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Extending Wireless Sensor Network Lifetime with Global Energy Balance Mehmmood A. Abd, Sarab F. Majed, Brajendra K. Singh, Kemal E. Tepe+ , Rachid Benlamri
Abstract—In this paper, a decentralized routing algorithm, called Game Theoretic Energy Balance Routing Protocol (GTEB), is proposed to extend the network lifetime by balancing energy consumption in a larger network area using geographical routing protocols (GRPs). The objective of the proposed protocol is to make sensor nodes deplete their energy at approximately the same time, which is achieved by addressing the load balance problem at both the region and node levels. In the region level, evolutionary game theory (EGT) is used to balance the traffic load to available sub-regions. At the node level, classical game theory (CGT) is used to select the best node to balance the load in the selected sub-region. This two-level approach is shown to be an effective solution for load balancing and extending network lifetime. This paper shows the use of evolutionary and classical game theories in designing a robust protocol that offers significant improvement over existing protocols in extending network lifetime. Index Terms—Energy balance, geographical routing protocols, game theory, wireless sensor networks.
I. I NTRODUCTION
E
XTENDING network lifetime and sensor functionality is crucial for the successful utilization of wireless sensor networks (WSNs) in applications where replacing or charging energy storage units (i.e. batteries) is impractical or not cost effective. For example, the ARGO [1] project deploys thousands of floating sensors to gather hydro-graphic data from oceans and their energy supply cannot be replaced or recharged after they are released into the environment. Prolonging the sensors’ lifetime can significantly reduce the cost of the ARGO project and help the researchers to understand the health of the oceans better. Considering the importance of such large data gathering projects, lifetime expansion of WSNs is extremely important. Although different techniques were proposed to extend the lifetime of sensor networks, the most prominent approach is to balance the WSN communication in the network in order to deplete energy at a similar time or rate [2]–[4]. In such approach, routing decisions play an important role in selecting candidate paths in order to balance energy in the network [5]– [8]. Geographical routing protocols (GRPs) are more suitable for WSNs because they do not need routing tables, and therefore do not require route discovery and route maintenance mechanisms which incur large overhead. However, GRPs require location information, which can be provided using Mehmmood A. Abd, Sarab F. Majed, Brajendra K. Singh, Kemal E. Tepe are with the Department of Electrical and Computer Engineering, University of Windsor, ON, Canada, e-mail:
[email protected], + Corresponding Author Rachid Benlamri is with the Department of Software Engineering, Lakehead University, ON, Canada Canada, e-mail:
[email protected]
a Global Positioning System (GPS) in outdoor deployments, signal strength and time of arrival based location estimation techniques in indoor deployments. Although these may increase the complexity of the GRPs for networks where nodes do not move and the location of sinks are fixed, the benefits of simplicity of GRPs exceed the extra complexity of obtaining location information. For this reason, routing protocol for low power and lossy networks (RPL) as a GRP has been adapted for smart grid applications [9]. Furthermore, one problem with GRPs is that they do not have a global view of the network, including energy information at regions and nodes. Providing this information can incur large overheads and increases complexity. This issue is addressed in this paper by adopting distributed and relatively simple algorithms to balance energy in order to extend WSN lifetime. A game theoretic (GT) approach is proposed to build a viable load balancing solution to extend the WSNs lifetime. GT offers an interesting decision making mechanism in a distributed and dynamic environment in absence of the global view and certainty. That is why, in this work, GRP is combined with GT in order to take advantage of inherent benefits of this combination. This paper significantly enhances our initial work in [10] and provides detailed analysis and results. The energy balance problem is solved at the region and node levels. In region level energy balance (RLEB), the objective is to balance the energy consumption around a sender such that