A correlation model for MAC protocols In Event-driven Wireless Sensor Networks

Rajeev K. Shakya, Stu. MIEEE, Yatindra Nath Singh, SMIEEE, and Nishchal K. Venna, MIEEE Department of Electrical Engineering, Indian Institute of Technology Kanpur

Email: {rajeevs.ynsingh.nishchal}@iitk.ac.in

Abstract-In event-driven scenario, each event triggers a large number of nodes for sensing and transmission, thus the nodes encounter spatially-correlated contention due to correlation be­tween nodes in spatial domain. To mitigate the correlated contention inside event area, a correlation model is proposed to describe the correlation characteristics of sensor nodes using sensing coverage of nodes. The CoINS algorithm using correlation model is introduced to exploit the spatial correlation inside the event area. Further, a random correlated event traffic model for NS-2 network simulator is developed to apply the results of model with existing MAC protocols for measuring the effectiveness of proposed CoINS algorithm. The simulation results using MAC protocols show that by exploiting spatial correlation network performance in terms of energy consumption and delay guarantee improves drastically. The analytical results of proposed correlation model also indicates better spatial correlation between nodes for higher density of nodes and larger sensing range.

Index Terms-Energy-Efficient MAC protocols, performance analysis, Wireless Sensor Network.

I. INTRODUCTION

The recent developments of wireless sensor network (WSN) have enabled low cost, low power sensor nodes which are capable of sensing, processing and transmitting sensory data from sensing environment such as surveillance fields. These sensor nodes cooperatively monitor physical environmental conditions (for examples temperature, sound, pressure etc.) accurately in space and time to detect the events of interest. In densely deployed WSN, sensor nodes encounter spatially­correlated contention, once an event is detected in sensing field. The mUltiple nodes of same neighborhood sense it and try to report data to the sink. As a result, synchronized burst of transmissions is observed which cause severe collisions in the event area. At the same time, sensor nodes transmit redundant data about the sensed event to the sink. Thus large amount of energy is consumed due to collisions and transmission of redundant data. In fact, it is sufficient that a smaller number of nodes can transmit event information to the sink to fulfill the application requirement. Recent works show that it is possible to allow the smaller number of sensor nodes to send the data in order to remove redundancy. Thus, the channel contention as well as redundant transmission can be minimized at MAC layer. Hence, correlation characterization is of great significance to prolong the network lifetime by developing new energy-efficient MAC protocols to exploit the spatial correlation.

There have been many MAC protocols published in litera­ture [1]. But there are only few which taken the characteristics

of spatial correlation into consideration for the design. In this paper, a correlation model have been proposed using sensing coverage of nodes. Then, using the proposed model, a Correlation-based Iterative Node Selection (C-INS) algorithm has been presented. It exploits the spatial correlation in an event area for energy conservation. In addition, an application have been described to show how spatial correlation can be exploited at MAC layer in event-driven wireless sensor networks.

The paper is organized as follows. The related work has been summarized in section II. The proposed correlation model and C-INS algorithm are introduced in section III along with numerical results. Section IV describes the Random Correlated Event Traffic model for NS-2 network simulator. It has been is used as an example to show how to apply our correlation model to exploit the spatial correlation in event­driven workload. The results using NS-2 are discussed in Section V. Finally the conclusions are given in Section VI.

