A Multi-node Renewable Algorithm Based onCharging Range in Large-scale Wireless Sensor

Network

Guowei Wu, Chi Lin, Ying Li, Lin Yao, Ailun ChenSchool of Software

Dalian University of Technology

Dalian, China

Email:wgwdut@dlut.edu.cn

Abstract—Recently, wireless energy transfer technologies haveemerged as a promising approach to address the power constraintproblem in Wireless Sensor Networks(WSNs). In this paper, wepropose an optimized algorithm, Multi-node Renewable based onCharging Range (MRCR), for large-scale WSNs, where multiplesensor nodes are charging simultaneously. A mobile chargingvehicle (MCV) is responsible for energy supplement of thesenodes group by group at specified docking spots. These spotsare selected based on charging range of a MCV, which cannot only maximum the charging coverage, but also improvethe energy efficiency as the minimum number of stops and theshortest travel path. We organize MCV schedule into roundsand each round is divided into slots: judgment, charging andrest. Then, we provide the objective output to maximize thenetwork lifetime and the computation complexity of our MRCRalgorithm. Finally, extensive experimental results show MRCRalgorithm can guarantee a short TSP length in every round andall sensor nodes live immorally.

Index Terms—multi-node charging; docking spot selection;large-scale wireless sensor network;

I. INTRODUCTION

In a Wireless Sensor Network (WSN), the constrained

energy storage in batteries limits the network lifetime or

confines its short-term application. Thus, the limited battery

issue has become a big challenge in WSNs. To solve this

problem, energy-efficiency has been widely studied in the liter-

ature where duty-cycling and various energy-efficient medium

access and routing protocols have been proposed. Existing en-

ergy conservation schemes can slow down energy consumption

rate, but cannot compensate energy depletion. To address the

problem of energy decay, harvesting energy from surrounding

energy sources including solar [1], vibration [2], wind [3],

biochemical process [4] or passive human movement [5] has

been proposed. However, the drawback of these schemes lies

in those high reliance on unpredictable and uncontrollable

ambient conditions. For instance, it is impossible to harvest

energy for some sensor nodes deployed in shadow areas or

cloudy weather at a satisfied level.

Wireless energy transfer technology can be adopted to

increase the lifetime of a new class WSN, called wireless

rechargeable sensor network. With this ever-lasting energy

replenishment, we have found two particular breakthroughs in

the areas of wireless energy transfer [6], [7]and rechargeable

lithium batteries [8].It means power can be transferred from

one energy storage device to another without any plugs or

wires. Kurs et al. also have developed an enhanced technology

to transfer energy towards multiple receiving nodes simultane-

ously [9]. Delightfully, they have proved that the overall output

efficiency of charging each device individually is inferior to

that charging multiple devices. And what’s more, wireless

energy transfer is not subject to the objective neighboring

environment and it does not require any mediums between

the mobile charger and the receiver.

Recent advances in charging sensors dispatch a mobile

charging vehicle (MCV) carrying certain amount of energy

to move around the network [10], [11], [12], [13]. A MCV’s

capacity is high enough to maintain the eternal network

lifetime before it returns to the base station. Different from

these works, we also consider about the docking spot selection

to balance the power consumption of a MCV’s movement and

the distance between a MCV and every sensor node. We adopt

Traveling Salesman Problem (TSP) [14], [15] to balance them.

TSP aims to find the shortest Hamiltonian cycle during visiting

every vertex.

In this paper, we propose an optimized algorithm Multi-

node Renewable based on Charging Range (MRCR) in the

large-scale WSN, where a mobile charging vehicle is allowed

to charge a group of sensor nodes. Every MCV only needs

to visit the specified docking spots to charge those nodes at

one time. Though the selection of docking spots with length-

objective is a NP-hard problem, it can certainly be transformed

to the cover-objective problem. We also formulate how to

schedule MCV’s charging sensor nodes. The whole process

is organized into rounds and a round is divided into slots: 1)

judgment, 2) charging, 3) rest. To make a WSN’s lifetime as

long as possible even immortal, we develop a provable solution

combining the number of data packets transmitted over the link

and the total charging time at docking spot.

The remainder of this paper is organized as follows. We

survey the related work in Section II. Section III introduces

the basal information including parameters and system models.