all subregions around the sender will participate fairly and deplete their energy approximately at the same time. After selecting the participating region, node level energy balance (NLEB) is required to select the most favorable forwarding node in this sub-region. Because the objectives of RLEB and NLEB are different, RLEB employs evolutionary game theory (EGT) and NLEB employs classical game theory (CGT). EGT captures the dynamic energy changes in the sub-regions, whereas CGT captures the selfish behavior of the nodes to preserve their energy. The main contribution of this paper is twofold. First, a new method is developed for extending the network lifetime by balancing traffic load at two levels: over regions and at the nodes in these regions. The energy balance at the region level is achieved using EGT, while that at the node level is achieved using CGT. Second, the energy hole problem in the WSN geographical routing is mitigated using EGT. The energy hole problem occurs due to an uneven traffic load distribution. For instance, nodes closer to the sink have to carry heavier traffic load, which leads to a faster rate of energy consumption and can partition the network. The remainder of the paper is organized as follows. Sec-
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tion II presents background knowledge, while Section III provides a detailed description of the proposed protocol. Details of region level energy balance is provided in Sub-section III-A and node level energy balance is provided in Sub-section III-B. Section IV presents the results and discussion. Finally, conclusions are drawn and further research is suggested in Section V. II. R ELATED W ORK Extending network lifetime can be achieved using different methods such as altering transmission power as in [11], designing a power aware routing protocol as in [12] and distributing traffic load among least power routes as in [3], [6]. Although each of those methods offers benefits, the most plausible is load balancing. However, there is no globally applicable load balancing solution for extending the network lifetime in GRPs. This paper provides a globally applicable solution to extend network lifetime by balancing traffic load over regions and nodes, with scalable and distributed manner using GT and GRP. GRPs are gaining popularity and are being employed for industrial applications such as advanced metering infrastructures for smart grid [13]. Ahmed and Fisal in [4] proposed a quadrant based directional forwarding scheme, called realtime load balance distribution protocol (RTLD), which limits the forwarding task to a quadrant of the forwarding nodes. However, redundant transmissions in the selected quadrant may occur and some quadrants could be utilized more than others depending on the location of the source. That is why it does not provide global load balance. GTEB distributes the load evenly among the regions as well as selects better nodes in the selected region. These features enable it to be more adaptive to changes in the energy dissipation in the subregions, as well as other parameters of the network such as node densities. Both, RTLD and GTEB offer a RLEB but through different means. GTEB does RLEB as well as NLEB, but RTLD only does RLEB. It is interesting to explore the impact of the combination of RLEB and NLEB on the network performance by comparing with the RLEB only protocol. For example, if the network is dense, there can be more subregions and a lower number of participating nodes in forwarding. Another common problem in WSNs is over utilization of nodes around sinks. Charilaos et. al in [2] presented a solution to this problem by adjusting the transmission power of the nodes to by-pass these vulnerable nodes around sinks and transmitting directly to the sink with certain probability. Although using more transmission power is energy expensive, it helps to extend the lifetime of the network. Chipara et. al in [14] developed ALBA-R localized and distributed GRP for balancing traffic load on nodes that are located around energy holes so that the nodes do not run out of energy too early. In our case, GTEB can detect the energy hole problem areas and does not forward any traffic towards such areas. Chipara et. al in [15], suggested a real-time power aware routing protocol (RPAR) to find balance between end-toend delay and energy consumption using transmission power adjustment. RPAR is considered as a NLEB only protocol. Therefore, GTEB is compared with RPAR to understand the
