research article an efficient bypassing void routing algorithm...

Research ArticleAn Efficient Bypassing Void Routing Algorithm forWireless Sensor Network

Xunli Fan and Feifei Du

School of Information Science amp Technology Northwest University Xirsquoan 710127 China

Correspondence should be addressed to Xunli Fan xunlfannwueducn

Received 16 February 2015 Accepted 16 April 2015

Academic Editor Yasuko Y Maruo

Copyright copy 2015 X Fan and F Du This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Since the sensor nodersquos distribution in a wireless sensor network (WSN) is irregular geographic routing protocols using the greedyalgorithm can cause local minima problem This problem may fail due to routing voids and lead to failure of data transmissionBased on the virtual coordinate mapping this paper proposes an efficient bypassing void routing protocol to solve the controlpacket overhead and transmission delay in routing void of WSN which is called EBVRPVCM The basic idea is to transfer therandom structure of void edge to a regular one through mapping the coordinates on a virtual circle In EBVRPVCM somestrategies executed in different regions are selected through virtual coordinates to bypass routing void efficiently The regularedge is established by coordinate mapping that can shorten the average routing path length and decrease the transmission delayThe virtual coordinatemapping is not affected by the real geographic node position and the control packet overhead can be reducedaccordingly Compared with RGP and GPSR simulation results demonstrate that EBVRPVCM can successfully find the shortestrouting path with higher delivery ratio and less control packet overhead and energy consumption

1 Introduction

In recent years wireless sensor network (WSN) has beenwidely used in various fields [1] Routing is one of the keytechnologies in WSN Geographic routing [2] selects pathonly relying on the location information of neighbor nodesSince geographic routing protocol has the characteristic ofbetter scalability and is less affected by the network size ithas broad application prospects [3] in large-scaleWSNs Dueto the nodersquos irregularity in distribution geographic routingprotocol using greedy algorithm can cause local minimaproblem thus leading to data transmission failure eventually[4] which is called routing void problem

To solve the routing void [5] designated a quarantineprogram around the cavityThe program using the ban in thearea of separation node acts as a relay node to avoid routingvoid Reference [6] put forward a RCF (Ring-ConstraintForwarding) algorithmRCF creates an annular cavity aroundthe band To avoid voids the policy routing is created byselecting the relay node in the annular band Chang et alproposed the RGP (Route-Guiding Protocol) algorithm [7]

To avoid routing voids RGP is selected for each node inthe network from the overall perspective of the destinationnode according to the position relationship between the relaynode and the void areaWhile the abovemethods are adoptedto select a special area designating relay node to reduce com-putational complexity the implementation process will havegreater control packet overhead and transmission delaysRGP is not conducive to network energy-saving and alsounable to resolve planning given special area inside the noderouting void problem Reference [4] proposed GPSR (greedyperimeter stateless routing) protocol To solve the problemGPSR used a network link topology through a combinationof greedy mode and edge forwarding mode Reference [8]presented a subeffective interface routing algorithm But therouting algorithms in [4 8] need to build and maintainperipheral node link diagram (such as Gabriel Graph)which is not conducive to the expansion of large-scalenetworks

At present the method which uses virtual geographyinformation to solve the routing void problem has achievedsome initial research results [9 10] But the key problem is

Hindawi Publishing CorporationJournal of SensorsVolume 2015 Article ID 686809 9 pageshttpdxdoiorg1011552015686809

2 Journal of Sensors

that network nodes use the preselected reference node [9] orthe neighbor node information to rebuild their coordinateinformation [10] If the network node corresponding tothe destination node is changed it uses the virtual recon-struction location information It can only apply to a fixeddestination node and the network is inevitably void Node invirtual position based routing protocol is limited by the realphysical position and the virtual location can be adjustedAlthough the greedy algorithm is simple and less complexthe existing virtual routing protocols are not suitable for everynode in the network

To overcome the drawbacks of the above protocols aneffective bypass void routing protocol based on the virtualcoordinates mapping (EBVRPVCM) is proposed in thispaper The protocol not only maps the routing void of edgenode coordinate to a void in the center of the cavity soas to cover a virtual circle in the network but also createsthe virtual coordinate of the edge node Therefore the edgenode with a virtual coordinate can be selected as a relaynode For the void area on the network a circular virtualstructure can effectively bypass routing void Compared withthe traditional protocols the proposed protocol selects therelay node by greedy algorithm on one node and saves theenergy consumption effectively Through establishing thevirtual location it is independent of the destination nodeThere is no need to rebuild the virtual location informationeven if the destination node changes

The rest of the paper is organized as follows Section 2describes the related work of routing void generation andnetwork edge structure Section 3 describes the compo-nents stages and design of the proposed protocol Section 4analyzes the virtual coordinated actual coordinates pathand control cost of EBVRPVCM Section 5 evaluates theperformance throughnumerical simulation onNS2 platformSection 6 is the conclusion and future work

2 The Related Work

21 Routing Void Generation For routing based geographicinformation we use the greedy algorithm to choose therelay nodes which is closer than their neighbor nodes tothe destination If such neighbor node does not exist therewill be routing void [11] Figure 1 illustrates the void generateschematic

As shown in Figure 1 node 1198992receives the data transmit-

ted by 1198991 and the destination node is 119889

1 A set of neighbor

nodes for the node 1198992is 1198991 1198993 and 119899

4 since the distances

from the nodes 1198991 1198993 and 119899

4to the destination node 119889

1

are greater than that of 1198992 the route appears void according

to the greedy algorithm [12] The data will not be able topass through Similarly when the node 119899

5sends data to the

destination node 1198892 routing void will appear too

22 No Routing Void Network Edge Structure Suppose inWSN the number of edge nodes around an obstacle area is119873

119887

Obstacle region

n2 n5

d2

d1

n1

n3

n4

Fringe nodeHomogeneous sensor nodeDestination node

Figure 1 Void generate schematic

and the set of edge nodes is 119887119896| 119896 = 1 2 119873

119887 The edge

node must meet

119889 (119887119896 119887119896+1

) lt 119879119888 119896 = 1 2 119873

119887minus 1

119889 (1198871 119887119873119887

) lt 119879119888

119887119896+119894

| 119889 (119887119896 119887119896+119894

) lt 119879119888 = 120601

119896 = 2 119873119887minus 2 2 le 119894 le 119873

119887minus 119896

119887119896| 119889 (1198871 119887119896) lt 119879119888 = 120601 119896 = 3 119873