Then in Section IV we investigate the problem formulation and

2015 9th International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing

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94

solution of multi-node renewable. Further studies in section

V show that our algorithm can achieve the computation

complexity of Liguang Xie’s. Section VI presents experimental

results. Finally we conclude this paper in Section VII.

II. RELATED WORK

Wireless energy transfer technologies can be classified into

three categories, inductive coupling [16], electromagnetic ra-

diation [17] [18], and magnetic resonant coupling [6]. While,

we focus on a MCV carrying certain amount of energy and

moving around the network in this section.

In [19], the author investigated three key aspects of recharg-

ing: a) traversal strategies of the mobile charger, b) full

versus partial charging, and c) energy percentage available

to charger. However, the adaptive circular traversal strategy

must be implemented under the conditions of the symmetric

geometry, uniform density and uniform data generation rate of

the network.

Xie [10] recently studied the multi-node case of renewable

sensor networks with wireless energy transfer. Based on the

charging range of a wireless charging vehicle, the authors

propose a cellular structure that sensor nodes can be charged in

a cell and the vehicle only needs to visit the center of the cell.

However, the hexagonal cell structure has three weaknesses.

One is that it ignores the ”edge effect” where most sensor

nodes gather far away from center, which energy efficiency is

quite low. Second, their solution is a static, centralized joint

routing with perfect communication channels. Third, inflexible

partition under asymmetrical distribution can no doubt prolong

the traveling path.

While, a more practical and efficient joint routing and charg-

ing scheme employing energy-balanced routing and energy-

minimum routing is proposed [11]. Under the dynamic and

imperfect communication environment, it uses constraint of

limited charging capability, and heterogeneous node attributes.

During every charging activity scheduling interval, the base

station determines the schedule based on the information

reported by each node. The collection tree protocol [20] is

used as the routing protocol to report sensory data and nodes’

status to the base station.

Until now, the problem of bundling the mobile charging

vehicle and wireless energy transfer [12], [13] has not been

explored thoroughly from the aspect of energy efficiency. The

general objective aims to maximize the number of sensors that

are replenished in one group and minimum length of travel

path among groups. While, we consider it in our paper.

III. MODELS AND PARAMETERS

In this section, we introduce the system model and some

basic concepts.

A. System Model

We consider a system composed of four main components

as illustrated in Fig 1: sensor nodes (S) with rechargeable

battery of limited capacity, a wireless mobile charging vehicle

(MCV) carrying a wireless power charger, a base station (BS)

as a sink node, and a service station (SS)to supply energy for

a MCV. The wireless rechargeable sensor network is static

with a set of N sensor nodes. Every sensor monitors its

nearby environment and generates a report to the sink node

periodically.

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Fig. 1. System Model overview. The MCV starts from the SS and travelsin the optimal path. When it arrives at a docking spot (ds) i, it will chargeall the sensor nodes nearby wirelessly. After a time period ti, the MCV willmove to the next ds(i+ 1).

B. Wireless Charging Model

Fig 2 shows the wireless charging model. A MCV is

employed to recharge the nodes at some selected docking

spots. It can return to the service station before its energy

runs out.

Fig. 2. Wireless Charging Model. Rmax is the max charging range and diis the distance between the MCV and sensor i

In this paper, we adopt the Friis Transmission Equation

to calculate the power received from MCV, separated by a

distance d between MCV and the receiver:

Pr

Ps= GsGr(

λ

4πd)2, (1)

where (Ps) means the power from MCV, (Pr) is the received

power, Gs is the source antenna gain, Gr is the receiver

antenna gain, λ is the signal wavelength (electromagnetic

wave) and α is a path-loss exponent (α ⊆ [2, 5]). Except for

95

the distance d, all other parameters in Equation 1 are constant.

To ease the description, we simplify the charging model as:

Pr = Ad−α, (2)

where A represents other constant environment parameters as

βPFullGrGs(λ/4π)α and β = Ps/PFull and PFull is the

initial full power of the MCV. In Equation 2, we observe

that the further the MCV is away from the sensor node, the

lower efficiency we get. Therefore how to choose docking spot

carefully is one of our research emphases.

C. Energy Consuming Model

Equation 3 shows a MCV’s energy consumption model. Etr

and Ech represents the battery consumption of traveling and

charging respectively. Let L be the length of the whole round-

way traveling path and e be the rate of energy consumption

for corresponding propulsion force per unit of length.