II. RELATED WORK

In WSN, the research on MAC protocol design has been focused mainly on energy-latency trade-offs. S-MAC [2] is de­signed to save the energy by using listen and sleep periodically with collision avoidance facilities of IEEE 802.11 standard. S­MAC uses synchronization mechanism to form virtual clusters of sleep/wakeup schedule to avoid overhearing problem. Other protocols based on S-MAC proposed to further decrease the energy consumption, listed as D-MAC [3], T-MAC [4], DW­MAC [5], RMAC [6] etc. These variants deal with major source of energy waste such as idle-listening, overhearing and collision problems. S-MAC [2] uses RTS/CTS/ACK packets based on IEEE 802.11 for medium access control and inte­grates a sleep/wakeup schedule to minimize the energy waste. In RMAC [6], the RTS/CTS packets are replaced by Pioneer frames. A Pioneer frame forwards over multiple hops along the route for giving notification about next wakeup. Hence, nodes are informed in advance using Pioneer frame when they have to wakeup for receiving data frames. Similar to S-MAC, DW­MAC [5] is a synchronized duty-cycled MAC protocol, and reduces energy consumption by synchronizing both sleep and wakeup times of nodes. These protocols add complexity and overhead for clock synchronization. Unlike synchronized duty­cycled MAC protocols, B-MAC [7] uses a low power listening mechanism, best suitable for low data rate wireless sensor net­works. In low power listening mechanism, before transmitting

actual data frame, a sender initiates preamble transmISSIOn for duration longer than receiver's periodic wakeup interval. Similar to S-MAC, and RMAC, B-MAC also makes use of a periodic on/off cycle of radio transceiver. However it is unsynchronized duty cycle protocol, each node maintains its own independent sleep/wakeup schedule. RI-MAC [8] is also un synchronized duty cycle protocol which uses receiver­initiated approach with wakeup beacon instead of preamble. Since beacons are shorter than a preamble, collisions are minimized significantly [8].

For specific event-driven sensor network applications, fol­lowing work has been published which has taken spatial correlation of sensor data into consideration. CC-MAC [9] was proposed based on theoretical framework of correlation in WSN [10]. In this framework, a relation between location of sensor nodes and event information reliability is investigated to design efficient communication protocols. Specifically, dis­tortion function is derived and Iterative Node Selection (INS) algorithm is proposed. Then CC-MAC regulates the minimum number of packets to be transmitted by exploiting the spatial correlation. CC-MAC consists of two components: the event MAC (E-MAC), which filters the correlated measurements from nodes and the network MAC (N-MAC), which is respon­sible to route the reporting packets to the sink. E-MAC uses an Iterative Node Selection (INS) algorithm to determine the correlation radius (Tearr) inside event area and only one node is allowed to transmit event information within a correlation radius. Other nodes periodically sleep to save energy and wake up to forward the packets. Initially, all nodes within T carr radius contend to access the channel like contention based protocol. Only a node winning the contention is selected as representative node of that region while other nodes turn to sleep. E-MAC uses slightly modified version of standard RTS/CTSIDATAIACK scheme in the IEEE 802.11 to route the packets to the sink. Following a similar philosophy to CC-MAC, SC-MAC [11] presented as an alternative to further optimize the node selection in the event area. It offers priority node selection strategy according to received signal strength of event source observed by the nodes in the event area.

III. ARCHITECTURE AND CORRELATION MODEL

In an event-driven WSN, since the spatially-correlated traffic is observed by sensor nodes in an event area, it also results in higher amount of contention. In an event area, suppose there are N sensor nodes that can sense the event, we denote them as N = {nl, n2, n3, ... } with spatial coordinates, {8l' 82, 83 ... }. There exists correlation between these nodes based on location, which can be exploited to solve the high contention problem by selecting only !vI sensor nodes out of N sensor nodes (!vI < N) to report the event.

A. Sensor Deployment Model

Consider a sensor network application where large number of sensor nodes are deployed randomly over the surveillance region. An example of nodes' deployment for WSN is shown in Fig. I. The continuous circle area indicates the event area;

Fig. 1: The model architecture

the dashed circle represents valid sensing area of the sensors; black node represents sink node; white nodes represent sensor nodes; and a random event is represented by star. Recall that wireless sensor networks are characterized by their coverage range (i.e., sensing range for detecting the events) and trans­mitting range (for communicating with sensor nodes). The followings are few reasonable assumptions, (i) All the sensor nodes are assumed to follow the boolean disk coverage model, which means that sensor nodes have fixed sensing radius and sensing area is represented by a disk centered at the sensor node's spatial position. All the events within such a disk is sensed by the sensor node while no event outside of the disk, is sensed. This sensing model is traditionally known as omni­directional sensing model [12]. (ii) Apart from sensing range, each sensor node has a communication range which is much larger than sensing range. (iii) The sink node is only interested in collective reports from all nodes of a detected event. (iv) There is no movement among sensor nodes after deployment, so the location information of each node is known and distance between its neighbors can also be acquired.