119887minus 1

(1)

where 119889(119909 119910) is the Euclidean distance between the nodes 119909and 119910 119879

119888is the communication radius of the node 119894 is an

integer the edge node set is 119887119896

| 119896 = 1 119873119887 and any

node can only communicate with the two adjacent nodesIf the distance between the edge node of obstacle and a

fixed node 119874 satisfies

119889 (119887119896 119874) = 119877 119896 = 1 119873

119887 (2)

the distribution of the edge node to the center of the circle119874 is determined 119877 is the radius of the circle as shown inFigure 2 In the edge of the structure around the area of theobstacle each edge node has only two neighbor edge nodesFrom isotropic circular geometry the packet routing is notvoid for any destination node while going through the region

Each node uses the greedy algorithm to select the relaynode path As an example the source node 119904 sends packets todestination node 119889 and shows the generation of free routingvoidThe edge node 119887

1receives the packet and uses the greedy

algorithm to find the next hop relay nodeThe same is for edgenode 119887

2 The two nodes are distributed in a concentric circle

and the distance of 1198872to destination node 119889 is less than that

of 1198871 Then 119887

1selects 119887

2as the next hop node and the routing

void problem does not occur Packets in the edge node 1198873

will not either incur routing void problem The edge node1198874uses greedy algorithm to select the next hop node 119899

5 and

Journal of Sensors 3

o

d

R

Obstacle region

b1

b2s

b3

n5

n6

b4

b


Nb

Figure 2 No routing void network diagram

the packet is sent to the edge node 1198874 Until the data is sent to

the destination node 119889 in this process the greedy algorithmmechanism has not failed

3 EBVRPVCM Routing Protocol

EBVRPVCM is composed of the greedy mode and the voidprocessing mode In this protocol the relay node uses theconventional greedy mode to forward data If the greedymode fails and the routing void appears it changes to thevoid processing mode According to the execution sequencethe void processing is divided into void detection virtualcoordinate mapping and void area division Through thevoid processing the virtual coordinates of edge node areestablished After starting the greedy mode again these edgenodes with virtual coordinates can be selected as relay nodesThe details of designing the void processing mode aboutEBVRPVCM are given in the following subsectionThere arethree main stages of the given protocol

31 Void Probe Stage The void detection stage is responsiblefor collecting information of the void edge node after routingvoid appearsWhen the packets meet the routing void duringdata transmission within the network we called it the failednode of the greedy algorithm and try to find a substitutenode When the substitute node detects the routing void itcaches the data packets generates a void robe packet andinitiates the process of void detection The void probe packetstores the whole founded time and labels each edge nodeand geographic coordinates The detection process can beimplemented through using left (right) hand technology [11]When the detection packet goes back to the founded node itcontains the information of the edge node set that is named119887119896| 119896 = 1 2 119873

119887

In the detection process it is found that there aremultiplenodes and multiple probe packets within the same voiddetection area simultaneously To reduce the detection ofrepeated forwarding different probe packets to the samenode the node receives probe packets and labels the void

founded time recorded in the probe packets According tothe void founded time it discards the probe packets if thefounded time in the node labeled by newprobe packets is laterthan that in the node and otherwise continues to probe untilit reaches the corresponding founded node Eventually onlythe probe packets sent by the earliest founded node completethe void detection in the entire void region

32 Virtual Coordinate Mapping Stage The virtual coordi-nate mapping stage mainly maps the node information to avirtual circle where the founded node is obtained from thevoid edge node Eventually it is converted into the structurewithout the routing void network edge as mentioned inSection 22

The probe packets launched by the discovery nodeand eventually returned to the founded node contain theID and the corresponding geographic coordinate informa-tion of the edge nodes in the routing void Let (119909

1 1199101)

(1199092 1199102) (119909

119873119887 119910119873119887

) denote the coordinates of each edgenode and the coordinates of the void center point 119874 are

(119909119900 119910119900) = (

1

119873119887

119873119887

sum

119896=1

119909119896

1

119873119887

119873119887

sum

119896=1

119910119896) (3)

The maximum distance from the edge node to the voidcenter is

119889119900= max119896=12119873119887

119889119896| 119889119896= radic(119909

119896minus 119909119900)2

+ (119910119896minus 119910119900)2

(4)

Here void center119874 is the center of the circle and 119889119900is the

radius of virtual circle formapping of virtual circleWhen themapping of virtual circle is determined the virtual coordinatemaps the void edge node [12]

Let 119880 indicate the line segments of the connection ofadjacent edge node which maps the virtual circle of center119874 as a starting point and denotes the rays passing by node119887119896as 119903119896 119872 is a set temporarily storing a plurality of node

information 119888 stands for the base and the virtual coordinatesof the edge node need to be determined respectively Thepseudo code of virtual coordinate mapping algorithm isshown in Pseudocode 1

Figure 3 is the diagram of virtual coordinate mappingschematic As shown in Figure 3119874 stands for the void centerand the arc is the part of the mapping virtual circular Edgenodes 119887

1and 119887

5are the mapped virtual location of 119887

1015840

1and

1198871015840

5 respectively After mapping the virtual positions of edge

nodes 1198872 1198873 and 119887

4are between the virtual nodes 1198871015840

1and 119887

1015840

5

The mapped nodes are 11988710158402 11988710158403 and 119887

1015840

4 respectively

Once the virtual coordinate mapping is completed thediscovered node initializes the virtual location distributionpackage Also it distributes the virtual location coordinatesof the edge nodes and the void center to the edge of thecorresponding node and sends the probe packets along withthe path (void edge) After receiving the virtual locationof the distribution package each edge node broadcasts theinformation to the neighbor nodes The broadcast messagecontains a virtual coordinate of edge node itself and that ofthe void center point


initialize 119894 = 119895119872 = 120601

while (119894 le 119873119887) do

if 119903119894with 119880only has one intersection point (1199091015840 1199101015840) then(1199091015840119894 1199101015840119894) = (1199091015840 1199101015840)

if 119872 == 120601 then(119909temp 119910temp) = (1199091015840 1199101015840)

elsewhile 119888 = 0 do1199091015840

119894minus119888= 1199091015840+ (1199091015840minus 119909temp) times 119888(119888 + 1)

