Modeling Information Generation and Dissemination in Event-Driven Wireless Sensor

Networks G.Balasubramanian1 and Saswat Chakrabarti2

1 Department of Electronics and Electrical Communication Engg. , IIT Kharagpur, India 2 G.S.Sanyal School of Telecommunications, IIT Kharagpur, India

E.mail: balaji@gssst.iitkgp.ernet.in , saswat@ece.iitkgp.ernet.in

Abstract— Event-driven wireless sensor networks gain precedence over data-driven networks due to the effective manner in which they reduce the redundancy in data transmitted. In this paper, an attempt has been made to model the events of information generation and dissemination in an event driven wireless sensor network with uniformly distributed sensor nodes. Two existing definitions for the lifetime of sensor network have been used and a comparison of performance metrics like network lifetime, packet throughput and energy utilization have been made. Moreover, for a given region, analysis of the coverage and connectivity have been performed to obtain the average number of nodes required to be deployed in a given area to achieve a required coverage fraction or connectivity.

I. INTRODUCTION

IRELESS sensor networks can be considered as a collection of mobile or static nodes capable of communicating with each other without any prior

infrastructure. They have the potential to collect data more cost-effectively, autonomously and robustly as compared to a few macro sensors. Recent improvements in efficient and affordable integrated electronic devices, digital signal processors and short-range radio electronics have led to the evolution of wireless sensor networks as a special type of wireless embedded networks. Sensor networks are widely used in a variety of applications such as seismic, acoustic, climatic data gathering, environmental monitoring, surveillance and national security, military and health care etc. Communication among the sensor nodes occur in different ways which vary depending on the network topology and the underlying application. Depending on the manner in which the sensor nodes communicate, sensor networks can be classified mainly into three categories: [a] clock-driven or data driven, [b] event-driven and [c] query-driven sensor networks [1]. Data-driven sensor networks collect and transmit data at regular intervals (data gathering cycle) to a sink which collects data generated from all the sensor nodes. This type of communication involves a lot of redundancy in data, especially when the network is deployed in an area which is seldom or occasionally active. This results in wastage of energy resources of the sensor network. In a query-driven network, a sensor node transmits data only when it receives a

query request from the sink. A sensor in an event-driven network generates and transmits data packets only when an event occurs. The definition of an event may vary according to the application at hand. In a broad sense, an event may be defined as any significant change in the parameter monitored by the sensor nodes in a network. The issue of energy consumption in heterogeneous sensor networks has been considered by Melo et.al. in [1]and they have developed a deterministic procedure to determine the optimal number of clusters to cover a given area of interest. In [2], Bharadwaj et.al. have suggested an approximate upper bound to the lifetime of a data-driven sensor network and have applied it to various network topologies. Furthermore, they have established that there exits networks which achieve maximum lifetime that is very close to the derived bounds. Modeling the energy consumption for a regular arrangement in a one dimensional scenario has been addressed in [3], [4] and a procedure to optimize the energy dissipation for the whole network has been developed. The evaluation of network lifetime and its enhancement by using energy efficient node scheduling and deployment has been demonstrated in [7] and [8]. Evaluation of lifetime of a sensor network using the concept of residual lifetime has been studied by Sha et.al. in [6]. Although several studies on the energy dissipation, evaluation of network lifetime have been carried out in an isolated manner, as highlighted above, none of them have attempted to model the event driven network on the whole. In order to study the performance of any event-driven network, it is important to have a theoretical model which depicts the manner in which information is generated by the events in a service area. In this paper, we have made an attempt towards developing an analytical model for information generation and dissemination in an event-driven wireless sensor network. Two existing definitions of network lifetime have been applied on this model, performance parameters like network lifetime, energy utilization and packet throughput have been compared for both the scenarios. The remainder of the paper is organized as follows. The model for the generation of information in an event driven sensor network is presented in Section II. The energy model used for the analysis is described in Section III. Analysis of the network lifetime is done in Section IV, following which we present the simulation results and discussion in Section V. Section VI concludes the paper.