B. The correlation Model

In this section, we derive a correlation coefficient to describe the degree of correlation between sensor nodes ni and nj

in the event area. Since a Boolean Disk Coverage Model is considered with sensing range T at locations 8i, 8 j, the fraction of overlapped area covered by two circular disks represents the correlation coefficient, denoted by Ke{118i - 8jll} which is function of distance between sensor node ni and r1j as shown in Fig. 2. Here e will be a control parameter and is discussed later.

It should be noted that intuitively, the spatial correlation between sensor nodes is directly related to the correlation characteristics of event information observed by sensor nodes in spatial domain [9].

To find the correlation coefficient among N nodes in event area, assuming that N nodes observe the event source S in the event area. We then construct a mathematical model to compute the correlation with respect to event source S.

Consider event area S as random field, total sensor nodes, N = {nl, n2, n3, ... } are within the event area with spatial coordinates, {8l,82,83 ... }. The data set Z =

{z(nd, z(n2), z(n3), ... } contains the measured information

y

,/(r ,

, ,

P'\ : , ,

, ,

,

x

Fig. 2: The spati I circular correlation model

TABLE I: Notations

Symbol

5i 5j A

dCi,j)

(Pi� ' Pi� ) Lij

Description

Sensing region of node ni of r-radius disk centered at itself

Sensing region of node nj of r-radius disk centered at itself

Area of the Sensing region

Euclidean between nodes ni and nj located at Si and Sj Intersection points of two r-radius disks of nodes A cornman chord length which is length of the line segment joining two intersection points Pi� and Pi� Area of region surrounded by arc denoted by Pi� Pi� for Si and chord denoted by Pi� Pi� as shown by shade� area

Area of region surrounded by arc denoted by Pi� Pi� for Sj and chord denoted by Pi� Pi�

where Ke(d(i,j)) is the decreasing function with distance d, following the limiting value of I at dCi,j) = 0 and of 0 for dCi,j) :;0. 2r.

The Ai and Aj are same due to symmetry as shown in Fig. 2.

. r2 cos-1 (dU,;) ) AJ =

2r , 2

From Eq. (2) , we get

2 cos-1 (d�;i) ) d( i,j) Ke(d(i,j)) =

---Jr--'--�

"':" - -Jr-r-2 .

(3)

(4)

Let B = 2r be a control parameter, Eq. (4) can be simplified as

-1 (dU.:i) ) _ 2 cos -e- 2d(i,j)

V 2 2 Ke(d(i j)) - - -B2 . (B - dc' .)) ,

1f 1f 't,) (5)

We see that when d(i,j) = 2r, the correlation model gives zero value. It means that there is no correlation between sensor nodes. So, we introduce a control parameter B equal to 2r, as a variable to control the correlation among nodes. Thus, the correlation model can be rewritten in general form as follow.

K (d ) 2COS-1C¥) _ 2d(i,j) /(B2 -d2 ) e (i,j) = 1r ----:;r(j2 ·V (i,j)

for 0 :::; d(i,j) :::; B; = 0 for d(i,j) > B.

where B = 2r, and d(i,j) = I isi - sjll.

(6)

It is clearly seen from Eq. (6) that when covariance function ------------------------- Ke(d(i,j)) is 0, it means that there is no correlation between

sensor node ni and nj, located at distance dCi,j) from each other. If it is equal to 1, the sensor nodes are highly correlated.

