DCFR: A Novel Double Cost Function based Routing Algorithm for Wireless Sensor Networks Anfeng Liu*,++, Ju Ren*, Xu Li+, Zhigang Chen*, Xuemin (Sherman) Shen++ * College of Information Science and Engineering, Central South University, Changsha, 410083, China, Email: {[email protected], [email protected], [email protected]} + INRIA Lille - Nord Europe, Univ Lille Nord de France, USTL, CNRS UMR 8022, LIFL, France, Email: {[email protected]} ++ Department of Electrical and Computer Engineering, University of Waterloo Waterloo, Ontario N2L 3G1, Canada, Email: {[email protected] }

Abstract—Cost function based routing has been widely studied in wireless sensor networks for energy efficiency and network lifetime elongation. Existing algorithms however have limited effects because they adopt a single cost function that does not fully capture nodal energy consumption situation. In this paper, we propose a novel Double Cost Function based Routing (DCFR) algorithm, which takes into account end-to-end energy consumption, nodal remaining energy, and energy consumption rate altogether. An extensive simulation indicates that DCFR can lead to more balanced and efficient energy usage among nodes than existing algorithms. Keywords- wireless sensor networks; double cost function routing; energy balance; network lifetime

I.

INTRODUCTION

It is recognized that wireless sensor networks (WSNs) have great potentials in many important applications such as military surveillance, environmental monitoring, and so on [1]. In WSNs, one of the main challenges is to maximize network lifetime without degrading sensing performance (coverage and reliability). To meet this goal, an energy-efficient routing algorithm that minimizes overall energy usage and balances energy consumption among individual nodes should be adopted for data communications [2, 3]. Many centralized routing algorithms were appeared. Ettus [4] proposed MTE routing algorithm, which selects a route that has the smallest overall energy consumption for transmission. Zytoune et al [5] proposed a routing protocol UBERP. This protocol only uses nodes whose remaining energy is greater than a threshold value and meanwhile attempts to minimize transmission power. Li et al [6] designed the max-min zPmin algorithm that calculates a path based on nodal remaining energy level and rejecting any path whose total cost is more than z times of the minimum-energy path. These ccentralized algorithms assume that all sensor nodes know the topology and energy consumption statues of the network. This assumption is with considerable high overhead to implement in WSNs in practice. On the contrary, localized routing algorithms make protocol decisions using only local knowledge, without resorting to any global information, and

are thus desirable. In particular, cost function based routing [5, 8, 9] has been extensively studied for energy efficiency. It is an add-on technique to an existing routing protocol for reducing and balancing the protocol’s energy consumption on sensor nodes. The logic is to calculate the cost of each neighbour node based on a cost function, and then choose the node with smallest cost as next hop, when there are multiple choices according to the routing strategy (e.g., greedy routing) engaged. DEBR [7] is a typical cost function based routing algorithm. It defines the energy cost (ECij) for a transmission from node i to node j as

eij / Eir , where eij is the required

r

energy power, and Ei the available energy of node i. The total energy cost TECik of a neighbor k acting as the next hop of sensor i is the sum of the energy costs for transmission from i to k and from k to the base station, namely, TECik ECik  ECk , BS (1) Based on this metric, sensor i can select the smallest-cost node K from its next hop candidate set N i :

K

Arg min(TECij )

(2)

jN i

Most of existing energy cost function based routing algorithms adopt similar strategy as DEBR; they differ only in the definition of energy cost function. For example, energy cost function proposed in [8] is different from previous research in that they take node energy consumption and remaining energy within two hops into consideration. Other cost functions can be found in [9, 10]. These existing algorithms deploy a single cost function that considers only end-to-end energy consumption and node remaining energy level. It does not fully capture nodal energy consumption situation and balances energy usage at a very coarse level. In this paper, we study cost function design and propose a Double Cost Function based Routing (DCFR) algorithm, based the same routing strategy used in DEBR [7]. Unlike existing schemes, it additionally takes into account energy consumption rate when computing nodal energy cost. Its cost function has a slope rising rapidly such that a small difference in energy consumption rate or available energy level can lead to a large

difference in the function value. Hence, DCFR has a fine level of control over energy usage and balancing during routing. We evaluate the performance of DCFR through extensive simulation using various performance metrics. We compare DCFR with three well-known energy cost function based routing algorithms DC (Direct Communication) [11] MTE (Minimum Transmission Energy) [4], and DEBR (Distributed Energy Balanced Routing) [7]. Our simulation results indicate that DCFR has significantly better performance in energy balancing and network lifetime elongation.

intuition, those that can transform an energy change to a bigger change in the return value is more favorable. Following the above idea, we can design many energy cost functions with better performance than existing routing algorithms. The exponential and sine functions are functions where small changes in variables can cause big changes in function values. We may put these two types of functions together and construct an exponential function in the following form: (5) f ( x) exp(1/ sin( x)) r

Denote by E0 nodal initial energy, Ei the current II.