W

II. INFORMATION GENERATION MODEL

In this paper, the sensor network is assumed to be deployed over a square area of side ‘R’ units with the sink placed at the center with co-ordinates (0,0). There are ‘N’ sensor nodes deployed in a uniformly distributed manner, i.e. the abscissa and ordinates of the sensor nodes location are uniformly distributed from ,

2 2R R⎛−⎜

⎝ ⎠⎞⎟ . It is assumed that all nodes have an

initial energy of ‘Eo’ Joules. The network is assumed to have 100% connectivity, so that a data packet generated by any one of the nodes can be routed to the sink, provided all nodes in the path have sufficient energy to reliably transmit and receive the packets. An event is defined as any significant change in the parameter observed by the nodes in the sensor network. The event occurrence is assumed to be uniformly distributed in the region of interest. It is assumed that only one event occurs at a time. Let (X,Y) be the co-ordinates of occurrence of the event, and let (Xj,Yj) be the co-ordinates of location of the jth sensor node where 1 j N≤ ≤ . The pdf of the event can be described as

2

1 ,( , ) 2

0XY

R Rx yf x y R

elsewhere

⎧ ⎫− ≤ ≤⎪ ⎪= ⎨ ⎬⎪ ⎪⎩ ⎭

2 (1)

Let ‘r_sense’ be the sensing range of the sensor node. Given that an event has occurred, it will be detected only by those sensors which are within sensing range from the point of occurrence of the event. The probability that one such event is sensed by a sensor ‘j’, 1 j N≤ ≤ is given by ‘Pej’, where

( ) ( ){ 2 2 2( _ )ej j j }P P X X Y Y r sense= − + − ≤ (2)

The X and Y co-ordinates of the event are independent of each other and so the joint probability density function in (1) can be split up as a product of individual probability density

functions. By substituting Z = ( ) (2 2

j j )X X Y Y− + − in (2)

and by simple manipulations, we arrive at

(3) 2( _ )

0

( )r sense

ej ZP f= ∫ z dz

where ( )Zf z is given by

22

21 1 2

2

2 21 1 1 1

2

2 2 2 2 2

21 1 1 1

2

2 ; 0

1 sin sin2

1 sin sin sin sin

; 2

1 1 1 1( ) sin sin sin sin2 2 2Z

z aR

a z a a z bzR z

b a z a z bz zR z z

b z b a b a

b a z af zzR z z

π

π − −

− − − −

− − − −

≤ ≤

⎡ ⎤⎛ ⎞−⎛ ⎞⎢ ⎥⎜ ⎟+ − ≤ ≤⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦⎡ ⎤⎛ ⎞ ⎛ ⎞− −⎢ ⎥⎜ ⎟ ⎜ ⎟+ − −

⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦≤ ≤ + ≤

⎛ ⎞−⎜ ⎟= + − −⎜ ⎟⎝ ⎠

2

2

2 2 2 2 2

21 1 2 2

2

; 2

1 sin sin 22

0

z bz

b z b a b a

b z b b a z bzR z

elsewhere

− − 2

⎧ ⎫⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎡ ⎤⎛ ⎞⎪ ⎪−⎢ ⎥⎜ ⎟⎨ ⎬⎜ ⎟⎢ ⎥⎪ ⎪⎝ ⎠⎣ ⎦⎪ ⎪

≤ ≤ + ≥⎪ ⎪⎪ ⎪⎡ ⎤⎛ ⎞−⎛ ⎞⎪ ⎪⎢ ⎥⎜ ⎟− +⎜ ⎟ ≤ ≤⎪ ⎪⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎪ ⎪⎩ ⎭

(4)

where2

2

2 jRa X⎛ ⎞= −⎜ ⎟

⎝ ⎠and

22

2 jRb X⎛= +⎜

⎝ ⎠⎞⎟ . Thus equation

(3) gives the probability of generation of a packet by jth node due to occurrence of an event.