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impact of the combination of RLEB and NLEB on the network performance over a NLEB only protocol. RPAR is compared to the proposed protocol in the results and discussion section. Game theory was proven to provide versatile solutions for dynamic and distributed networking problems [16]. CGT is used in GRPs for various problems related to end-to-end delay optimization, task allocation, relay selection, and network congestion [17]–[19]. Behzadan et al. in [20] proposed a game theoretic heterogeneous balanced data routing (HBDR) algorithm for WSNs with a tree topology. In this protocol, a hierarchical network is constructed using CGT to provide a load balanced tree that maximizes network lifetime. Kamhoua et al. in [21] proposed a GT based congestion avoidance mechanism for a GRP around the line between the source and destination. Naserian and Tepe in [22] used the game theoretic routing to reduce routing overhead by selecting forwarding nodes to provide connection without network partitioning. Neda et al. in [19] proposed to use CGT in base stations for relay selection and transmission power allocation for the network. Lin and Wang [23] used GT approaches to balance energy consumption by alternating cluster head roles among the nodes based on their available energy. Hui et al. [24] proposed a cooperative game theoretical load-balancing routing protocol to find out the best possible route in terms of end-to-end delay. EGT is emerging as an important tool to solve dynamic networking problems due to changes in energy state, channel state and topology. For example, Niyato and Hossain in [25] used EGT to allocate bandwidth for users based on the service cost of various wireless networks. Anastasopoulos et al. in [26] employed EGT for traffic routing over multi-path wireless back-haul networks experiencing rain attenuation. Khan et al. in [16] applied EGT to fairly distribute users to various wireless access network technologies for bandwidth and cost optimization. Altman et al. in [27] designed an EGT based routing protocol for WSNs to control congestion and reliability which were influenced by the wireless channel’s characteristics. In [28], EGT is implemented to solve the packet forwarding problem when a network consists of heterogeneous nodes operating in networks with different authorities. This shows that the forwarding cooperation among authorities can evolve and provide stable communication. In this paper, both CGT and EGT are utilized simultaneously for energy balance in geographical routing to prolong the network lifetime. III. PROTOCOL DESCRIPTION The proposed GTEB protocol is designed to provide energy balance to uniformly and randomly deployed multi-hop WSNs with homogeneous nodes where the transmission range is r. Initial energy of a node is E Joules. The nodes know their locations and the location of the destination node. The nodes learn their neighbors’ location by exchanging an initialization packet, which includes the location information of the node. The energy cost of this initialization incurs a one packet transmission cost for each node and one overhearing cost to its neighbors. The GTEB protocol considers geographical routing in a stationary network. If the node is equipped with GPS, the GPS needs to only run in the initialization phase to acquire
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A forwarding node is selected using Classical Game theory (CGT)
A subregion is selected using EGT
R1
r R2
S R3
D
Geographical routing R4
S :Source/Sender , Rk: subregion k D: Destination, r: Transmission range
Fig. 1: Subregion and node selection in the proposed protocol. Game Theoretic Energy Balance (GTEB) Routing Protocol
decision making processes in the GTEB protocol. The node neighbor discovery function depicted in the figure is executed once at the deployment time of the network in order to allow nodes to learn the number of single hop neighbors. Other functions will be executed whenever a node receives a new packet from one of its neighbors. The node drops a received packet if a node is not located in the designated forwarding sub-region or if the packet has been forwarded before. A sender node evaluates the energy levels of K subregions, hence the computational complexity of executing EGT is linear, that is O(K) 1 . Since CGT runs once in each node in a forwarding sub-region, the computational complexity of this step is constant. Therefore, the complexity of running the protocol at each node is O(K). Energy consumption of these computations is very small when compared to transmission and reception, therefore those were not considered in this paper.
