lower traffic load each node in that neighborhood will have to bear. The rest of the paper is organized as follows. We first introduce the problem scenario and ...
Lifetime Enhancement of Wireless Sensor Networks by Differentiable Node Density Deployment Demin Wang, Yi Cheng, Yun Wang and Dharma P. Agrawal OBR Center for Distributed and Mobile Computing Department of ECECS, Univ. of Cincinnati Email: {wangdm, chengyg, wany6, dpa}@ececs.uc.edu
Abstract- A wireless sensor network (WSN) is composed of wireless sensors using batteries with energy constraints, which limits the network lifetime. How to maximize the network lifetime is an important issue in the design of WSNs. We establish a relationship between node density and network lifetime in a periodically data delivery scenario of WSNs with sensors transmitting data to the sink node periodically. Based on our analysis, we propose a sensor node density deployment method that could implement a differential node density in WSNs so that the lifetime of the network could be maximized. Both theoretic analysis and simulation results show that our method outperforms the uniform node distribution method in terms of the network lifetime.
II. PROBLEM SCENARIO AND ASSUMPTIONS
I. INTRODUCTION
Wireless sensor networks (WSNs) can be used in many applications [1]. Based on the operation mode, WSNs can be classified into two types: proactive networks and reactive networks [2]. In this paper, we focus on the proactive approach. In the literature, most existing works in sensor network consider a uniform node density in the whole network. To our knowledge, no work has been done on the analysis of the network when node density in various parts of the network is different. We analyze the lifetime problem of a WSN from the node density point of view. In a WSN, the sensor nodes far away from the sink have to use multi-hop communication to transmit data to the sink node. So, the nodes closer to the sink will have to transmit not only their own data (defined as originating traffic) but also relay data for other nodes (defined as relaying traffic) and their energy will be used up first among all sensor
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nodes. We define the lifetime of the network as the cumulative active time of the network until the first sensor is out of power, which is the same as in [3]. Our proposition is to increase the node density near the sink. The higher density near the sink, the lower traffic load each node in that neighborhood will have to bear. The rest of the paper is organized as follows. We first introduce the problem scenario and assumptions in part 11. Part III analyzes the relationship between node density and network lifetime in both one-dimensional case and two-dimensional case. Part IV is the conclusions. Network Model: We focus on the scenario where several sensors are deployed in a flat area and with a sink node to collect the information. We divide the network area into n levels based on the distance to the sink. From the sink to the outside nodes, we name the levels as level 1, 2, n. The most outside nodes belong to level n. Ni represents the number of sensor nodes in level i. N represents the total number of sensor nodes in the network. There are two kinds of traffic in the network: originating traffic and relaying traffic. Assume that the originating traffic load of each level is proportion to the area of this level. The relaying traffic load of level i includes the originating traffic load of level n, n -1,. . . and level i + 1. The transmission always starts from level n. After level i receives the relaying traffic from level i 1, it starts to transmit both relaying traffic and originating traffic to level i -1. We define the period from the start transmission of level n till level n's
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data reach the sink as one round. The network lifetime is evaluated by the maximum number of rounds that could be performed by the sensors with given batteries. Since many researches have been done in multi-path and energy aware routing [4], [5], [6], [7], we assume the traffic load of each level can be evenly divided by nodes in this level. The detailed routing protocol is not discussed in this paper. Also, there is no data aggregation during the transmission. Energy Model: In this paper, we only discuss communication energy consumption. The first order radio model presented in [8] is used. In this model Eelec = 5OnJ/bit is the energy dissipates to active the transmitter or receiver circuitry and Camp lOpJ/bit/rM2 for the transmit amplifier to transmit. We can get the energy consumption to transmit a k-bit packet to distance d denoted as ET, (k, d) and the energy to receive the same packet denoted as ER,(k, d) as follows:
Level n
Level n-l,n-2,...,2
Level 1
Sink Node
Fig. 1. One-dimensional case
consumption of different levels in one round to be the same. In each level, nodes are randomly but uniform distributed. We will analyze this problem from one-dimensional and two-dimensional cases and use our differential node density approach to reach a balance in energy consumption and have a longer network lifetime. III. ANALYSIS
Based on the assumptions mentioned in section II, we first consider one-dimensional case and then extend to a two-dimensional case. We want to find out the optimal node number ratio among different (k, d) = Eeiec *k+amp*k*d2 (1) levels of the network. When the deployment fulfills ERx (k, d) Eelec * k (2) this requirement, we can make sure that the nodes We assume the transmission range of each sensor of different levels die at the same time (i.e. run out node is r. Then, we can simplify equation (1) to: of energy at the same time).