SENSOR NETWORK MODEL AND PROBLEM STATEMENT

A. Network topology and problem statement We adopt the same network model in [7]. The network is composed of n homogenous sensors randomly and uniformly distributed in a target area. Events occur uniformly such that every sensor has one data packet to report periodically. The neighboring distance is the maximal reachable distance of radio frequency with the maximum transmission power. Each sensor is aware of the current energy level of its neighbors or energy required to transmit from each of its neighbors to the base station by anticipating and/or eavesdropping for data from the neighbors [12, 13, 14]. The lifetime of the network is the time elapsed till the first sensor node in the network depletes its energy [10, 15, 16]. The goal is to maximize the network lifetime by designing an energy-efficient cost function based distributed routing algorithm. B. Energy consumption model Sensors consume energy when they sense, receive and transmit data. The amount of energy consumed for sensing is not related to routing; there is only a small difference between the power consumption for nodes in the idle mode. Hence, we consider only the energy usage for transmitting and receiving. According to the radio model in used [11], Eq. 3 represents the energy consumption for transmitting, and the energy required for receiving an l -bit packet is as given by Eq. 4. The parameter settings are same as adopted in [11].

­° Et lEelec  lH fs d 2 if d  d 0 ® 4 °¯ Et lEelec  lH amp d if d ! d 0 Er (l ) lEelec III.

remaining energy of a node iˈand ei j the energy consumed for transmitting a packet between node i and node j. We define the energy cost ci j of the link between i and j as

ci j = eij exp(1/ sin(S 

S Eir 2 E0

))

(6)

The total cost ( TCik ) of a neighboring node k at node i (from i’ perspective) is the sum of the energy costs from i to k and from k to the base station: (7) TCik Cik  Ck , BS Based on this metric, a sensor i can select the best candidate K as next hop: (8) K Arg min(TCij ) jN i

y

Fig. 1 network topology 1

(3) (4)

DOUBLE COST FUNCTION BASED ROUTNG

In general, when the nodal remaining energy in a routing path is smaller than other paths, its cost function should rise, forcing data traffic to be forwarded via those other routing paths. However, for a short path with low remaining energy, its total energy cost is not high, and may remain very busy if the cost function used biases toward minimizing the overall energy consumption. This causes unbalanced energy usage and reduces network lifetime. An optimal energy cost function should map small changes in nodal remaining energy to large changes in the value of the function. Such an function can rise sharply the cost of a path whose nodal remaining energy is small and offset the cost saving by path length reduction (if any exists), forcing nodes to select the path with more remaining energy. Among the energy cost functions in line with this design

Intuitively, the cost function presented above can result in more balanced energy consumption than existing ones. However, it still has limited effect on energy balancing. Observe the network scenario depicted in Fig. 1. There are 457 nodes deployed in the rectangular network with two obstacles. Data in the red area can be sent to the sink via Route-1 and Route-2. Since Route-1 is much shorter than Route-2, it will be repeated used for data communication. As a consequence, the nodal remaining energy in Route-1 is less than Route-2, no matter how good the proposed cost function is. Moreover, the path segment B-B’ in Route-1 can be shared by many other routes, bearing a larger amount of traffic load and consuming more energy than other nodes. We call the path segments like B-B’ hotspots. Since the network lifetime is defined as the time elapsed till the first node dies, the nodal lifetime in hotspots determines the lifetime of the entire network. We note that the energy consumption rate of nodes in hotpots is much higher than that of other noes. If we take into consideration this factor when designing energy cost functions, we will be able to further improve their energy-balancing

capability. Therefore, we propose to use double cost functions, considering end-to-end energy consumption, nodal remaining energy, and nodal energy consumption rate altogether, for routing. The resultant Double Cost Function based Routing (DCFR) algorithm can generally result in more balanced and efficient energy usage among nodes than the algorithms that uses a single cost function. DCFR employs a cost function of energy consumption rate in addition to Eq. 7. We define the energy consumption rate esi of a node as follows:

Etri  Etrj

esi We map

esi into [S / 2, S ] . Let the maximum value of

esi be Rmax . The mapping function can be easily obtained as S S esi  rsi f (esi ) (10) 2 2 Rmax The cost function of energy consumption rate is

TRCij

RCi 

¦

x

(9)

t j  ti

RCi = eij exp(1/ sin(

y

S 2



S esi 2 Rmax

))

RCk

(11) (12)

Fig. 3 Scene-2: network with two obstacles.

Two different network scenarios, both with 457 randomuniformly-deployed nodes, are considered in our simulation. The first is a network in a circular area whose radius is 300m, with the sink located at the center (0,0), The node deployment is shown in Fig. 2. The second network is similar to the network given in Fig. 1. It is deployed in an 805m u 525m area, where there are obstacles. Point (0, 0) is located at the upperleft corner. The positive direction of the X-axis is pointing to the right; that of the Y-axis is pointing down. The sink node is placed at (294, 469). The node deployment is shown in Fig. 3.

k path| j ..base

Based on the double cost functions Eqs 7 and 12, a sensor node i takes the smallest-cost candidate K as routing next hop. (13) K Arg min(TCij  TRCij )

A. Energy balancing

jNi

IV.

EXPERIMENTAL RESULTS

In this section, we provide experimental results to validate the effectiveness of DCFR algorithm. We compare it with three existing algorithms: direct communication (DC) [11], minimum transmission energy (MTE) [4], and distributed energy balanced routing (DEBR) [7]. In DC, every sensor simply transmits data directly to the base station without considering any energy efficient indirect path. MTE considers multi-hop routing to save sensor power, but always chooses the path with the least energy cost of transporting a packet to the sink. Both DEBR and DCFR employ the same main routing strategy and select routing next hop based on the value of cost function when multiple choices are possible. We carried out experimental verification using OMNET++ [14].

Fig. 4 Energy usage map of MTE when the first node died in Scene-1

Fig. 5 Energy usage map of MTE when all nodes died in Scene-1

Fig. 2 Scene-1: Circular network with sink located at (0, 0)

Figs. 4 and 5 plot the node energy consumption map of MTE in Scene-1, respectively at the moment when the first node died and at the moment when all nodes died. We already observe energy imbalance in Fig. 4. From Fig. 5, the nodes within a circular region, of communication radius r , around the sink used up their energy. After they died, the remaining nodes can no long be delivering data to the sink and considered died too, but with unused energy in their batteries.

B. Network lifetime

lifetime is relatively high and energy balancing is better, few nodes die at the beginning, but most nodes die at the same time in the later period. It is worth noting that in this experiment, dead nodes including nodes disconnected from the sink for no paths to the sink. In Scene-1, when nodes around the sink all die and the range of the dead zone around the sink is larger than r , there are no paths for outside nodes to the sink, they are considered to be dead nodes, and for this reason, in the experimental results of Scene-1, we can see that lots of nodes die at the same time at last in the energy consumption balanced routing paths. In Scene-2, when nodes die, nodes away from the sink are separated from the sink, resulting in a sharp increase of death rate of nodes.

Number of alive nodes

400

DC MTE D BER D C FR

300

200

100

0 100

200

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lifetim es

500

600

700

(round) 250

DC MTE DBER DCFR

Number of alive nodes

400

200

network lifetime (rounds)

500

S c e n e -2 network lifetime (rounds)

Fig. 6 The number of living sensors over time in Scene-1

S c e n e -1

150

100

50

300 0 DC

MTE

DEBR

DC FR

DC

MTE

DEBR

D CFR

200

Fig. 8 lifetime of different algorithms in Scene-1 and Scene-2 100

0 200

4 00

life tim e s

600

(ro u n d )

Fig. 8 shows the network lifetime of different algorithms in these two scenes. The network lifetime by DC is very short; DCFR and DBER have a longer network lifetime than MTE. DCFR can improve the network lifetime more than DBER.