[Neighbor information]
Node’s neighbor discovery
NODE i FR determination
[executed once at deployment]
Region’s packet population
NR== FR
[Drop ]
[Forward]
No [Selected node]
Yes [attach to packet: selected forwarding region (FR), # of nodes in region, region packet share, sender coordinates]
Play CGT for (NLEB))
Play EGT for (RLEB)
Node’s packet population
[NR: Node’s region]
Fig. 2: GTEB’s functional diagram. the location of the node, then it can be turned off. That is why the energy cost of this initialization is not included in this paper. In the network, any node can be a source and can report events periodically or at the instant they occur. The problem of achieving a network wide energy balance is broken down into the following two sub-problems: i) RLEB at sub-regions and ii) NLEB within the sub-region. The energy balance at the region level is achieved using EGT and the energy balance at the node level is achieved using CGT. The transmission range of a sender is divided into K forwarding sub-regions based on the network density ρ. Fig. 1 illustrates this scenario. In the figure, the selected region is shaded and the selected forwarding node is labeled. Based on EGT, a sender forwards a packet to its neighborhood with the following information: i) angle, θ, which bounds the selected forwarding sub-region, ii) Nk , the number of neighbors in this sub-region, iii) sender’s location (x, y), and iv) proportion of packets, λk , assigned to this subregion. Carrying these 4 fields requires 5 bytes in the packet header. This information, provided by the packet, will allow the surrounding nodes to identify whether they are in the forwarding sub-region. Then the nodes in the selected subregion will play a Nk -player non-cooperative classical game to identify which one will be the potential forwarding node. One of the potential forwarding nodes in that sub-region, who wins the game becomes a sender node and plays its own evolutionary game to select the next forwarding region in order to balance energy consumption in its own surrounding. Fig. 2 shows a schematic functional diagram of the distributed
A. Region level energy balance The objective of RLEB is to spread the forwarding task around the sender node fairly such that the surrounding nodes deplete their energy at the same time. EGT is employed to achieve this objective. We assume the total number of packets sent by the sender is λ, which represents the total population of region level evolutionary game (RLEG). This population of the packets is distributed to K forwarding sub-regions throughout the operation. Hence, a subregion k will forward λk packets and consequently the total number PKof packets that are forwarded by all sub-regions is λ = k=1 λk . The task of RLEG is to define the proportion of packets that can be forwarded by each sub-region in every game interval. Senders play the RLEG on behalf of the packet and select one of K forwarding sub-regions as a strategy from the set R, where R = {R1 , R2 , ..., RK }. The proportion of the packets forwarded through the kth sub-region is specified by Xk , which is given by λλk . Thus, the packet proportion distribution vector (population state) X over all sub-regions is given by X = [X1 , X2 , ..., XK ]. The goal of employing EGT is to find the stable proportion distribution of packet population in all sub-regions in order to make all sub-regions consume their energy at approximately the same time. This stable vector is called the equilibrium packet proportion distribution vector or stable state X ∗ . This vector can be obtained by modeling the energy balance problem into a set of differential equations, which will be the replicator dynamics of the RLEG. Replicator dynamics evolve a new packet distribution vector in every game interval until it reaches a stable state. The most important part of EGT is to design a fitness function which captures the energy consumption in the network. The fitness function will be used to identify the switching probability from one region to another region. Both of these will be utilized to obtain the replicator dynamics to find the equilibrium solution. The fitness function Fk (X) for a packet in a RLEB is expressed in terms of gain and cost of utilizing a subregion for forwarding. The gain, Ek , represents the available remaining energy in the sub-region k. The cost of sending a 1 O(.)
is big O notation.
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packet through a sub-region depends on i) packet transmission and reception energies, ii) number of nodes in that region Nk , and iii) number of packets sent through this region λk . In order to capture these, the fitness function is given by Fk (X) = Ek − [λ × Xk × (2 × Nk × Etr + Etx )],
(1)
where Etr and Etx are the energy consumed by a node while receiving and transmitting a packet, respectively. Etr and Etx are both dependent on packet length of m bits, the transmission radius of d meters and a few hardware parameters. Energy consumption by a node for transmitting a packet can then be expressed as Etx (m, d) = m × (etc + eta × dα ),
