, where sensor nodes can transmt the harvested energy to neghbors by wreless power transfer technque. We

6 Normalzed error Volaton of constrant Iteraton Fg. 4. The normalzed error of nodes samplng rate Max volaton of equalty constrants Max volaton of nequalty constrants Iteraton Fg. 5. The volaton of constrants at each teraton study the workload maxmzaton problem n EC-EH-WSN, and propose a jont optmzaton model of data routng and energy routng. By the ad of energy cooperaton, the harvested energy can be fully utlzed, so that the EC-EH-WSN wll acheve a hgher energetcally sustanable workload. We also propose a dstrbuted jont optmzaton algorthm for n-network processng. We explot the structure of the jont optmzaton problem by dual decomposton and acqure the soluton teratvely usng the projected subgradent algorthm. In each teraton of the algorthm, each sensor node exchanges data wth neghbors and does smple computatons locally. The optmal data routng and energy routng strategy wll be acqured smultaneously as the algorthm terates. There are stll a lot of open questons for future works. In ths paper, we only consder the case that all sampled data wll be routed to the snk node. In applcatons where there s data loss, such as data aggregaton, the optmzaton model needs to be reformulated. ACKNOWLEDGMENT Ths work was supported by the NSF of Chna Grant No ). REFERENCES 1] C.-Y. Chong and S. Kumar, Sensor networks: evoluton, opportuntes, and challenges, Proc. IEEE, vol. 91, no. 8, pp , Aug 03. ] I. F. Akyldz, W. Su, Y. Sankarasubramanam, and E. Cayrc, Wreless sensor networks: a survey, Comput. Networks, vol. 38, no. 4, pp , Mar 0. 3] J.-H. Chang and L. Tassulas, Maxmum lfetme routng n wreless sensor networks, IEEE/ACM Trans. Networkng, vol. 1, no. 4, pp , Aug 04. 4] M. E. Keskn, K. Altnel, N. Aras, and C. Ersoy, Wreless sensor network lfetme maxmzaton by optmal sensor deployment, actvty schedulng, data routng and snk moblty, Ad Hoc Networks, vol. 17, pp , 14. 5] S. Sudevalayam and P. Kulkarn, Energy harvestng sensor nodes: Survey and mplcatons, IEEE Commun. Surv. Tutorals, vol. 13, no. 3, pp , Thrd 11. 6] E. Lattanz, E. Regn, A. Acquavva, and A. Boglolo, Energetc sustanablty of routng algorthms for energy-harvestng wreless sensor networks, Comput. Commun., vol., no. 14, pp , 07. 7] D. Hasenfratz, A. Meer, C. Moser, J.-J. Chen, and L. Thele, Analyss, comparson, and optmzaton of routng protocols for energy harvestng wreless sensor networks, n Proc. IEEE SUTC, June, pp ] L. Ln, N. Shroff, and R. Srkant, Asymptotcally optmal energy-aware routng for multhop wreless networks wth renewable energy sources, IEEE/ACM Trans. Networkng, vol. 15, no. 5, pp. 1 34, Oct 07. 9] B. Gurakan, O. Ozel, J. Yang, and S. Ulukus, Energy cooperaton n energy harvestng communcatons, IEEE Trans. Commun., vol. 61, no. 1, pp , December 13. ] L. Xe, Y. Sh, Y. Hou, and A. Lou, Wreless power transfer and applcatons to sensor networks, IEEE Wreless Commun., vol., no. 4, pp , August ] A. Kurs, A. Karals, R. Moffatt, J. D. Joannopoulos, P. Fsher, and M. Soljacc, Wreless power transfer va strongly coupled magnetc resonances, Scence, vol. 317, no. 5834, pp , JUL ] A. Kurs, R. Moffatt, and M. Solja, Smultaneous md-range power transfer to multple devces, Appl. Phys. Lett., vol. 96, no. 4, pp.,. 13] L. Varshney, Transportng nformaton and energy smultaneously, n Proc. IEEE ISIT, July 08, pp ] K. Huang and V. Lau, Enablng wreless power transfer n cellular networks: Archtecture, modelng and deployment, IEEE Trans. Wreless Commun., vol. 13, no., pp , February ] S. Zhang and A. Seyed, Analyss and desgn of energy harvestng wreless sensor networks wth lnear topology, n Proc. IEEE ICC, June 11, pp ] D. P. Bertsekas and J. N. Tstskls, Parallel and dstrbuted computaton: numercal methods. Prentce-Hall, Inc., ] R. Madan and S. Lall, Dstrbuted algorthms for maxmum lfetme routng n wreless sensor networks, IEEE Trans. Wreless Commun., vol. 5, no. 8, pp , Aug ] W. Henzelman, A. Chandrakasan, and H. Balakrshnan, An applcaton-specfc protocol archtecture for wreless mcrosensor networks, IEEE Trans. Wreless Commun., vol. 1, no. 4, pp , 0. 19] S. Sudevalayam and P. Kulkarn, Energy harvestng sensor nodes: Survey and mplcatons, IEEE Commun. Surv. Tutorals, vol. 13, no. 3, pp , 11. ] C. Perkns and E. Royer, Ad-hoc on-demand dstance vector routng, n Proc. Second IEEE Workshop on Moble Computng Systems and Applcatons, Feb 1999, pp