1199101015840


deleted 119887119894minus119888

from119872

EndwhileEndif

else add the 119887119894to119872

Endif119894++

Endwhile

Pseudocode 1 Pseudocode of virtual coordinate mapping

o

Fringe nodeVirtual coordinate after mapping

998400

998400

998400

b998400

b1

b1

b2

b2

d0

b3

b3

b4

4

b5

998400b5

Figure 3 Virtual coordinate mapping strategy

33 Void Zone Division Stage In order to perform differentrouting strategies in different regions the void zone divisionstage is responsible for the current void surrounding dividingAccording to the location of void and the destination nodethe void and the surrounding area are divided into the closerregion and the free zone as shown in Figure 4

In Figure 4 119874 is mapped as the virtual circle center 119889 isthe destination node and the dotted line as shown in thecircle determines the mapping of virtual circle We draw twotangents from the destination node 119889 to the mapped virtualcircle which crosses at the points 119898 and 119899 respectively Thequadrilateral region surrounded by 119874 119898 119889 and 119899 is thedetachment area of the mapped virtual circle which is thearea 119861 shown in Figure 4 The rest of the region within thetwo tangent lines and mapped virtual circle with the removalof detachment area is called the closer region of the mapped

d

Cn

m

B

C

AO

Fringe node

Figure 4 View of the region division of the void

virtual circle that is the area119860 shown in Figure 4The lateralregion from the tangent of themapped virtual circle is knownas the free zone of the mapped virtual circle which is the area119862 shown in Figure 4The three areas are divided according tothe current route void based on the different destination nodecorrespondingly

34 Virtual Coordinate Based Routing Design After per-forming above three phases the edge node of the voidcontains the location information of the actual coordinatesand virtual coordinates According to the destination nodethe peripheral void is divided into three different regionsThefounded nodes use the virtual coordinate to initiate a routingevent and send the cached packets in the first phase to therelated nodes In route search the nodes distributed in threedifferent regions select the relay nodes in different ways Butthey adopt the conventional greedy algorithmThemain stepsof EBVRPVCM are as follows

Step 1 A node receives a data packet

Step 2 Thenode determines whether itself or a neighbor usesthe virtual coordinates If it does go to Step 3 otherwise toStep 4

Step 3 If the node is closer to the area it uses the virtualcoordinates to select a relay node if the node is out of thearea it uses the actual coordinate prior to selecting nonedgenode as the relay node if it is in the free zone it uses the actualcoordinate to select a relay node

Step 4 If there is no void during the process of selecting relaynode using the greedymode go to Step 6 otherwise to Step 5

Step 5 The node starts void processing mode and establishesthe current void virtual coordinates and returns to Step 2

Step 6 The node sends data packets to the selected relaynode

Since the mapping of virtual round void constitutes anonvoid edge routing structure the packets going throughthe void can bypass the void It is not affected by the positionof source node and destination node


4 Analysis of EBVRPVCM

41 The Virtual Coordinates and Actual Coordinates Afterexecuting the virtual coordinate mapping algorithm virtualcoordinates of edge nodes are sequentially distributed onthe current mapped virtual void circle correspondingly Soit is possible that there exists the dislocation among themapped edge virtual coordinates and the nonvoid edge nodecoordinates It is known from Section 33 that the virtualcoordinate is only used between the void edge node and itsneighbor nodes According to the routing steps mentionedin Section 34 it uses the virtual coordinate to select therelay node in the closer region Once bypassing the currentvoid and entering the detachment region it prefers to usethe actual coordinate to select the relay node The virtualcoordinate plays a guiding role in the process of selectingrelay node Since it is independent of geographical coordi-nates [13] the execution of greedy algorithm [12] is onlylimited either within the geographical coordinates or withinthe virtual coordinatesTherefore even if there is coordinatesoverlap between the virtual coordinate of the edge and thecoordinates of nodes on the nonvoid edge it does not affectthe routing selection

42 Path Analysis From Section 32 it is known that allthe neighbor nodes of edge node receive the broadcast voidinformation after mapping the virtual coordinate Nodesuse this void information to judge the void in advanceand correspondingly the transmission path is shortened Asshown in Figure 5(a) the node 119887

119904sends a packet to the

destination node and the void appears when 119887119904sends data

packets to node 119887V using the greedy algorithm [12] before theestablishment of virtual coordinates

If we use the edge forwarding protocol to solve void prob-lem the packet is always at 119887V to enter the edge forwardingmode Assuming that there is a uniform distribution of thenetwork nodes the node density is 120588 When the current voidvirtual coordinate is established using EBVRPVCM routingprotocol the probability of at least one edge node falling inthe communication radius of node 119887

119904and node 119887V is

119875 = 1 minus expminus120588120590 (5)

where 120590 is the area of intersection region within communi-cation radius that does not contain the obstacle region Inthis case the edge node 119887

119889will be directly selected as the

forwarding node according to the virtual coordinate whichshortens the transmission path With the increase of thenodersquos probability density 120588 the probability of shortening thetransmission path is increased gradually Therefore EBVR-PVCM can obtain the shortest routing path Meanwhile itis conducive to further shorten the routing path in the caseof using the whole information of void during the process ofrelay node selection

As shown in Figure 5(b) nodes 119904 and 119889 are the sourcenode and destination node respectively 119875

2is the ideal

transmission path of nonvoid 1198751is the transmission path

selected by routing protocol based on the edge forwarding1198753is the transmission path selected by EBVRPVCM

Obstacle region

Fringe nodeHomogeneous sensor node

bs bv

bd

(a)

dObstacle

regionObstacle

region

Homogeneous sensor node

P1

P2

P3

(b)

Figure 5The transmission path of the discovered virtual coordinateand optimization scheme

Because edge forwarding protocol can only forwardpackets in one direction the selected path is longer Virtualcoordinate chooses forwarding direction flexibly accordingto the void information Correspondingly it shortens therouting path