ETx
ETx(k) = KTx* k
(3) A. One-dimensional Case
*r It is easy to get KT, = Eeiec + 2amp Sensor Parameters: We focus on the MICAz nodes from crossbow. The transmission range is 20 meters indoor [9]. A MICAz node uses two AA batteries which have total a total energy of 21600J. The maximum message size is 36 bytes and maximum MAC layer frame size is 56 bytes. We use these values as corresponding parameters in the following sections. Problem Definition: We describe the problem as follows. Given an area A, and a sink node. The sink node needs to gather the information of the area periodically. How to deploy the sensor nodes to maximize the lifetime of a sensor network? First we know that the sensor network deployment needs to fulfill the requirement of coverage and connectivity. There are several papers that discuss these two problems [10]. Secondly, how can we deploy the sensors in an area and achieve a longer lifetime? In order to achieve a longer lifetime, we want to make the average node energy
We consider the one-dimensional situation shown as Fig. 1. The sink node is located at one end. We divide the straight line into n levels evenly. The length of each level is the same. Assume for each round, each level has L bits information to transmit back to the sink node. Using the energy model given in part II, we can compute the energy consumption of level i in one round denoted by Ei.
Ei = Eelec* (n- i) *L+KT(n-i+1)*L (4) The average energy consumption of each node in level i denoted by ei = E. If nodes are uniform distributed, Nn = Nn-, = ... = N1. It is easy to notice that el is greater than en. To balance the energy consumption, we make the number of nodes different of each level. Since nodes of level n don't need to relay traffic, we keep Nn equal to the minimum node density requirement. The object is to make the average energy consumption of each level to be the same in one round. From ei = ei-1
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0 Uniform I Differential
...dx
of]
if]
if]
I[]
IF Level
Fig. 2. Lifetime comparison of differential node density method and uniform node distribution, total node number is 155 and 160 respectively, one-dimensional case
we get
Ni _
Ni1I
Eelec* (n- i) +KT
* (n -i+ 1)
Eelec * (n-i + 1) + KTx * (n-i + 2)
Using iterative method we get
Nn N1
KTx
Eelec* (n- 1) + KT*n
(5) (6)
Fig. 3. Two-dimensional case
distributed to each node. From the lifetime point of view, differential node density is more effective. B. Two-dimensional Case Now we discuss the two-dimensional case shown as Fig. 3. We assume the network area is to be a disk area with radius R. The sink node is located at the center of the disk. As shown in Fig. 3, we divide the area into n levels from the sink to the outside. Rn = R. The boundaries of level i are the circles of radius Ri and Ri-I. The difference with one-dimensional case is that the size of different level is different, therefore the originating traffic of each level is different. We assume the originating traffic of unit area need to report back as I bits in each round and the area of each level as Ai. Similar as one-dimensional case, we can get:
Then, we can compute the number of nodes in each level based on Nn to get the optimal number ratio. When the deployment fulfills this requirement, we can make sure that the level n nodes and level 1 nodes die at the same time. The initial node energy is denoted by E. We can compute the life time of level i as Ti = E. The lifetime of the network T T1 Ej The following example illustrates the usefulness of our method. We make the length of each level Ai = wF(R2 -R2) (7) as r2. r is the transmission range of a node. The length of the area is 100 meters and the sink node's Ei = Eelec*W(R2 -R2)*l+KTx*w(R2_ -Ri_l2) *1 position is at one end. We assume 10 levels, with (8) r = 20meter, E = 21600J, and n= 10. Assume Similarly ei = ei-1, we get sensing range is 10 meters, N1o = 2 fulfills the coverage requirement. The originating traffic of Ni-I each level in