(2)
where the energy spent by transmitter electronics is denoted by etc and transmitter amplifier by eta . These are hardware dependent parameters related to processing and sending the packets. α is the path loss exponent whose value is larger than 2 in sensor networking applications. The energy consumption by a node for receiving a packet is given by Etr (m) = m × erc ,
(3)
where erc is the transceiver effeteness during the start-up time, which is ignored due to its dependence on the type of used MAC protocol. All the nodes located in the same sub-region (in transmission range of forwarding/sender node) will spend their receiving energy cost since they all receive the packets. After the sub-region selection, only one node will be selected based on Nk -player non-cooperative classical game to forward the packet in NLEB and the forwarding node will spend the transmission cost. The values of transmission and receiving cost can be obtained from any sensor node’s data-sheet. For example, the energy consumption for transmission and reception of an IRIS sensor node is 51 and 24 milliwatts, respectively [29]. During the protocol run time, packets that have been forwarded in sub-region k will be further forwarded by a next hop neighbor in a given game interval. The fitness function in (1) expresses that a packet will be forwarded to a sub-region as long as the available energy in that region is more than the energy threshold value, Ek λk ≥ (Etx + Etr ), which is the required energy to receive and forward that packet further. That is why the packet’s share of energy will be decreased with an increase in the number of packets in a forwarding sub-region. The sender forwards a packet to a sub-region as long as the available energy in that sub-region, Ek , is more than the sum of required energy to receive and transmit a packet, Etx + Etr . Otherwise, the sender considers that sub-region as dead and will not forward any packet to this sub-region. 1) Replicator dynamics: The replicator dynamics captures the proportions of inflow and outflow packets from one subregion to other. The selection of a sub-region is considered a strategy for a packet. In every game interval, a sender decides the proportions of packets to be forwarded through various forwarding sub-regions based on their residual energies. The switching probability from sub-region l to sub-region
k, Pk,l (X), is associated with a region fitness values Fl (X) and Fk (X), respectively. This switching probability can be defined as βXk [Fk (X)−Fl (X)] if Fk (X) > Fl (X), k 6= l Pk,l (X) = 0 if Fk (X) ≤ Fl (X), k 6= l P 1 − i6=k,i∈K βXl [Fi (X)−Fk (X)] if k = l, (4) where Xl and Xk are the proportions of packets in the subregion l and k respectively. The normalization factor for the total energy is given by β = PK1 E . The sum of all i i=1 probabilities of switching from sub-region k to all other subregions including the sub-region itself must be one, which is reflected by the following equation: X Pk,k (X) + Pk,l (X) = 1. (5) l6=k
The rate of the change in the number of packets that are forwarded through sub-region k represents the difference between the inflow and outflow packets. The expected number of inflow packets that mightPswitch from another region to the region k is expressed as l6=k Xk Pk,l (X) and the expected number of outflow packets that might Pswitch from region k to the other sub-regions is given by l6=k Pl,k (X). Accordingly, the differential equations of the replicator dynamics that capture the net change in the number of packets in the game interval (unit time) in sub-region k can be given by X X X˙k = (Xl )Pk,l (X) − Xk Pl,k (X). (6) l6=k
l6=k
Using (5), the simplified replicator dynamics equation can be written as K X X˙k = (Xl )Pk,l (X) − Xk , (7) l=1
Therefore, the transition probability matrix P for a scenario with two sub-regions, using (4), is provided by 1 βX1 [F1 (X) − F2 (X)] P (X) = . (8) 0 1 − βX1 [F1 (X) − F2 (X)] The change in the proportions of packets over all sub-regions for a sender is obtained by substituting (8) in (7), which can be expressed in matrix form as X˙ = P (X)X − X.
(9)
When the number of inflow and outflow packets from all subregions are equal then the system is in a stable state. 2) Evolutionary equilibrium: The RLEG reaches the equilibrium state when the rate of change in the proportions of ˙ becomes a zero vector. At this packets in all sub-regions, X, equilibrium state, the proportion of packets is represented by X ∗ . In order to find the equilibrium packet distribution vector (equilibrium strategy), X ∗ , the solution of the system of equations in (9) must be obtained as follows X˙k = 0
∀ k = 1, ..., K K X k=1
Xk = 1.
(10a) (10b)
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X˙ 1 = βX1 X2 [F1 (X) − F2 (X)] X˙ 2 = −βX1X2 [F1 (X) − F2 (X)].