43 Control Cost Analysis Note that the control packet size isCPSgr in the greedy routing algorithm while the void probepacket size and the distribution package size are VPSdet andDPSdis respectively in EBVRPVCM route The number ofvoid edge nodes is VENvs the average number of hops toreach the destination node is hrdEBVRPVCM and the numberof control packets used to send 119899 packets is 119871EBVRPVCM in thefollowing

119871EBVRPVCM = (VPSdet + DPSdis)VENvs

+ CPSgrhrdEBVRPVCM119899

(6)

The average size of a control packet for each data packetis

ACPEBVRPVCM =

(VPSdet + DPSdis)VENvs

119899

+ CPSgrhrdEBVRPVCM

(7)


As the number 119899 of packet sent across the networkincreases the average size of the control packet in EBVR-PVCM protocol is close to the greedy algorithm

To compare with the edge forwarding protocol we havethe following notations The edge forwarding control packetsize is FCPefp the ratio of the greedy algorithm for routingis 119903 and the average number of hops data reaching thedestination node is hrdgr and then the number of controlpackets used to send 119899 packets is

119871gr = (CPSgr119903 + FCPefp (1 minus 119903)) hrdgr119899 (8)

The average size of a control packet is

ACPefp = (CPSgr119903 + FCPefp (1 minus 119903)) hrdgr (9)

From Section 42 because under the edge forwardingmode FCPfp gt CPSgr and 0 lt 119903 lt 1 it is known that

hrdEBVRPVCM lt hrdgr (10)

Correspondingly we obtain the following results

CPSgrhrdEBVRPVCM lt CPSgrhrdgr lt ACPefp

lt FCPefphrdgr(11)

For the same fixed node of wireless sensor network 119903 isconstant From (9) the average control packet size ACPefpis independent of the amount of data packet size 119899 and therange of the value is set in (11) While 119871EBVRPVCM is reducedwith the increase of data packets sent in the network thereexists 119899

119888that satisfies ACPEBVRPVCM lt ACPefp when 119899 gt 119899

119888

So the size of control packet used in EBVRPVCM is smallerthan that in the edge forwarding protocol

5 Simulation Analysis

51 Parameter Setting To verify the performance of EBVR-PVCM routing protocol this paper simulates it on theplatform of NS2 [14] and compares it with RGP and GPSRSimulation scenario is a square area and sensor nodesare evenly distributed within the square area We simulaterouting void of the real application environment throughprohibiting deploying nodes around the center

For the convenience of comparison we randomly selectthe destination nodes in the lower region of the square areaand source nodes in the upper region respectivelyThe sourcenodes send packets to the destination nodes During thesimulation we randomly select one node as the destinationnode and 4 nodes as the source nodeThe void radius changesfrom 90m to 270m The simulation performance indexesare ratio of packet successfully transmitted end-to-end delayaverage number of hops cost of control packet and energyconsumption Because the routing protocols of [5 9] do notguarantee that any node in the network is effective even ifthere exists a routing path it may not be possible to establisha link So we compare the performance of EBVRPVCM withRGP [7] and GPSR [4] Specific parameters are shown inTable 1

Table 1 Simulation parameters

Parameter ValueSimulation area 1000m times 1000mThe number of nodes 1000Node communication radius 50mBandwidth 200KbpsPacket transmission rate 1 pktsTransmitting power 16WReceived power 12WIdle listening power 004WSimulation time 200 s

EBVRPVCMRGPGPSR

100 260240220200180160140120

100989694

Tran

smiss

ion

succ

ess r

atio

()

92908886848280

Void radius (m)

Figure 6 Effects of void radius on transmission ratio

52 Scenario 1 Effects of Void Radius on Transmission RatioEffect of void size on the successful transmission ratio isshown in Figure 6

With the gradual increasing of void radius the successfultransmission ratios of EBVRPVCM and GPSR are in thetrend of decreasing While the successful transmission ratioof RGP keeps at around 95 When the void is small theperformance of EBVRPVCM and GPSR is better than that ofRGP

With the increase of void radius RGP remains the stablesuccess transmission ratio because it is a flooding basedrouting protocol that has stronger ability to establish aneffective pathWhen the void radius is over 210m the successtransmission ratio of EBVRPVCM is lower than that of RGP

53 Scenario 2 Effects of Void Radius on Average TransmissionDelay Figure 7 illustrates the effects of void size on theaverage transmission delay

The average transmission delay is mean value of trans-mission delay of packet successfully reaching destinationnode As the RGP needs to establish a routing path firstlyand then transmits data the transmission delay is higherand the transmission delay is two times more than that of


07

06

05

04

03

025

035

045

055

065

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)

Tran

smiss

ion

delay

(s)

Figure 7 Effects of void radius on average transmission delay

Aver

age h

ops

35

30

25

20

15

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)

Figure 8 Effects of void size on average hop

the other two kinds of routing protocols When the voidis small the transmission delay of EBVRPVCM is slightlysmaller than that of GPSR With the increasing of voidradius the transmission delay is increased accordingly butthe growth of transmission delay of GPSR is faster than thatof EBVRPVCM

54 Scenario 3 Effects of Void Size onAverageHops Theeffectof void size on the average hops is shown in Figure 8 Thenumber of average hops of EBVRPVCM is around 8 hops lessthan that of RGPWith the increasing void radius the numberof average hops becomes larger gradually

When the void radius is over 240m there is relativelysubstantial increase of the average number of hops of GPSRrouting As the EBVRPVCM routing can select the shortestpath to bypass the void region according to position of voidand the destination the corresponding growth of average

150 500450400350300250200

100

95

90

85

80

Tran

smiss

ion

succ

ess r

atio

()

75

70

Size of packet (byte)

EBVRPVCMRGPGPSR

Figure 9 Effect of packet size on success transmission ratio

transmission delay and hop increases flatly with the growingof the void radius as shown in Figures 7 and 8

55 Scenario 4 Effects of Void Size on Average EnergyConsumption Table 2 shows the statistical results of averageenergy consumed by sending the unit packet under differentvoid radius during the simulation periods of 0sim100 s and0sim200 s respectively