EMCV = Etr + Ech = eL+∑j⊆D

Ejch, (3)

where D is the set of docking spots selected in advance and

Ejch is the energy required for charging at the docking spot

dsj .

Equation 4 shows the total energy consumption of sensor

node j at time t. Bmax means a maximum battery level and

Bmin denotes the minimum battery level in case of death.

When every node j generates one unit of sensing data , it

may consume esj , the average energy consumption. etj denotes

the average energy cost for transmitting one unit data from

the sensor node j to the next sensor node, while erj denotes

the energy consumption for sensor node j to receive one unit

data. Let rj,t represent the data sampling rate of sensor node

j at time t. Each sensor node consumes energy for data sense,

transmission and reception.

Wj,t = (esj + etj)rj,t + (erj + etj)rk,t,K ⊆ PSN(j), (4)

where PSN(j) is the set of previous sensor nodes that use

sensor node j in all routing path.

Equation 5 shows the remaining energy of a given sensor

j at time t . Cj is the energy charging rate of node j. When

the MCV charges a group of sensor nodes at the docking spot

ds, each node in the same group usually does not reach the

same energy charging rate because of the different distance

from MCV.

Bj(t) = Bmax +

∫ t2

t1

Cjdt−∫ t

0

(esj + etj)rj,tdt (5)

+∑

K⊆PSN(j)

(erj + etj)rk,t.

IV. PROBLEM FORMULATION AND SOLUTION

In this section, we propose our algorithm Multi-nodeRenewable based on Charging Range (MRCR) for large-

scale WSNs. Because the energy consumption of a MCVincludes traveling and charging, we try to optimize the length

of traveling path so as to acquire minimum power cost

and maximum energy efficiency by exploring the multi-node

charging simultaneously. First, we design the docking spot

selection algorithm with less number of stops and more

rational geometrical positions. Then, we formulate the problem

how to schedule MCV charging sensor nodes.

As to the charging scheduling, we have to balance the total

energy consumed by the MCV for both moving and charging.

In each round of charging, the MCV predicts sensor’s residual

energy and parties the nodes that need to be charged group

by group in an optimal order to replenish them energy. The

paper solves wireless charging problem in WSNs for multi-

node case, which maximizes the number of sensors wirelessly

charged and minimum energy cost by the MCV.

A. Docking spot selection Algorithm

There are two methods to reduce the energy cost during

traveling. One way is to diminish the number of stops and the

other is to select some random points to stop. As to reduce the

number of stops, we have to group nodes into one collection

as many as possible. So we use intersecting circles with a

radius of charging range to divide the group. Fig 3 depicts an

example where shorter tour length may be achieved when the

docking spots are not confined to the locations of the existing

sensors.

Fig. 3. The Selection of Docking Spot. Given two selected docking spots, alonger tour for d2 and a shorter tour for d1. Both d1 and d2 can cover allthese sensor nodes.

Fig 3 shows that each node at least lies in a circle with

radius r, where these circles may overlap arbitrarily with one

another. We use intersecting circles with a radius of charging

range to divide these sensors into groups. Every point in these

overlap regions is the docking spot candidate to charge sensor

nodes.

Theorem 1 Given a sensor nodes set S such that there is a

corresponding set C(| C |=| S |) of circles centered at each

vertex si ⊆ S with a radius ri > 0. If the circle ci overlaps

with another circle cj , ci and cj are in the same group.

Theorem 2 All points in the overlap regions among inter-

secting circles are candidates for docking spots.

Denote P as the traveling path P= (d0, d1, ..., dm, d0)

cruised by the MCV throughout a charging round, which

starts from and ends at the service station (d0 = SS), and di

96

represents docking spot i that multiple nodes can be supplied

energy where 1 ≤ i ≤ m. Denote Ddidi+1 as the distance

between the docking spot i and docking spot i+1 visited along

P respectively. Based on Theorem 1 and 2, we can achieve

the minimum number of groups, m. The MCV should move

along the shortest Hamiltonian cycle, which can be obtained by

solving the well-known Traveling Salesman Problem (TSP).

Therefore, Theorem 3 can be deduced.

Theorem 3 The traveling path P consisting of absolute

docking spots and links that touches every sensor node is a

minimum-length.