Covariance matrix computed by a node with its neighbors

Area of the Sensing region

K8(11·11) A

from all the sensor nodes. The sink node will be responsi­ble for collecting these readings to compute the correlation characteristics between sensor nodes.

Note that since event area is random variable, so Z is also assumed to be random variable. We use the notations Zi,Zj instead of z(ni), z(nj) for simplicity. The data set Z is associated with covariance function K e ( .) , which is function of correlation coefficients between the sensor nodes. Now, we found from statistical properties:

{ } _ COV{Zi,Zj}

{ II I } carr Zi,Zj - = Ke Si - Sj I , (I) . jvar{zi}.var{zj}

where K e { II Si - S j II} denotes the correlation coefficient of sensor node ni and nj. The Ke{llsi - sjll} decreases monotonically with distance d (i.e. I isi - sjll) between sensor node ni and r1j, located at Si and S j respectively.

1) The correlation model: Symbols and notations used in Fig. 2 are shown in Table I. If dCi,j) < 2r, 5i overlaps with 5j, and we can define the correlation as

(2)

C. Discussion

In sensor network applications, as long as area of interest is specified, the correlation characteristics of observations of sensor nodes can be obtained as given above. The proposed correlation model can be used to design differential source coding between sensor nodes as well as aggregation of sensor measurements in WSNs. The proposed model is a generalized one that can be applied to all sensor network applications, as the assumptions used in this model are common for most of the WSNs. the sensor coverage model used by us is the tradition­ally used one for WSNs. In general, nodes are equipped with temperature, humidity, and magnetic sensors. These sensors can sense within 3600 range . So unit disk coverage model (also known as omni-directional sensing model) is a valid model for WSNs [12]. The proposed correlation model is different from common covariance models introduced in [13] because it considers the real network conditions of WSNs such as location of nodes, sensing range, and distance between them.

In addition, the proposed correlation model can help in design of energy-efficient communication protocols for WSNs.

25

o 25 50 75 100 125 150

Fig. 3: Random distribution of 200 nodes with e = 9 m.

For example, Vuran et al. [9] and Guoqiang et al. [11] have used different covariance functions [13] to determine the relationship between the locations of sensor nodes and event estimation reliability in order to design energy-efficient MAC protocol. We can apply our proposed correlation model to the work by Vuran et al. [9] and Guoqiang et al. [11] respectively.

25 50 75 100 x (mp.tp.r�)

125 150

Fig. 4: Random distribution of 200 nodes with e = 14 m.

D. Performance Evolution of proposed Model

We present the analytical results using MATLAB for ran­domly distributed 200 nodes in 150 x 150 m2 area (as shown in Fig. 3 and 4) and for 30 nodes in 50x50m area (as shown in Fig. 5) . The correlation relationship between nodes has been drawn by varying control parameter e and if the value of Ke(d) between the nodes is greater then zero, then the two nodes are shown with connected by a solid line. In Figs. 3 and 4, a node-pair with Ke(d) equal to zero does not show any correlation, because both the nodes are out of sensing range of each other. The distribution of 200 nodes with e = 9 (i.e. sensing range = 4.5m) is shown with a few connected lines, it means less number of nodes are in correlation (see

50,-----�--�--:.:__�--�--,

40

30

•

20

/' '- � 0.06 0.064

Y 0.024 ; 0 00026 / 0 13 "" 0.11 �.0083'i o.17J 0 065 0 057-1 ''F--0 0110 16

0 091 ... 0.058 \ \- 0.0068.... 0.0044

0.0034 > \ 0.034 � r 0 011-4. ,r 0.028

10 0.14 0.18 • f 0.098

L O.0098-e

< 0.066 '-

��-�'��-�2�0--�30�-�40--�50 x (meters)

Fig. 5: Random distribution of 30 nodes with e = 9 m.