Because there are more nodes participating in path estab-lishment in RGP and needs to maintain the link the averageenergy consumption is far higher than that of the other twokinds of routing algorithms The routing path establishmentof EBVRPVCM and GPSR only needs the information ofneighbor nodes so the average energy consumption is lessthan that of RGP But after void is mapped through thevirtual coordinate EBVRPVCM uses the greedy mode toselect routing path Correspondingly the average energyconsumption of EBVRPVCM is less than that of GPSR

The subsequent routing uses greedy mode to alleviateit With the simulation time increasing the average energyconsumption reduces gradually So the longer the networkrsquosworking cycle the more the advantages EBVRPVCM has

56 Scenario 5 Effects of Packet Size on Routing Perfor-mance When the size of data packet increases the averagetransmission delay becomes higher The collision probabilityis increasing during wireless transmission The collisioncauses the decreasing of the transmission success ratio andincreasing of the transmission delay Figures 9 and 10 illus-trate the effects on transmission success ratio and averagetransmission delay when the source node sends differentpacket sizes under the condition of maintaining the voidradius at 150m respectively

As shown in Figure 9 EBVRPVCM has the minimumeffect caused by the packet size With the increasing of packetsize from 128 bytes to 512 bytes the transmission successratio of EBVRPVCM is decreased about 5 while that of


Table 2 Average energy consumed under different void radius

Void Radius (m)Average Energy Consumed (Jpkt)

EBVRPVCM GPSR RGP0sim100ms 0sim200ms 0sim100ms 0sim200ms 0sim100ms 0sim200ms

90 1523 1235 1617 1619 11046 6246120 1528 1278 1663 1693 23542 11542150 1529 1354 1787 1793 27064 12442180 1573 1423 1981 2032 38456 21432210 1654 1484 2236 2185 48445 23826240 1645 1503 2573 2498 84828 41635270 1686 1516 2664 2621 98095 56434

020406081012141618

2

Tran

smiss

ion

delay

(s)

150 500450400350300250200Size of packet (byte)

EBVRPVCMRGPGPSR

Figure 10 Effect of packet size on average transmission delay

GPSR and RGP is decreased by approximately 15 and 25respectively

Since there are more control packets in RGP with theincreasing of the packet size the collision probability duringwireless transmission becomes higher which leads to therapid increasing of packet loss rate GPSR did not optimizethe transmission path in path selection so the data isoverconcentrated in the edge nodes of the void which causedthe increasing of transmission collision While EBVRPVCMoptimized transmission path and rationally dispersed thedata packets it alleviated the transmission collision problem

Known from Figure 10 the average transmission delay ofRGP is very sensitive to data packet size and the averagetransmission delay increases nearly 8 times with data packetincreasing from 128 bytes to 512 bytes while EBVRPVCMandGPSR are less affected by the packet size and the transmissiondelay of EBVRPVCM is slightly less than that of GPSR

57 Scenario 6 The Cost of Control Packet The smallerrouting control packet overhead can improve the energyefficiency ofwireless sensor network and prolong the network

100 260240220200180160140120Void radius (m)

times105

04

06

08

10

12

14

16

Cos

t of c

ontro

l pac

ket (

byte

)

EBVRPVCMRGPGPSR

Figure 11 The relationship between control packet cost and voidradius

lifetime Figure 11 illustrates the relationship between the voidradius and control packet cost

As the EBVRPVCMgets the whole void information onlythrough one routing void detecting it makes the subsequentdata packets generated by other source nodes and bypass thevoid only work in the single greedy mode while passing thevoid Therefore EBVRPVCM not only has less control packetcost but also is less affected by the void size although thecontrol packet cost of RGP routing is less affected by voidradius since it uses the flooding mechanism which causesthe larger control packet cost

While each timeGPSR routing passes through the routingvoid it enters into edge forwarding mode using more controlpackets With the increasing of void correspondingly therearemore nodes switching to edge forwardingmodeAnd eachtime when the different data packets pass through the voidsurrounding they enter the edge forwarding mode whichcause the control packet cost growing faster


6 Conclusion and Future Work

For routing void problems in geographical position we usethe network edge structure of nonrouting void to designan EBVRPVCM routing protocol EBVRPVCM routing isimplemented through void detection and virtual coordinatemapping The void process is divided into three stagesIn the void and the surrounding area routing it selectsthe relay nodes using the corresponding virtual coordinateinformation For a routing void EBVRPVCM routing onlyneeds one probe and mapping process Thus it can greatlyreduce the complexity of routing protocols The simulationresults show that the proposed EBVRPVCM routing protocolhas a better performance of average transmission success ratedelay and the average hops The control packet overheadis less and the proposed EBVRPVCM is conducive to savenetwork energy

We are trying to monitor the habitat information andestablish the monitoring WSN of Qinling stub-nosed mon-key Because of its habitat Qinling Mountain is a complexterrain with many obstacles the void of monitoring WSNis unavoidable For the further work we will optimizeEBVRPVCM and use it in the habitat monitoringWSN of theQinling stub-nosed monkey

Conflict of Interests

The authors declare no conflict of interests

Acknowledgments

This work was supported in part by Natural Science BasicResearch Plan in Shaanxi Province of China under Grant2014KW03-02 and Natural Science Foundation of Chinaunder Grant 61202393 The authors are grateful to ProfessorZhang Dr Guan andDrWang that they help us to revise thepaper Also the authors are grateful to the anonymous refereefor a careful checking of the details and for helpful commentsthat improved this paper

References

[1] P Bull G Antonopoulos L Guan X Wang and X FanldquoA multi-class mobility model for dynamic and dependablesystemsrdquo in Proceedings of the 27th International Conference onAdvanced Information Networking and Applications Workshops(WAINA rsquo13) pp 1010ndash1015 Barcelona Spain March 2013

[2] F Cadger K Curran J Santos and S Moffett ldquoA surveyof geographical routing in wireless Ad-Hoc networksrdquo IEEECommunications Surveys amp Tutorials vol 15 no 2 pp 621ndash6532013

[3] B-Q Tang and L-H Zhang ldquoOptimization of energy multi-path routing protocol in wireless sensor networksrdquo SystemsEngineering and Electronics vol 35 no 12 pp 2607ndash2612 2013

[4] B Karp and H T Kung ldquoGPSR greedy perimeter statelessrouting for wireless networksrdquo in Proceedings of the 6th AnnualInternational Conference on Mobile Computing and Networking(MOBICOM rsquo00) pp 243ndash254 August 2000