Fig. 7 The number of living sensors over time in Scene-2

the next hop (through

eij Eir

), they lead to a network lifetime

slightly longer than MTE. In Scene-2, energy balancing plays an important role in the network lifetime. In an energybalanced network, the routing algorithm mainly improves the network lifetime through energy saving, while in an energyimbalanced network (for example, different routing paths have the same routing length and their probabilities to be chosen as routing path by nodes are the same), mainly through energy balancing to improve network lifetime; And b) In different networks, nodes die in different ways, that is, for networks whose lifetime is relatively lowly, nodes die very quick, and after the death of some nodes, since the network load is decreased, the data amount undertaken by the remaining nodes decreases, thus they die slow. While in networks whose

220

DC MTE DBER DCFR

200 180 160

lifetime (rouds)

This experimentation evaluates the performance of the algorithms with r =85m ( r is the maximum reachable distance for nodal transmission power, called node transmission radius) in the two network scenes. Figs. 6 and 7 plot the number of living sensors against the number of data communication rounds for each algorithm. In each data communication round, every sensor originates a single data packet. We can get the following conclusions from experimental results shown in Figs. 6 and 7: a). In both scenes, DCFR has longer lifetime than the other three algorithms. In Scene-1, the lifetime difference between DCFR, MTE and DBER is small. This is because the sink is located at the center, and the routing paths by these algorithms are basically the same. Because DCFR and DBER consider the energy efficiency of

140 120 100 80 60 40 20 0 150

200

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450

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550

R

Fig. 9 Network lifetime under different network scales.

Fig. 9 shows the network lifetime under different network scale. The circular network’s radius was varied between (200, 300, 400, 500), and the sink located at (0, 200). To maintain the same node density, the number of nodes deployed is respectively (203, 457, 812, 1269). It can be seen that the network lifetime has declined for all these algorithms, but DCFR is still higher than the other algorithms. C. Routing overhead System overhead is defined as the ratio of data packets to the total packets (including system messages and data packets). System messages must be updating only once in each round and can be propagated by mixed with data packets. In our experiments system messages are assumed to have the following length compare to data packet: 1 data packet long (i.e. the system messages length is equal to 1 data’s), 1/2 data packet long, 1/4 data packet long. So if a node forwards only one data packet in one round, the ratio of useful message load

will be 1 / 2 = 50%, 1/1.5 = 66.67%, 1/1.25 = 80%. Each node will generate one packet per round, but it may forward multiple or zero packet per round for other nodes. Different nodes thus have different ratio of useful system message load.

maximize the life span of an entire sensor network by means of power equalization. Simulation results have demonstrated that DCFR can more effectively improve network lifetime that the well-known solutions DC, MTE, and DBER in literature. ACKNOWLEDGMENT This research is supported by the National Natural Science Foundation of China (61073104, 61073186); Specialized Research Fund for the Doctoral Program of Higher Education of China (20090162120074), and Ontario Research Fund, Ontario, Canada.

the number of nodes

400

R=400 nodes=812 R=400 nodes=812 R=300 nodes=457

300

system mesaage is 50% of one packets system mesaage is equal one packets system mesaage is equal one packets

200

REFERENCES [1]

100

[2] 0 0.5

0.6

0.7

0.8

0.9

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[3]

the ratio of useful message load

Fig. 10 The number of nodes have different ratio of system useful message load [4]

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[5] system useful load ratio

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message is quater a packets 80

[7] message is half a packets

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message is a packets

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[9]

Fig. 11 System useful load ratio vs. network radius R

Fig. 10 demonstrates this situation in a circle network with radius R = 300m, 400m, the sink is located in (0, 200). It can be seen from Fig. 10, a large part of nodes only send a single packet in one data collection cycle, the number of nodes are 192,423 (if the length of system message and data packet equals, then the node whose useful load ratio is 50% must only send a single packet in one data collection cycle, and the number of such nodes is respectively 192, 423). This is because for nodes who are within the distance r =85m from the network border, they do not need to forward data from other regions. These nodes constitute a large portion of the network. Since there are a fixed number of system messages transmitted by each node in a data collection round, the more data packets a node forwards, the higher the useful ratio. Fig. 11 shows the average useful ratio in the entire network with R=200,300,400,500 and the sink being located at (0, 200). V.

[10]

[11]

[12]

[13]

[14]

[15]

CONCLUSION

Wireless sensor networks enable efficient monitoring of physical environments. The main operating constraint is the available energy. In order to maximize efficient usage of batteries by randomly placed sensors, we have proposed a Double Cost Function based Routing (DCFR) algorithm to

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