Note that Theorem 1 and Theorem 2 are only theoretical

basis to optimize traveling path length from the viewpoint

of geometrically computed positions. Theorem 3 determines

the candidate for docking spots. The selection of docking

spots with length-objective is a NP-hard problem since it

is polynomial-time incremental with the growth of sensor

nodes. However, it can certainly be transformed to the cover-

objective using the proposed Algorithm 1 especially adjustable

for the large-scale WSN. In the Algorithm 1, FindIntersec-tion(ni) is a function to group multiple sensor nodes. In the

form of a set traversal of sensor node set S, if there are

intersectant circles, they are put into InterSet[i]. InterSet[i]is a data structure that holds the sensor nodes in the group

i. IsoSet → si means putting sensor node si into the

set IsoSet, where keeps the center point of isolated circle.

D ← ComputeGroupDS(InterSet[i]) chooses the docking

point in the group from the set InterSet[i] characterized

by boundary points, which makes the whole path length

shorter. Then put it into docking spots set D. Similarly,

D ← ComputeIsolateDS(IsoSet[i]) is used to choose the

docking point from the node IsoSet[i]: link the center of

this isolated circle and the nearest docking spot, then set the

intersection point of straight line and circle as the docking

point and also put it into set Docking Spots Set D.

Algorithm 1 Calculate the Docking Spots Set.

Require:1) Sensor Node Set: S= {s1, s2, ..., sn}2) The max charging range: Rmax

Ensure:Docking Spots Set : D = {d1, d2, ..., dm}

1: while (i �= n) do2: InterSet[i] ← FindIntersection(si);3: if InterSet[i] is NULL then4: IsoSet ← si;5: Continue;

6: end if7: D ← ComputeGroupDS(InterSet[i]);8: end while9: while (i �= IsoSet.number) do

10: D ← ComputeIsolateDS(IsoSet[i]);11: end while12: m ← IsoSet.number + InterSet.number;

13: return

In our algorithm, designated docking points are character-

ized by boundary points, where several circles cross to make

the whole path length shorter. As shown in Fig 4, point a and

point b are both the intersection points. We choose the right ainstead of the left b, because a makes the tour length shorter

generally perceived as the best candidate. For isolated circle,

the best candidate point is the one gliding along the circular

trajectory and making distance between two adjacent points

shortest theoretically.

Fig. 4. Selection of MCV’s Docking Spots. Point a is the bests candidatebecause of a shorter tour length. For isolated circle, we follow the principleof proximity in a more feasible way.

B. Charging Scheduling Algorithm

We formulate the problem how to schedule MCV charging

sensor nodes in WSNs. Let set AN = {SS}∪S, where SS is

the service station and S denotes the set of all sensor nodes,

with S∗ ⊆ S being the subset of sensors. Let G be the full

battery capacity of a MCV which is fully charged at service

station in the beginning of a charging round. The goal of MCVis to estimate those sensor nodes needing to be charged and

transfer energy to them. In our algorithm MRCR, the whole

process is organized into rounds and a round is divided into

slots: 1) judgment, 2) charging, 3) rest in Fig. 5.

����

������������

���

������

� ��

������

Fig. 5. Rounds and Slots. The first stage is to initialize the whole system.The rest rounds are all divided into 3 slots. Note that different rounds havedifferent length mainly because of different numbers of nodes imperative tocharge energy.

Algorithm 2 shows the charging scheduling algorithm.

When a MCV encounters a sensor,it determines whether the

power of this sensor node si falls below Bmin, corresponding

the function IsRecharged(si). If this node needs charging,

97

the MCV will add it into the recharging node set R. In the

judgment slot, MCV uses Algorithm 1 CalculateDS(R) to

compute the docking spots. A docking spot should be optimal

geometric position to cover multiple sensors for wireless

energy transfer. Then, all sensors in set R are assigned to

different Docking Spots Set D. In the charging slot, MCV

starts to travel around the optimized path to charge multi-nodes

simultaneously at every docking spot. The traveling path for

charging is a Hamiltonian cycle.

Algorithm 2 Charging Scheduling.

Require:Sensor Node Set: S= {s1, s2, ..., sn}

Ensure:Docking Spots Set : D = {d1, d2, ..., dm}

1: while 1 do2: while (i �= x) do3: S∗ ← IsRecharged(si);4: Continue;

5: end while6: D ← CalculateDS(S∗);7: ChargeNode(D);8: WaitNextRound;

9: end while10: return

V. ALGORITHM ANALYSIS

In this section, we analyze how our MRCR can prolong the

lifetime of a WSN as well as its computation complexity.