[5] F C Yu S Park Y Tian M Jin and S-H Kim ldquoEfficienthole detour scheme for geographic routing in wireless sensor

networksrdquo in Proceedings of the IEEE 67th Vehicular TechnologyConference (VTC rsquo08) pp 153ndash157 Singapore May 2008

[6] G Trajcevski F Zhou R Tamassia B Avci P Scheuermannand A Khokhar ldquoBypassing holes in sensor networks load-balance vs latencyrdquo in Proceedings of the IEEE Global Telecom-munications Conference (GLOBECOM rsquo11) pp 1ndash5 IEEE Hous-ton Tex USA December 2011

[7] C-Y Chang C-T Chang Y-C Chen and S-C Lee ldquoActiveroute-guiding protocols for resisting obstacles inwireless sensornetworksrdquo IEEE Transactions on Vehicular Technology vol 59no 9 pp 4425ndash4442 2010

[8] PHuang CWang and L Xiao ldquoImproving end-to-end routingperformance of greedy forwarding in sensor networksrdquo IEEETransactions on Parallel and Distributed Systems vol 23 no 3pp 556ndash563 2012

[9] Y Noh U Lee P Wang B S C Choi and M Gerla ldquoVAPRvoid-aware pressure routing for underwater sensor networksrdquoIEEE Transactions on Mobile Computing vol 12 no 5 pp 895ndash908 2013

[10] J X You Q Han D Lieckfeldt J Salzmann and D Timmer-mann ldquoVirtual position based geographic routing for wirelesssensor networksrdquoComputer Communications vol 33 no 11 pp1255ndash1265 2010

[11] W Wei X-L Yang P-Y Shen and B Zhou ldquoHoles detectionin anisotropic sensornets topological methodsrdquo InternationalJournal of Distributed Sensor Networks vol 2012 Article ID135054 9 pages 2012

[12] G L Xing C Y Lu R Pless and Q Huang ldquoOn greedygeographic routing algorithms in sensing-covered networksrdquo inProceedings of the 5th ACM International Symposium on MobileAd Hoc Networking and Computing (MobiHoc rsquo04) pp 31ndash42ACM Tokyo Japan May 2004

[13] I Stojmenovic A P Ruhil andD K Lobiyal ldquoVoronoi diagramand convex hull based geocasting and routing in wirelessnetworksrdquo Wireless Communications and Mobile Computingvol 6 no 2 pp 247ndash258 2006

[14] NS2 Manual httpwwwisiedunsnamnsdoc

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



that network nodes use the preselected reference node [9] orthe neighbor node information to rebuild their coordinateinformation [10] If the network node corresponding tothe destination node is changed it uses the virtual recon-struction location information It can only apply to a fixeddestination node and the network is inevitably void Node invirtual position based routing protocol is limited by the realphysical position and the virtual location can be adjustedAlthough the greedy algorithm is simple and less complexthe existing virtual routing protocols are not suitable for everynode in the network

To overcome the drawbacks of the above protocols aneffective bypass void routing protocol based on the virtualcoordinates mapping (EBVRPVCM) is proposed in thispaper The protocol not only maps the routing void of edgenode coordinate to a void in the center of the cavity soas to cover a virtual circle in the network but also createsthe virtual coordinate of the edge node Therefore the edgenode with a virtual coordinate can be selected as a relaynode For the void area on the network a circular virtualstructure can effectively bypass routing void Compared withthe traditional protocols the proposed protocol selects therelay node by greedy algorithm on one node and saves theenergy consumption effectively Through establishing thevirtual location it is independent of the destination nodeThere is no need to rebuild the virtual location informationeven if the destination node changes

The rest of the paper is organized as follows Section 2describes the related work of routing void generation andnetwork edge structure Section 3 describes the compo-nents stages and design of the proposed protocol Section 4analyzes the virtual coordinated actual coordinates pathand control cost of EBVRPVCM Section 5 evaluates theperformance throughnumerical simulation onNS2 platformSection 6 is the conclusion and future work

2 The Related Work

21 Routing Void Generation For routing based geographicinformation we use the greedy algorithm to choose therelay nodes which is closer than their neighbor nodes tothe destination If such neighbor node does not exist therewill be routing void [11] Figure 1 illustrates the void generateschematic

As shown in Figure 1 node 1198992receives the data transmit-

ted by 1198991 and the destination node is 119889

1 A set of neighbor

nodes for the node 1198992is 1198991 1198993 and 119899

4 since the distances

from the nodes 1198991 1198993 and 119899

4to the destination node 119889

1

are greater than that of 1198992 the route appears void according

to the greedy algorithm [12] The data will not be able topass through Similarly when the node 119899

5sends data to the

destination node 1198892 routing void will appear too

22 No Routing Void Network Edge Structure Suppose inWSN the number of edge nodes around an obstacle area is119873

119887

Obstacle region

n2 n5

d2

d1

n1

n3

n4


Figure 1 Void generate schematic

and the set of edge nodes is 119887119896| 119896 = 1 2 119873

119887 The edge

node must meet

119889 (119887119896 119887119896+1

) lt 119879119888 119896 = 1 2 119873

119887minus 1

119889 (1198871 119887119873119887

) lt 119879119888

119887119896+119894

| 119889 (119887119896 119887119896+119894

) lt 119879119888 = 120601

119896 = 2 119873119887minus 2 2 le 119894 le 119873

119887minus 119896

119887119896| 119889 (1198871 119887119896) lt 119879119888 = 120601 119896 = 3 119873

119887minus 1

(1)

where 119889(119909 119910) is the Euclidean distance between the nodes 119909and 119910 119879

119888is the communication radius of the node 119894 is an

integer the edge node set is 119887119896

| 119896 = 1 119873119887 and any

node can only communicate with the two adjacent nodesIf the distance between the edge node of obstacle and a

fixed node 119874 satisfies

119889 (119887119896 119874) = 119877 119896 = 1 119873

119887 (2)

the distribution of the edge node to the center of the circle119874 is determined 119877 is the radius of the circle as shown inFigure 2 In the edge of the structure around the area of theobstacle each edge node has only two neighbor edge nodesFrom isotropic circular geometry the packet routing is notvoid for any destination node while going through the region

