On-demand Mobile Charger Scheduling for Effective Coverage in Wireless Rechargeable Sensor Networks

Transcription

1 On-demand Mobile Charger Sheduling for Effetive Coverage in Wirele Rehargeable Senor Network Lintong Jiang, Haipeng Dai, Xiaobing Wu, and Guihai Chen State Key Laboratory for Novel Software Tehnology, Nanjing Univerity, Nanjing, Jiangu 20023, China Abtrat. In thi paper, we onider the problem of heduling mobile harger(mc) in an on-demand way to maximize the overing utility(cu) in wirele rehargeable enor network(wrsn), while nearly all previou related work aume the MC move along predefined path with perfet priori information. And the CU i defined to quantify the effetivene of event monitoring. We propoe three heuriti for thi problem after proving it NP-Completene. Finally we evaluate our olution through extenive trae-driven imulation. Key word: On-demand harging; event monitoring. Introdution Many exiting work [ 5] propoe to ue MC to work in WRSN with perfet priori information and predefined traveling path. On one hand, uing MC i muh more energy effiient than deploying multiple tati harger. On the other hand, it i neeary to hedule the MC to provide intenive harging power within a hort ditane. In thi paper, we onider the enario where eah MC repond the harging requet in an on-demand way and reharge the requeting enor via wirele to enable it ontinuou work. The main ontribution of thi work are a follow. To the bet of our knowledge, thi i the firt work onidering the on-demand heduling problem of MC in WRSN aiming to maximize the CU. We prove that the on-demand heduling problem i NP-Complete and propoe three algorithm by exploiting the patial redundany of WRSN. We evaluate algorithm through extenive trae-driven imulation. 2 Related Work The heme propoed by [ 5] are baed on the aumption of the availability of perfet priori knowledge. He et al. [6, 7] onider the on-demand hedule of

2 2 Lintong Jiang, Haipeng Dai, Xiaobing Wu, and Guihai Chen mobile element in a different enario, i.e., data olletion appliation. There i an online-like mobile harging hedule [3] targeting on prolonging the lifetime in WRSN, but it i ontrained by peifi etting and thu not general. In thi paper, we relax the ontraint they et and fou on the goal of maximizing the CU rather than purely elongate the lifetime of network. 3 Problem Statement Aume that m enor V = {v, v 2,..., v m } are randomly ditributed in a 2D area along with n Point of Interet(PoI) O = {o, o 2,..., o n }. The ening range of every enor i r. The event at a PoI emerge one after another, and the arrival of event at PoI i patially and temporally independent. Different enor may over ome PoI in ommon due to patial redundany [8]. Let O i repreent the et of PoI overed by enor v i. Furthermore, we aume that all enor work an ommuniate diretly with the ink. Multiple ink [9] might be deployed [0] in the field for fear that the overage of a ingle ink i limited. A enor only report it data (with ize of b bit) to the nearet ink diretly one it ene an event, but it requet for reharging an be relayed by the ink to the mobile harger ine the ink are out of energy onern and over the whole field olletively. For onveniene of expoition, we divide the enor into two ubet, the et of ative enor V a and the et of enor requeting reharging V r. An MC maintain a requeting queue for the reharging requet and we aume an M/G/ queue in Kendall Notation. All the reharging requet will be reorded and thoe enor that end thee requet will be kept in the requeting queue by the MC. For any enor i, we aume the reeived power = η i P MC, whih i far greater than it working power P i, where η i denote the harging effiieny of enor i and P MC i the working power of MC. The reharging time mainly depend on P MC, η i, and total battery apaity, W, of the enor, i.e. t (i) = W η i P MC. In addition, for enor i, the ervie time t (i) P (i). A for enor i, it working power P i depend on the rate of event generating f i and the unit energy onumption e i, i.e. P i = f i e i b. Notably, we adopt the energy onumption model ued in [, 2] to meaure e i. Hene, the average arrival rate (AAR) of onit of the traveling time t (i) t and the harging time t (i) m P i i= the requet λ an be etimated a λ = ( α) W, where α denote the reharging threhold fator. After finihing the ervie for the lat requet, the MC hooe the next target among the member in it requeting queue with it predefined rule and then move for the target. In order to define CU, we define Global Effetive Coverage(GEC), the et of PoI overed by ative enor, at time t a G(t) = O i and Global v i V a Coverage(GC) a M = O i. Intuitively, the (CU) denote v i V the ratio between above two a follow,

3 On-demand Mobile Charging Shedule for Effetive Coverage in WRSN 3 U(t) = G(t) / M. () We define Inremental Effetive Coverage(IEC) a the et of PoI that are going to be effetively overed. Formally, I (i) j = O i O i if enor v i V a {j} v i V a j i hoen before the MC make it i-th eletion. Additionally, we aume a greedy trategy in order to maximize the overall CU. The MC trie to hooe the next to-be-erved enor by updating the i-th Pieewie (PCU) with maximum of the average CU during the ervie time of the promiing enor j eah time the MC finihe the lat ervie. U (i) = max j { t (j) ti +t (j) t i U(t)dt}. (2) To um up, we formally formulate our problem a follow. Maximize N N i=.t. ()(2), where N denote the number of the requet. U (i) 4 Theoretial Analyi and Solution By imilar analyi of [3], we an redue the Geometri TSP problem to the problem and how it NP-ompletene. Sine it i NP-Complete, we reort to greedy algorithm. In the following part, we will propoe three greedy heuriti. Due to pae limit, we jut keth thee algorithm. 4. Maximal Next Coverage Utility Firt(MNCUF) Algorithm MNCUF require that the MC hooe the urrent maximal IEC to erve. In other word, MC hek the requeting queue and hooe the enor with maximum IEC urrently a the next to-be-erved enor, whih an be regarded a a peifi intane for the trategy of maximizing PCU(2). 4.2 Maximal Average Coverage Utility Firt(MACUF) Algorithm MACUF take the trade-off between the travel time and IEC of every ervie into onideration and greedily elet the target with the following formulation. U (i) j = G(t i ) t (j) t + G(t i ) + I (i) j t (j) t (j) M (3) where U (i) j perform a the approximation andidate for PCU, whih ubtitute the right hand ide of (2).