The purpose of the recharging WSN is to make its lifetime

as long as possible even immortal. To analyze this, we first

assume a node generates sensory data packet on a fixed rate

during the whole network lifetime similar to [10]. ωi,t is

denoted as ω. T is the network lifetime. fi,j is the total number

of packets transmitted from node i to j during the network

lifetime. Eac is average energy consumed for MCV’s charging

operation and Δk is the MCV’s charging efficiency. Then, etais the total amount of time that theMCV charges at docking

spot k. Derivation is as follows:

Purpose : maxT (6)

T ∗ ω +∑

j⊆PSN(j)

fj,i =∑

j⊆PSN(j)

fi,j (7)

T ∗∑i⊆S

ω =∑

j⊆PSN(BS)

fj,BS (8)

es ∗ T ∗ ω + er ∗∑

j⊆PSN(j)

fi,j + et ∗∑

j⊆PSN(j)

fi,j (9)

≤ Emax +Δk ∗ Eac ∗ η (10)∑k⊆D

Δk ≤ T (11)

Output : fi,j ,Δk (12)

Constraint (6) represents that all data generated and received

need to be sent out hop by hop towards the sink node.

Constraint (7) represents the base station is responsible for

receiving data generated by all sensor nodes. These two

constraints reflect the flow conservations. Each sensor node

consumes energy for data sense, reception and transmission,

while the consumption should be smaller than the max battery

capacity that the node can possess or the energy charged from

the MCV. Constraint (9) states the time limitation that the

bound of the total charging time should not exceed the network

lifetime. Finally the output (fi,j ,Δk) combines the number

of data packets transmitted over the link (i, j) and the total

charging time at docking spot k.

The computation complexity of our algorithm is determined

by the docking spot selection and charging scheduling. The

docking spot selection one is to compute the spots where the

MCV can stop to transfer energy to multiple sensor nodes

within the charging range. If each node traverses the N -1

sensor nodes to find its group members and compute the

stop position. There is a time complexity O(n2) and it is

infeasible to compute the optimal solution for a large scale

sensor network. To reduce the time complexity, we use binary

search tree to storage the nodes’ position. For a given node

at (a, b), its group members is within the scope of (a − r, y)

and (a + r, y). Therefore, the time complexity for all nodes

is n ∗ (lgn). The charging scheduling is to find those sensor

nodes need to be charged, whose number has an upper bound

N . In each round, the difference lies the number of nodes

found by the MCV. Hence, combined with this aspects, we

obtain the total computation complexity n ∗ (lgn).VI. SIMULATION RESULTS

In this section, extensive simulations are conducted to eval-

uate the performance of our MRCR algorithm under different

configurations of large-scale networks.

A. Experimental Setup

We consider a rectangular field of 1000m*1000m where

N = 100, 500, 1000 and static sensor nodes are randomly

deployed. The base station is placed in the center of the field

at (500,500) and the MCV’s home service station is assumed to

be at the origin. Table I lists the default simulation parameters.

We suppose all sensor nodes are homogeneous, whose battery

for each is the regular NiMH 1.2V/2.5Ah. Bmax = 1.2V ∗2.5A ∗ 3600sec = 10.8KJ and Bmin = 0.05% ∗ Bmax =540J hold. We set the wireless energy transfer max range

Rmax = 2.7m. We adopt the TSP in the Concorde package

[21]. This algorithm is a fast and effective heuristic even for

large-sized instances.

We will compare our algorithm MRCR with L.Xie’s renew-

able sensor networks(LX) [10]. In [10], a cellular structure is

used in which the MCV visits these cells and charges sensor

nodes from the center of a cell. Assuming that the MCVis powered enough for all sensor nodes renewable, we have

r = 2.7m both for our circle radius and cell’s length of side.

98

TABLE ISIMULATION PARAMETERS

Parameter Meaning ValueBmax Battery maximum capacity of each

node10.8(KJ)

Bmin Battery minimum capacity of eachnode

540(J)

Eac Average Energy consumed for M-CV’s charging operation

3(J)

α Energy consumed for transmittinga packet

0.05(J/pkt)

β Energy consumed for receive apacket

0.06(J/pkt)

η MCV’s charging efficiency 1.5(%)v MCV’s moving speed 5(m/s)ω Data generating rate 15(pkt/h)

In each setting, the whole charging process is divided into

rounds. For each round, we first calculate the docking spots set

under MRCR algorithm and then measure both the charging

time and path length of MCV’s traveling achieved by the

Concorde.