each round is 2 packets. Each packet Eelec * 7r(R2 -R 2) + KT, * -(R - Ri- 2) is 56 bytes of length. Using our theory, we get the Eelec * 7(R2 Ri-2 ) + KT, * 7r(R2 - Ri-22) total number of nodes N = 155. (9) Fig. 2 compares the life time of 155 nodes using our differential node density strategy and 160 nodes using uniform node density. The lifetime of level 1 * Rn I2) _ (10) N1 * Eeiec w(R2- R2) + KTx * 7rR2 is the lifetime of the network. We can see that using differential node density method, we get a much Nn is decided by the connectivity and coverage longer lifetime. The energy consumption is evenly requirement in An. -
Nn
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KTx wF(R2
o Differential 5000000000
[2] D. P. Agrawal and Q-A Zeng, Introduction to Wireless
* Uniform
[3]
4000000000
[4]
2000000000
1000000000
2
3
Level
4
5
[5]
Fig. 4. Lifetime comparison of differential node density method and uniform node distribution with the same total number of nodes 476, two-dimensional case
[6]
We give the following example. Make Ri . r is the transmission range of a node. Ri The radius of the area is R = 50meters and the sink node's position is at the center of the area. We assume 5 levels, with r = 20meter, E = 21600J, n = 5 and N5 = 27. Each round the originating traffic of the level n nodes is 27 packets. Each packet is 56 bytes. Using our theory, we get the total number of nodes N = 476. Fig. 4 shows the lifetime of each level. We can see with the same number of nodes, the network using differential node density deployment method has longer lifetime than uniform deployment.
[7]
[8]
[9]
[10]
IV. CONCLUSIONS
In this paper, we analyzed the lifetime of sensor networks from node density point of view. Based on the analysis, we provide a differential node density method to deploy sensor nodes in order to increase the lifetime. Both one-dimensional case and two-dimensional case are analyzed and our method has better performance than the uniform node distribution. This can be used as a guide when we deploy a sensor network. ACKNOWLEDGMENT
This work has been supported by the National Science Foundation under grant BES- 0529063. REFERENCES [1] D. Culler, D. Estrin, and M. Srivastava, "Overview of sensor networks," IEEE Computer, vol. 37, no. 8, pp. 41-49, August 2004.
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and Mobile Systems. Brooks/Cole Publishing, Aug. 2003. Q. Xue and A. Ganz, "Maximizing sensor network lifetime: Analysis and design guidelines," in Proceedings of MILCOM, October 2004. N. Jain, M. D. Kutty, and D. P. Agrawal, "Energy aware multipath routing for uniform resource utilization in sensor networks," in The 2nd International Workshop on Information Processing in Sensor Networks (IPSN 2003), Palo Alto Research Center (PARC) Palo Alto, California, April 2003, pp. 473-487. N. Jain, D. Kutty, and D. P. Agrawal, "Exploiting multipath routing to achieve service differentiation in sensor networks," in The 11th IEEE International Conference on Networks (ICON 2003), Sydney, Australia, September 2003. N. Jain, R. Biswas, N. Nandiraju, and D. P. Agrawal, "Energy aware routing for spatio-temporal queries in sensor networks," in invited paper, IEEE Wireless Communications & Networking Conference 2005 (WCNC'05), New Orleans, March 2005. N. Jain, D. K. Madathil, and D. P. Agrawal, "Midhoproute: A multiple path routing framework for load balancing with service differentiation in wireless sensor networks," acceptedfor publication on the Special Issue on Wireless Sensor Networks of the International Journal of Ad Hoc and Ubiquitous Computing. W. R. Heinzelman, A. Chandrakasan, and H. Balakrishnan, "An application-specific protocol architecture for wireless microsensor networks," IEEE Transactions on Wireless Communications, vol. 1, no. 4, pp. 660-670, 2002. Crossbow. [Online]. Available: http:Hwww.xbow.com X. Wang, "Qos issues and qos constrained design of wireless sensor networks," Ph.D. dissertation, University of Cincinnati, February 2006.