Algorithm 1 Correlation-based Iterative Node Selection (C­INS)

S = NodeSelectCorr({NI, N21 ",}, {Ke(.)}N*N, M) begin S={0},N = {NI' N2, ... }, Ke{Ni' Nj} = Ke(i,j). Find the (Ni, Nj) = argminNi,NjEN {Ke(Ni, Nj)}; /*Find the least correlated pair of nodes. */ Add the corresponding Ni and Nj into S. if M > 2 then

for k = 1 to M - 2 do for Nz E N, Nz � S do

end for

Ke(Nz, S) = JJ!��{Ke(Nz, Nj)}.

Nm = argmin {Ke(Nm,S)}; NmEN,NmrtS

Add Nm into S. end for

end if return S = {NI' N2, ... , NM} end

Fig. 3) . Given the same location of nodes, if we change the sensing range, more connected lines will appear. It indicates more correlated nodes (see Fig. 4) . In Fig. 5, we see the calculated correlated data value in the middle of the lines connected between two nodes. It is clearly seen from plots that according to sensing range and position of nodes, the nodes gets divided into groups like clusters. Based on this analysis, we can determine how many nodes are in weak correlation or strong correlation according to sensing range and location of sensor nodes.

IV. ApPLICATION OF CORRELATION MODEL

The proposed model can be used to exploit the spatial correlation for the development of specific MAC and routing

TABLE II: Simulation Parameters

Initial power 100 J NS-2 energy model EnergyModel

Tx power 0.660 W Carrier Sensing range 550 m

Rx power 0.0395 W Communication range 250 m

Idle power 0.035 W Size of RTS/CTSI ACK lO B

Bandwidth 20 Kbps Size of SCH/PION 14 B

DlFS lOms Size of Data 100 B

SIFS 5ms Contention Window 64 ms

Retry Limit 5 ruty Cycle 5%

protocols in event-driven WSNs. According to the results obtained from previous section, we found that some nodes are weakly correlated and some are strong correlated for given sensing radius T and location of nodes. To apply these results in design of MAC protocol, we introduce a Correlation-based Iterative Node Selection (C-INS) algorithm (Algorithm-I) to determine the least correlated nodes in order to exploit the spatial correlation. In next section, we introduce a traffic model to use the results of algorithm-I in existing MAC protocols. This is one of the example showing how to apply our correlation model to exploit the spatial correlation under event-driven workload.

A. Random Correlated Event traffic Model (RCET)

Let event area be a round region of radius Rc with center at (x, y) location in two-dimensional plane. The nodes within circular area of radius Rc are allowed to be active for generat­ing the traffic (i.e. UDP packets in NS-2). All the UDP packets are routed to the sink via intermediate nodes. Sink is placed at one of the corner of gird network. We adjust the Rc for changing the number of reporting nodes (i.e. denoted by N). We integrate the feature of our correlation model into NS-2 using RCET model. In our experiments, RCET model picks a random (x,y) location for each event and C-INS algorithm determines the least correlated nodes by exploiting the spatial correlation between all active nodes inside the Rc-radius event area. These selected nodes then act as representative nodes (i.e. UDP source) for given event area. In this paper, we denote this number as least correlated reporting nodes (denoted by lvI) for an event. Therefore only lv[ out of N nodes are selected using RCET model for simulating event driven workload in NS-2.

V. SIMULATION RESULTS USING EXISTING MAC PROTOCOLS

In this section, we present simulation results using our model to evaluate the impact of reporting nodes by taking spatial correlation into consideration. The simulation scenario contains 49 nodes grid network distributed into 2000x2000m area. A random event will be generated after a fixed time interval (i.e. 100 sec.) with different event area using RCET model and total N nodes will be activated to send the reports to the sink node. The least correlated reporting nodes (i.e. lvI) out of N nodes are selected inside the event area

140

120

100

80

60

40

20

DCC-MAC [] R-MAC • RI-MAC [] DW-MAC

12 15

Number of reporting nodes in the event area (N)

Fig. 6: average time required to report an event without using correlation model.