III. ENERGY DISSIPATION MODEL The sensor node is assumed to be either in transmitting mode, receiving mode or in sleep mode. It has been assumed that energy spent by the node in sleep state is negligibly small as compared to the amount spent while being in transmitting or receiving mode. The model for radio communication is similar to the one used in [3][4]. The energy required for transmitting a packet is assumed to be

(5) .( ( ))nt j t d nearE e e d j= +

where ‘ ’ is the energy spent in the transmitter electronics per packet, ‘ ’ is the energy spent by the node to reliably transmit the data packet to its immediate neighbour towards the sink,’ ’ is the distance to the immediate neighbour in the direction of the sink, which is less than the radio range of the sensor node and ‘n’ is the path loss exponent where . Let ‘ ’the energy required to receive a packet successfully by a sensor node. In an event-driven sensor network, lifetime is defined as the number of events that occur in the sensor network before the network dies. Let ‘Ne’ the lifetime of the sensor network considered. The average energy dissipated by the j

te.( ( ))n

d neare d j

( )neard j

2.0 4.0n≤ ≤ re

th sensor node for receiving packets during the course of the network lifetime of the network is

. .R j e jE N S re= (6) where ‘ jS ’ is the average number of packets received by the

jth sensor node due to occurrence of a single event. To find ‘ jS ’, it is necessary to first evaluate the probability that any generated packet is routed through the jth sensor node. This problem can be approached in the following manner. Let ‘ jsd ’ be the distance of the jth sensor node from the sink and let ‘ ρ ’ be the average number of sensor nodes per unit area of the sensor network. Therefore, the average number of sensor nodes inside a circle of radius jsd units with

the sink placed at the center is 2. .jsdπ ρ . As a result the probability that any sensor node lies at a greater distance from the sink than the jth sensor is

2

' jsN dp

Nπ ρ−

= (7)

Figure 2 Communication among the sensor nodes

As shown in Figure 2 region of deployment of the sensor network, is divided into annular strips, by concentric circles having integral multiples of ‘r’ (radio range) as their radius. The data is assumed to traverse from one strip to its adjacent strip towards sink in a single hop. Consider one such strip

constituted by the circles having radii .jsdr

r⎢ ⎥⎢ ⎥⎣ ⎦

and 1 .jsdr

r⎡ ⎤⎢ ⎥

+⎢⎢ ⎥⎢ ⎥⎣ ⎦⎣ ⎦

⎥ . This is the annular strip enclosing the jth

sensor node. Now, the average number of sensors in the above mentioned strip is

2 22' .( ) . . 1djs djsN r

r rπ ρ

⎡⎡ ⎤⎢ ⎥ ⎢ ⎥= + −⎢⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎣ ⎦⎢⎣

⎤⎥⎥⎦

= 2.( ) . . 2. 1jsdr

rπ ρ

⎡ ⎤⎢ ⎥+⎢ ⎢ ⎥

⎢ ⎥⎣ ⎦⎣ ⎦⎥ (8)

It has been mentioned in Section II that the data packet moves from one strip to the adjacent one towards the sink in a single hop. So given that the data packet is in the above mentioned strip area, the probability that it will be routed through the jth sensor node is

2

1'.( ) . . 2. 1

jjs

Pd

rr

π ρ=

⎡ ⎤⎢ ⎥+⎢ ⎥⎢ ⎥

⎣ ⎦⎣ ⎦

(9)

Now, a packet generated anywhere in the sensor network will be routed through the jth sensor node if the packet is generated by a sensor node beyond the jth sensor and it is relayed through the jth sensor when that packet passes through the corresponding strip containing that node. Thus, from equations (7) and (9), the probability that any generated packet will be relayed through the jth sensor is

'. 'j jP p P= (10) Suppose that each event falls within the sensing range of ‘m’ sensor nodes where the value of ‘m’ may vary depending on the distribution of the sensor nodes. Each of these nodes will generate a packet corresponding to the occurrence of the event and then transmit it towards the sink. The probability that ‘i’ number of packets ( i m≤ ) is routed through jth node is ‘ i

jP ’. As a result, the average number of packets that traverse through the jth node due to any event is

1.( )

Mi

ji

S i P=

= ∑ j (11)

Hence we can compute R jE in equation (6). The average number of packets transmitted by jth node is equal to the sum of average number of packets it has received and the number it has generated due to occurrence of events within its sensing range. This has been derived under the assumption that there is no loss of packets in the medium, i.e. all the packets sent are correctly received by the receiver node. From equation (3), it can be seen that probability that an event occurs in vicinity of jth node is . Therefore the total number of packets generated by the j

ejPth node is . So the average

energy spent by the j.e ejN P

th node in transmission mode is

. . . ( nTj e j ej t d nearE N S P e e d j⎡ ⎤⎡ ⎤= + +⎣ ⎦ ⎣ ⎦) (12)