B. Performance of the Algorithm

We first evaluate the performance of the initialization.

During the initialization, the MCV with full battery is ready to

charge sensors group by group. Each docking spot is computed

by docking spot selection algorithm. In LX, the MCV visits

each cellular center to charge nodes. While, MRCR selects

the center of intersection among circles as docking spots. The

shortest Hamiltonian cycle is found by using the Concorde

solver and is shown in Fig 6 for the 1000-node sensor network.

The initial position of WSN is considered to be random shown

in the top. The middle is the result of LX, where 1000 nodes

are distributed in 318 cells and each cell center is represented

as a point. The number of multi-node charging groups is 211

and the docking spots are shown as points in the bottom.

Comparing with these two solutions, we can see the charging

stops in MRCR are sparser and less irregular than those in

LX.

We conduct extensive simulations to evaluate the initializa-

tion performance under different configurations with N = 100,

500, 1000. The traveling path length is recorded and plotted

in Fig 7. When N is 1000, the path is 22973 meters long after

all nodes are traversed without group division. By contrast, the

optimal length with group division is 16651 meters long for

LX and 13121 meters long for MRCR respectively. Judging

from the trends in Fig 7, we can draw a conclusion that LX has

better performance in small scale of WSNs. And our MRCR

is more competitive in the large-scale WSNs, because it is

difficult for circles to overlap one another within the covering

ranges in a highly dispersive environment.

We are also interested in investigating the system perfor-

mance after rounds. Different sensory data generation models

may cause the different results of energy distribution. In

this simulations, we configure the energy consumption of

sensor nodes randomly with a linear decrease. That is to say

abstracting the energy consumed for receiving and sending

Fig. 6. The Comparison Results with 1000 nodes in the Concorde. The topone is the random situation without group nodes. The middle is the result ofLX and the bottom is the MRCR’s result.

100 120 140 160 180 200 220 240 260 280 300400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

N: the number of sensor nodes

The

leng

th o

f TSP

LXMRCROriginal

Fig. 7. TSP Length with Different Nodes. With N = 100, TSP length is 5302meters long for LX and 7304 for MRCR. With N = 500, TSP length is 12146meter long for LX and 11903 for MRCR. With N = 1000, TSP length are16651 meter long for LX and 13121 for MRCR.

package as one fixed value. Energy consumption of these

nodes at different rates brings about supplement from the

MCV at different rounds. In each round, nodes below Bmin

are grouped to compute docking spots and wirelessly charged

simultaneously. The TSP length of the MCV for each round

is shown in Fig 8, where there are 1000 sensor nodes. We

can see all nodes are charged in every round no matter how

much energy is used, so the TSP length is invariable in LX.

Compared with the top curve, the TSP length of MRCR is

shorter. In this instance, the MCV takes significantly less time

and energy on moving around the path as shown in Fig. 9.

99

1 2 3 4 5 6 7 8 9 106

7

8

9

10

11

12

13

14

Round

The

leng

th T

SP o

f eac

h ro

und LX

MRCR

Fig. 8. TSP length From Round 1 to 10. The unit for y-coordinate is kilometer.

1 2 3 4 5 6 7 8 9 101.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Round

The

char

ging

tim

e of

eac

h ro

und LX

MRCR

Fig. 9. The Charging Time for MCV From Round 1 to 10. The unit of they-coordinates is thousand second.

VII. CONCLUSION

In this paper, we have designed and validated an optimized

algorithm Multi-node Renewable based on Charging Range

(MRCR) in the large-scale WSN. Our MRCR can provide ef-

fectiveness on energy usage and prolong the network lifetime.

Simulation results show that our MRCR can possess better

performance. In the future work, we will deeply study how to

schedule multiple chargers simultaneously.

ACKNOWLEDGMENT

This research is sponsored in part by the National Nat-

ural Science Foundation of China (contract/grant number:

No.61173179, No.61202441, No.61402078) and Program for

New Century Excellent Talents in University (NCET-13-0083).

This research is also sponsored in part supported by the

Fundamental Research Funds for the Central Universities

(No.DUT14YQ212, No.DUT14RC(3)090).

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