90 Tr=====�==��'------------------' DCC-MAC

80

70

20

10

[] R-MAC • RI-MAC [] DW-MAC

4 5 7 10

Number of least correlated reporting nodes in the event area (M)

Fig. 7: average time required to report an event using corre­lation model.

using proposed correlation model. Except for the networking parameters shown in Table-I, we have used default settings as used for evaluations of CC-MAC, RMAC, RI-MAC, and DW-MAC by the respective authors. We have simulated CC­MAC [9], RMAC [6], RI-MAC [8], and DW-MAC [5] to show the efficiency of our correlation model in terms of energy and latency for event-driven workload over NS-2. These protocols are contention based or contention based combined with schedule for WSNs. We first simulate using RCET model which determines the total reporting nodes (i.e. N) inside event area according to a trigger event. We then apply our correlation model into RCET model to determine the least correlated reporting nodes (i.e. lvI) using Algorithm­I with e = 140 meters.

Figs. 6 and 7 show the end-to-end event latency correspond­ing to number of reporting nodes ( achieved by varying the event radius). Basically it is the average time required to report an event. In other words, event latency is the time required to send all UDP packets generated by the nodes which are located inside an event area. On an average 637.45 packets are generated for an event. It is shown that CC-MAC achieves

0.5

0.45

0.4

O. 5

O. 0.25

0.2

0.15

0.1

0.05

D CC-MAC [I] R-MAC • RI-MAC [] DW-MAC

7 12 15 Number of reporting nodes in the event area (N)

Fig. 8: average amount of energy consumed by the network to transmit an event without using correlation model.

0. 5 Tr=============�------------------'

� o. E

j 0.25

'0 .� 0.1

.S! 0.15

f 8 0.1

f � 0.05

DCC-MAC [I] R-MAC • RI-MAC [] DW-MAC

10

Number of least correlated reporting nodes in the event area (M)

Fig. 9: Average amount of energy consumed by the network to transmit an event using correlation model.

low latency compared to other protocols in both cases because it is minor modification of IEEE 802.11 without duty-cycle mode and forwarding of packets is routed based on priority handled by E-MAC. In the case of least correlated reporting nodes (see Fig. 7) , event latency has been reduced to 20 -40 % for all the protocols because of reducing the number of reporting nodes to NI based on location. It decreases the traffic and hence correlated contention is minimized. Figs. 8 and 9 show the average amount of energy consumed per unit time for an event by varying number of reporting nodes (i.e., varying the event radius) . We see the impact of reporting nodes on energy consumption due to increased traffic load. With our correlation model, energy consumption is obviously reduced as less number of nodes (NI) are selected for same scenario taking spatial correlation into consideration. Hence, we see that energy consumption and event latency both are reduced by exploiting the spatial correlation.

VI. CONCLUSION AND FUTURE WORK

A novel correlation model, in this paper, is introduced to determine the accurate information about correlation charac­teristics between sensor nodes based on location. Based on correlation model, C-INS algorithm is proposed to exploit the spatial correlation. The results of correlation model are applied to existing MAC protocols using NS-2. Using simulation

results, we have demonstrated that a significant amount of energy saving is possible by exploiting the spatial correla­tion. Further, end-to-end delay in event reporting can also be reduced significantly. The analytical results of proposed correlation model show that degree of correlation between nodes depends on sensing range and location of nodes. Based on correlation relationship among nodes, the nodes form correlated clusters of different sizes, depending on control parameter e and node density.

In future, we will extend our work by comparing proposed correlation model with existing correlation models, given by Vuran et al. [9] and Guoqiang et al. [11]. We also need to design a protocol to implement the C-INS algorithm in distributed fashion with least overhead.

VII. ACKNOWLEDGEMENT

We thank to Mr. Yanjun Sun for providing us NS-2 source code for RI-MAC, DW-MAC and Mr. Shu Du for helping us with RMAC source code.

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