As a result, the total energy spent by jth node before the network dies is

j T j R jE E E= + (13)

IV. NETWORK LIFETIME

In this paper, we have evaluated the performance of the sensor network framework described in Section I, using two different definitions of network lifetime. Network lifetime for an event-driven sensor network can be defined as the number of events that take place before energy of any one of the nodes in the network is exhausted. This seems to be a proper definition to start with, but the problem with this is that, the death of any one of the nodes does not imply that no further packets can be routed to the sink. So we make use of another definition of lifetime which is explored in [6], where a measure called residual lifetime is used. This residual lifetime has been defined for individual sensor as well as for the sensor network as a whole. The Residual lifetime of individual sensor (RLIS) is defined as the normalized remaining energy of the sensor at any moment. It is obvious that the death of each sensor has a unique impact on the lifetime of the sensor network, which is inversely proportional to the square of the distance of that particular node

to the sink. For e.g. death of nodes nearer to the sink disrupts the communication is severe way compared to death of a node far away from the sink. So each node is thus assigned a weight as shown below

2

1. 1jjs

w c j Nd

= ≤ ≤ (14)

Thus the residual lifetime of sensor network (RLSN) is defined as follows.

1

( ) . ( ) ; 1N

j jj

RLSN i w RLIS i i N=

= ∑ e≤ ≤

−

(15)

The network is assumed to be incapable of further communication when it is not possible by any means to route the packets generated by the sensor nodes to the sink, thereby leading to the following condition:

( ) ( 1)RLSN i RLSN i= (16)

and this value of ‘i’ is taken as network lifetime.

V. RESULTS AND DISCUSSION

Simulation in MATLAB were done in order to evaluate the connectivity and coverage fraction of the network which enables the determination of average number of nodes required to ensure a given amount of coverage or connectivity. Also, the dependence of the connectivity on the radio range of a sensor node and sensing range, for a given region of interest has been studied and observed, whose plots are shown below:

Figure 3 Variation of Percentage of Connected nodes with Radio

range of a sensor node for R = 2000 units and N = 1500.

The results shown in tabulated form in Table 1 illustrate the variation of coverage fraction with number of nodes for a given region of interest for a sensing range of 10 units and radio range of 20 units.

Figure 4 Variation of Percentage of connectivity with

number of nodes for sensing range of 25 units and R = 2000

TABLE 1: COMPARISON OF COVERAGE FRACTION

R = 100

R = 250

R = 1000

N

Coverage Fraction

N Coverage Fraction

N Coverage Fraction

20 0.719 20 0.252 20 0.018 60 0.969 60 0.556 100 0.087 80 0.975 100 0.710 500 0.408

100 0.990 500 0.977 750 0.581 150 0.993 750 0.993 1000 0.663 200 0.999 1000 0.998 1500 0.934

Figure 5 Comparison of Coverage Fraction for

R = 100, 250 and 1000 as a function of number of nodes

Figure 6 Variation of RLSN as a function of number of nodes whose energy has been fully consumed

The simulation for evaluating the RLSN variation (as shown in Figure 6) was performed in MATLAB with the R = 100

units, r_sense = 5 units, r_radio = 10 units, length of data packet = 512 bits, et = 150e-9*B J/packet, er = 150e-9*B J/packet, ed = 500e-12*B J/packet/m2, E_th = 38.4µJ and Eo = 3J. The energy parameters used for simulation are the values obtained from the datasheets of sensor nodes commercially available in market. From Figure 6 it can be seen that with the above parameters, when we increase ‘N’, the number of nodes which have exhausted their power increases as the value of RLSN decreases. The RLSN value finally approaches a constant value which is dependent on the network topology and energy parameters of the sensor nodes. This indicates that the energy dissipated in the network is negligible and that no further routing of data packets can be made to the sink, thus causing a disruption in the communication between the nodes and the sink in the sensor network. Furthermore, a comparison of performance metrics like network lifetime, packet throughput and energy utilization are illustrated in a tabulated manner in Table 2.