Each node uses the greedy algorithm to select the relaynode path As an example the source node 119904 sends packets todestination node 119889 and shows the generation of free routingvoidThe edge node 119887

1receives the packet and uses the greedy

algorithm to find the next hop relay nodeThe same is for edgenode 119887

2 The two nodes are distributed in a concentric circle

and the distance of 1198872to destination node 119889 is less than that

of 1198871 Then 119887

1selects 119887

2as the next hop node and the routing

void problem does not occur Packets in the edge node 1198873

will not either incur routing void problem The edge node1198874uses greedy algorithm to select the next hop node 119899

5 and


o

d

R

Obstacle region

b1

b2s

b3

n5

n6

b4

b


Nb







119887





1 1199101)

(1199092 1199102) (119909

119873119887 119910119873119887


(119909119900 119910119900) = (

1

119873119887

119873119887

sum

119896=1

119909119896

1

119873119887

119873119887

sum

119896=1

119910119896) (3)


119889119900= max119896=12119873119887

119889119896| 119889119896= radic(119909

119896minus 119909119900)2

+ (119910119896minus 119910119900)2

(4)






1and 119887


1015840

1and

1198871015840


nodes 1198872 1198873 and 119887


1and 119887

1015840

5


1015840

4 respectively



initialize 119894 = 119895119872 = 120601

while (119894 le 119873119887) do


if 119872 == 120601 then(119909temp 119910temp) = (1199091015840 1199101015840)

elsewhile 119888 = 0 do1199091015840


1199101015840


deleted 119887119894minus119888

from119872

EndwhileEndif

else add the 119887119894to119872

Endif119894++

Endwhile


o


998400

998400

998400

b998400

b1

b1

b2

b2

d0

b3

b3

b4

4

b5

998400b5




d

Cn

m

B

C

AO

Fringe node




















119875 = 1 minus expminus120588120590 (5)





2is the ideal



Obstacle region


bs bv

bd

(a)

dObstacle

regionObstacle

region


P1

P2

P3

(b)






(6)


ACPEBVRPVCM =


119899

+ CPSgrhrdEBVRPVCM

(7)











lt FCPefphrdgr(11)



119888







EBVRPVCMRGPGPSR

100 260240220200180160140120

100989694

Tran

smiss

ion

succ

ess r

atio

()

92908886848280

Void radius (m)








07

06

05

04

03

025

035

045

055

065

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)

Tran

smiss

ion

delay

(s)


Aver

age h

ops

35

30

25

20

15

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)





150 500450400350300250200

100

95

90

85

80

Tran

smiss

ion

succ

ess r

atio

()

75

70


EBVRPVCMRGPGPSR












90 1523 1235 1617 1619 11046 6246120 1528 1278 1663 1693 23542 11542150 1529 1354 1787 1793 27064 12442180 1573 1423 1981 2032 38456 21432210 1654 1484 2236 2185 48445 23826240 1645 1503 2573 2498 84828 41635270 1686 1516 2664 2621 98095 56434

020406081012141618

2

Tran

smiss

ion

delay

(s)


EBVRPVCMRGPGPSR






100 260240220200180160140120Void radius (m)

times105

04

06

08

10

12

14

16

Cos

t of c

ontro

l pac

ket (

byte

)

EBVRPVCMRGPGPSR











Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










o

d

R

Obstacle region

b1

b2s

b3

n5

n6

b4

b


Nb







119887





1 1199101)

(1199092 1199102) (119909

119873119887 119910119873119887


(119909119900 119910119900) = (

1

119873119887

119873119887

sum

119896=1

119909119896

1

119873119887

119873119887

sum

119896=1

119910119896) (3)


119889119900= max119896=12119873119887

119889119896| 119889119896= radic(119909

119896minus 119909119900)2

+ (119910119896minus 119910119900)2

(4)






1and 119887


1015840

1and

1198871015840


nodes 1198872 1198873 and 119887


1and 119887

1015840

5


1015840

4 respectively



initialize 119894 = 119895119872 = 120601

while (119894 le 119873119887) do


if 119872 == 120601 then(119909temp 119910temp) = (1199091015840 1199101015840)

elsewhile 119888 = 0 do1199091015840


1199101015840


deleted 119887119894minus119888

from119872

EndwhileEndif

else add the 119887119894to119872

Endif119894++

Endwhile


o


998400

998400

998400

b998400

b1

b1

b2

b2

d0

b3

b3

b4

4

b5

998400b5




d

Cn

m

B

C

AO

Fringe node




















119875 = 1 minus expminus120588120590 (5)





2is the ideal



Obstacle region


bs bv

bd

(a)

dObstacle

regionObstacle

region


P1

P2

P3

(b)






(6)


ACPEBVRPVCM =


119899

+ CPSgrhrdEBVRPVCM

(7)











lt FCPefphrdgr(11)



119888







EBVRPVCMRGPGPSR

100 260240220200180160140120

100989694

Tran

smiss

ion

succ

ess r

atio

()

92908886848280

Void radius (m)








07

06

05

04

03

025

035

045

055

065

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)

Tran

smiss

ion

delay

(s)


Aver

age h

ops

35

30

25

20

15

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)





150 500450400350300250200

100

95

90

85

80

Tran

smiss

ion

succ

ess r

atio

()

75

70


EBVRPVCMRGPGPSR












90 1523 1235 1617 1619 11046 6246120 1528 1278 1663 1693 23542 11542150 1529 1354 1787 1793 27064 12442180 1573 1423 1981 2032 38456 21432210 1654 1484 2236 2185 48445 23826240 1645 1503 2573 2498 84828 41635270 1686 1516 2664 2621 98095 56434

020406081012141618

2

Tran

smiss

ion

delay

(s)


EBVRPVCMRGPGPSR






100 260240220200180160140120Void radius (m)

times105

04

06

08

10

12

14

16

Cos

t of c

ontro

l pac

ket (

byte

)