4 4 Lintong Jiang, Haipeng Dai, Xiaobing Wu, and Guihai Chen 4.3 MACUF Algorithm with Multi-MC Suppoe that there are n MC in total, and they are numbered equentially, {0,,..., n }. Intuitively, although every MC reeive and reord the information of all the requet within the WRSN, the i-th MC only erve the (kn + i)-th requet, where k N, with MACUF diipline. 5 Performane Evaluation We utilize the ame value etting of η, W and P a in our previou work [4]. In our enario, the ening field i a m 2 quare with 00 randomly ditribute enor, 300 PoI and 0 ink. Furthermore, we et the ening range r = 5m, the threhold fator α = 20% and the meage ize i 2Kbit, i.e., b = A total number of 00 requet are erved during eah imulation MNCUF MACUF NJN FCFS Average Arrival Rate() x 0 4 (a) CU v. AAR MNCUF MACUF The Speed of MC(m/) (b) CU v. Speed NJN FCFS λ= λ= λ= λ= The Number of MC () CU v. Multiple Fig.. Performane Comparion from different perpetive To the bet of our knowledge, there are no exiting work deigned to maximize CU baed on on-demand mobile harging in WRSN. To exhibit the ytem performane of our algorithm, we tailor two on-demand mobile data olletion diipline, NJN [6] and FCFS [7], to adapt to the enario we onider. ) Evaluation of different rate of event generation: we vary the rate of event generation, proportion to the Average Arrival Rate(AAR), and ompare the CU of all four algorithm. In Fig.(a), the peed of MC v i et to 0.0m/, whih make the traveling time eential. A an be een, both of our algorithm outperform the exiting one in term of CU. 2) Evaluation of different peed of MC : we ontinue to fou on the CU of all of the algorithm influened by varied peed v. In thi evaluation, λ = 0 4. Intuitively, with the peed inreaing, the traveling overhead goe down, o a the repone delay to the harging requet, whih may lead to a higher CU. We plot the fat in the Fig.(b). We deploy different number of MC (n=, 2,..., 8) in the ening field and ompare the CU with the varying AAR λ together. Fig.() how that the larger number of MC we hooe, the higher overall CU we obtain.

5 On-demand Mobile Charging Shedule for Effetive Coverage in WRSN 5 6 Conluion In thi paper, we onider the on-demand mobile harger heduling problem to maximize the CU of event monitoring in WRSN. Due to the NP-ompletene of thi problem, we propoe three heuriti algorithm. We evaluate the propoed algorithm through extenive trae-driven imulation. Aknowledgment Thi work i upported by 973 projet under Grant No.202CB36200, National Natural Siene Foundation of China under Grant No , No and No , and National Undergraduate Innovation Program (G ), and Reearh and Innovation Projet for College Graduate Student of Jiangu Provine in 202 under Grant No.CXZZ Thi work i ompleted with the generou help from Qingyuan Jiang, Chenbin Ji and Gang He. Referene. L. Fu, P. Cheng, Y. Gu, J. Chen, T. He Minimizing harging delay in wirele rehargeable enor network, in Pro. IEEE INFOCOM, F. Jiang, S. He, P. Cheng, and J. Chen, On optimal heduling in wirele rehargeable enor network for tohati event apture in Pro. IEEE MASS, Y. Shi, L. Xie, Y. T. Hou, and H. D. Sherali, On renewable enor network with wirele energy tranfer, in INFOCOM, H. Dai, L. Jiang, X. Wu, David K. Y. Yau, G. Chen and S. Tang Near Optimal Charging and Sheduling Sheme for Stohati Event Capture with Rehargeable Senor, In MASS, H. Dai, X. Wu, L. Xu, G. Chen and S. Lin Uing Minimum Mobile Charger to Keep Large-ale Wirele Rehargeable Senor Network Running Forever, In ICCCN, L. He, Z. Yang, J. Pan, L. Cai and J.Xu Evaluating ervie diipline for mobile element in wirele ad ho enor network, in Pro.IEEE INFOCOM 2, L. He, Z. Yang, J. Pan and J. Xu Evaluating on-demand data olletion with mobile element in wirele enor network, in Pro.IEEE VTC, A. Alfieri, A. Biano, P. Brandimarte, C.-F. Chiaerini Exploiting Senor Spatial Redundany to Improve Network Lifetime,in Pro.IEEE GlobeCom 04, X. Wu, G. Chen, Dual-Sink: uing mobile and tati ink for lifetime improvement in wirele enor network, in Pro.IEEE ICCCN 07, V. Zoltan; V. Rolland; V. Attila, Deploying multiple ink in multi-hop wirele enor network,, in Pro.IEEE PERSER 07, B. Cheng; Z. Xu; C. Chen; X. Guan, Spatial orrelated data olletion in wirele enor network with multiple ink, Computer Communiation Workhop (IN- FOCOM WKSHPS), M. N. Halgamuge, M. Zukerman, K. Ramamobanarao,H. L. Vu An etimation of enor energy onumption, in PIER, C. Mario, S. Nikoletea, T. P. Rapti, C. Raptopoulo and F. Vailaki Effiient energy management in wirele rehargeable enor network, In MSWiM, 202