TABLE 2: COMPARISON OF PERFORMANCE METRICS

Model 2 Model 1

N Packet

Through put

T

E

Packet Through

put

T

E

300 74976 24327 3.03%

102351 39563 7.67%

500 77651 24982 3.16%

118068 57176 9.60%

1000 127248 26496 3.30%

238859 138612 13.26%

In Table 2, ‘N’ denotes number of nodes, ‘T’ denotes network lifetime and ‘E’ denotes the percentage energy utilization. Here Model 1 denotes the scenario where the lifetime was evaluated using the concept of residual lifetime and Model 2 denotes the situation where the lifetime has been evaluated as the number of events that occur before any one node fully consumes its energy. Firstly, from Table 2 it can be inferred that there is a significantly large difference in packet throughput for a given value of N between Models 1 and 2. It can also be observed that the variation in the values of ‘E’ and ‘T’ is more for Model 1 than for Model 2 as N increases. This is because as N increases, in Model 1, a larger number of nodes have to exhaust their energy in order to disrupt the communication and routing of data packets from source to sink. Thus the network lifetime value increases by a large amount for Model 1 than for 2, where as usual the Network is considered ineffective after 1st node exhausts its energy. This also increases the value of energy utilization of the network for Model 1, thus explaining the reason for increased variation in Model 1 as N increases. The performance of Model 1 is superior to that of Model 2 in terms of the above mentioned parameters. Thus, from the results obtained for Model 1 and 2, it can be seen that the former definition of lifetime is a more reasonable one as packet communication is not seriously affected after the first node exhausts its complete power.

VI. CONCLUSION In this paper, an analytical model for the generation and

dissemination of information from the point of occurrence of the event to the sink has been developed for an event-driven wireless sensor network. The theoretical model has been supported by relevant simulations performed in MATLAB. The coverage and connectivity analysis gives an idea of the approximate number of nodes that has to be deployed in order to achieve a given coverage fraction or connectivity. Moreover, the use of the concept of residual lifetime in the evaluation of lifetime of the sensor network has shown that the network can sustain itself beyond the point of time when the first node perishes. This has been supported by the simulation results obtained in Table 2, which indicates that the performance of the network is superior when this definition of lifetime is used. Moreover, as an extension, we can use this model to analyze the performance for different event occurrence statistics like hotspots etc. This model can now be further used to analyze the performance of various energy efficient node deployment and scheduling schemes in order to enhance the lifetime of wireless sensor networks.

REFERENCES [1] Duarte-Melo, E.J.; Mingyan Liu; “Analysis of energy consumption and lifetime of heterogeneous wireless sensor networks”, Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE, Volume 1, 17-21 Nov. 2002, pp:21 - 25 [2] Manish Bharadwaj, Timothy Garnett and Anantha P. Chandrakasan, “Upper Bounds on the Lifetime of Sensor Networks”, in the Proceedings of the International Conference on Communications (ICC ’01), Helsinki, Finland, June 2001, vol. 3, pp. 785-790. [3] Zach Shelby, Carlos Pomalaza-Raez, Heikki Karvonen and Jussi Haapola, “Energy Optimization in Multihop Wireless Embedded and Sensor Networks”, International Journal of Wireless Information Networks, Springer Netherlands, January 2005, vol .12, no. 1, pp. 11-21. [4] Q.Gao, K.J.Blow, D.J.Holding, I.W.Marshall and X.H.Peng, “Radio Range Adjustment for Energy Efficient Wireless Sensor Networks”, Ad-hoc Networks Journal, Elsevier Science, January 2006, vol. 4, issue 1, pp.7 [5] Chiasserini, C.-F.; Garetto, M.; “Modeling the performance of wireless sensor networks”, INFOCOM 2004. Twenty-third Annual Joint Conference of the IEEE Computer and Communications Societies, Volume 1, 7-11 March 2004 [6] K. Sha and W. Shi. “Modeling the lifetime of wireless sensor networks”, MIST-TR-2004-0011, Wayne State University, Apr. 2004. [7] Ashraf Hossain, S.Chakrabarti, P.K.Biswas, “An approach to balance energy dissipation in wireless sensor networks”, In the Proceedings of 1st IEEE WIE National Symposium on Emerging Technologies (WieNSET ’07) West Bengal University of Technology, Kolkata, India, 29-30 June 2007. [8] Anand Seetharam, Abhishek Bhattacharyya, G.Balasubramanian, Ashraf Hossain, S.Chakrabarti, “Energy efficient deployment and scheduling of nodes in wireless sensor networks”, communicated to WPMC-2007.