EBVRPVCMRGPGPSR











Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










initialize 119894 = 119895119872 = 120601

while (119894 le 119873119887) do


if 119872 == 120601 then(119909temp 119910temp) = (1199091015840 1199101015840)

elsewhile 119888 = 0 do1199091015840


1199101015840


deleted 119887119894minus119888

from119872

EndwhileEndif

else add the 119887119894to119872

Endif119894++

Endwhile


o


998400

998400

998400

b998400

b1

b1

b2

b2

d0

b3

b3

b4

4

b5

998400b5




d

Cn

m

B

C

AO

Fringe node




















119875 = 1 minus expminus120588120590 (5)





2is the ideal



Obstacle region


bs bv

bd

(a)

dObstacle

regionObstacle

region


P1

P2

P3

(b)






(6)


ACPEBVRPVCM =


119899

+ CPSgrhrdEBVRPVCM

(7)











lt FCPefphrdgr(11)



119888







EBVRPVCMRGPGPSR

100 260240220200180160140120

100989694

Tran

smiss

ion

succ

ess r

atio

()

92908886848280

Void radius (m)








07

06

05

04

03

025

035

045

055

065

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)

Tran

smiss

ion

delay

(s)


Aver

age h

ops

35

30

25

20

15

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)





150 500450400350300250200

100

95

90

85

80

Tran

smiss

ion

succ

ess r

atio

()

75

70


EBVRPVCMRGPGPSR












90 1523 1235 1617 1619 11046 6246120 1528 1278 1663 1693 23542 11542150 1529 1354 1787 1793 27064 12442180 1573 1423 1981 2032 38456 21432210 1654 1484 2236 2185 48445 23826240 1645 1503 2573 2498 84828 41635270 1686 1516 2664 2621 98095 56434

020406081012141618

2

Tran

smiss

ion

delay

(s)


EBVRPVCMRGPGPSR






100 260240220200180160140120Void radius (m)

times105

04

06

08

10

12

14

16

Cos

t of c

ontro

l pac

ket (

byte

)

EBVRPVCMRGPGPSR











Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















119875 = 1 minus expminus120588120590 (5)





2is the ideal



Obstacle region


bs bv

bd

(a)

dObstacle

regionObstacle

region


P1

P2

P3

(b)






(6)


ACPEBVRPVCM =


119899

+ CPSgrhrdEBVRPVCM

(7)











lt FCPefphrdgr(11)



119888







EBVRPVCMRGPGPSR

100 260240220200180160140120

100989694

Tran

smiss

ion

succ

ess r

atio

()

92908886848280

Void radius (m)








07

06

05

04

03

025

035

045

055

065

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)

Tran

smiss

ion

delay

(s)


Aver

age h

ops

35

30

25

20

15

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)





150 500450400350300250200

100

95

90

85

80

Tran

smiss

ion

succ

ess r

atio

()

75

70


EBVRPVCMRGPGPSR












90 1523 1235 1617 1619 11046 6246120 1528 1278 1663 1693 23542 11542150 1529 1354 1787 1793 27064 12442180 1573 1423 1981 2032 38456 21432210 1654 1484 2236 2185 48445 23826240 1645 1503 2573 2498 84828 41635270 1686 1516 2664 2621 98095 56434

020406081012141618

2

Tran

smiss

ion

delay

(s)


EBVRPVCMRGPGPSR






100 260240220200180160140120Void radius (m)

times105

04

06

08

10

12

14

16

Cos

t of c

ontro

l pac

ket (

byte

)

EBVRPVCMRGPGPSR











Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















lt FCPefphrdgr(11)



119888







EBVRPVCMRGPGPSR

100 260240220200180160140120

100989694

Tran

smiss

ion

succ

ess r

atio

()

92908886848280

Void radius (m)








07

06

05

04

03

025

035

045

055

065

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)

Tran

smiss

ion

delay

(s)


Aver

age h

ops

35

30

25

20

15

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)





150 500450400350300250200

100

95

90

85

80

Tran

smiss

ion

succ

ess r

atio

()

75

70


EBVRPVCMRGPGPSR












90 1523 1235 1617 1619 11046 6246120 1528 1278 1663 1693 23542 11542150 1529 1354 1787 1793 27064 12442180 1573 1423 1981 2032 38456 21432210 1654 1484 2236 2185 48445 23826240 1645 1503 2573 2498 84828 41635270 1686 1516 2664 2621 98095 56434

020406081012141618

2

Tran

smiss

ion

delay

(s)


EBVRPVCMRGPGPSR






100 260240220200180160140120Void radius (m)

times105

04

06

08

10

12

14

16

Cos

t of c

ontro

l pac

ket (

byte

)

EBVRPVCMRGPGPSR











Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










07

06

05

04

03

025

035

045

055

065

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)

Tran

smiss

ion

delay

(s)


Aver

age h

ops

35

30

25

20

15

EBVRPVCMRGPGPSR

100 260240220200180160140120Void radius (m)





150 500450400350300250200

100

95

90

85

80

Tran

smiss

ion

succ

ess r

atio

()

75

70


EBVRPVCMRGPGPSR












90 1523 1235 1617 1619 11046 6246120 1528 1278 1663 1693 23542 11542150 1529 1354 1787 1793 27064 12442180 1573 1423 1981 2032 38456 21432210 1654 1484 2236 2185 48445 23826240 1645 1503 2573 2498 84828 41635270 1686 1516 2664 2621 98095 56434

020406081012141618

2

Tran

smiss

ion

delay

(s)


EBVRPVCMRGPGPSR






100 260240220200180160140120Void radius (m)

times105

04

06

08

10

12

14

16

Cos

t of c

ontro

l pac

ket (

byte

)

EBVRPVCMRGPGPSR











Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













90 1523 1235 1617 1619 11046 6246120 1528 1278 1663 1693 23542 11542150 1529 1354 1787 1793 27064 12442180 1573 1423 1981 2032 38456 21432210 1654 1484 2236 2185 48445 23826240 1645 1503 2573 2498 84828 41635270 1686 1516 2664 2621 98095 56434

020406081012141618

2

Tran

smiss

ion

delay

(s)


EBVRPVCMRGPGPSR






100 260240220200180160140120Void radius (m)

times105

04

06

08

10

12

14

16

Cos

t of c

ontro

l pac

ket (

byte

)

EBVRPVCMRGPGPSR











Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Acknowledgments


References


















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article an efficient bypassing void routing algorithm...

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