(11)
Equating (11) to zero and solving by using (1) and (10) gives the elements of equilibrium vector:
0.95
Nash equilibrium probability (q*)
According to Brouwer’s fixed point theorem [30], there will be at least one fixed point (Nash equilibrium) for any continuous function over a closed interval. In this work, the set of equations given by (10a) depends on the switching probabilities in (4), which is a continuous function of X on the closed interval [0,1]. Consequently, (10a) will have fixed points that are denoted by X ∗ . From (9), the net changes in the two subregions are given by
q* with v= 30.16×δ q* with v= 20×δ q* with v=6.15×δ
0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15
E1 − E2 + λC2 E1 − E2 + λC2 , X2∗ = 1 − , (12) λ(C1 + C2 ) λ(C1 + C2 )
0.05 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Number of neighbors in a forwarding sub−region
where Ck = 2Nk Etr − Etx . At the equilibrium state the packet’s fitness will be the same in all sub-regions, that is F1 (X) = F2 (X) = ... = Fk (X), and no packet can increase its fitness by moving to another sub-region (strategy). 3) Stability analysis: In this section of analysis, the stability of X ∗ is examined. To prove the population distribution stability, (9) is linearized at X ∗ , F1 (X) = F2 (X), and Eigenvalues of the Jacobian matrix J(X1 , X2 ) are obtained. The Jacobian matrix is given by −λβC1 X1 X2 λβC2 X1 X2 J(X1 , X2 ) = . (13) λβC1 X1 X2 −λβC2 X1 X2
Fig. 3: Nash equilibrium q ∗ versus changes in reward value v with an increasing number of neighbors.
Eigenvalues of the Jacobian matrix, denoted by γ, can be found by solving the following equation: det(J(X1 , X2 ) − Iγ) = 0,
(14)
where I is the identity matrix. The solution of (14) shows that Eigenvalues are −λC1 βX1 X2 − λC2 βX1 X2 and zero. Since the real part of the Eigenvalues is negative, the evolutionary stable strategies condition is satisfied based on [31]. This proves that RLEG reaches a stable state. B. Node level energy balance The objective of NLEB game is to balance the energy consumption in a sub-region by selecting one forwarding node from Nk nodes in the sub-region k. This game is formulated as an Nk -player non-cooperative mixed strategy game, where Nk is the set of player nodes, denoted as N = {n1 , n2 , ..., nNk }, where Nk ≥ 2. If there is only one node in a sub-region, then this node will forward the packet without playing any game. Each node has two mixed strategies, represented by a set S = {T, T¯}, where T represents transmission and T¯ represents no-transmission. Being a mixed strategy game, a node, labeled A, plays one of its available strategies against Nk − 1 opponent nodes. Other players play their strategies with their corresponding probabilities as shown in Table I. Let the probability of transmission by a node be q, and notransmission 1 − q. The probability of transmission by at least another node is 1 − (1 − q)Nk −1 , hence the probability that all other nodes may not transmit is given by (1 − q)Nk −1 . The payoff function Ui (s) for a node i represents the award that
1 0.8 Probability (P)
X1∗ =
0.6 0.4 0.2 0
Power Ratio Probability (p) 2
4 6 8 10 12 Number of received packets per time unit
14
Fig. 4: Forwarding probability versus number of forwarded packets and the node’s residual energy.
it gains by playing one of its available strategies against other (Nk − 1) player nodes, which play their own strategies s. The matrix norm formulation that describes the game scenario is given in Table I. If two or more nodes are playing transmission strategy simultaneously, all of the nodes will incur a collision cost of ∆ and a transmission cost of δ, where ∆ is greater than δ. If one node plays transmission strategy and other nodes play no-transmission strategy, the first node receives a reward v and incurs a transmission cost δ, where v is greater than δ. If no node plays transmission, then the payoff will be zero for all nodes. The expected payoff calculated using Table I for a node ni to forward a packet is given by E[Ui ] = q[(−∆ − δ)(1 − (1 − q)Nk −1 ) + (v − δ)(1 − q)Nk −1 ]. (15) Correspondingly, the expected payoff for no-transmission strategy is zero. Therefore, setting E[Ui ] equal to zero will give probability q ∗ of a mixed strategy Nash equilibrium as q∗ = 1 − [
δ + ∆ 1/Nk −1 ] . (∆ + v)
(16)
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The transmission cost δ and collision cost ∆ = 2 × δ can be extracted from a datasheet of hardware, which are used in the system. For example, δ is 51 milliwatts for IRIS motes [29]. Each node has its own Nash equilibrium and forwarding probability. However, reducing the number of forwarding nodes may lead to network disconnectivity. Therefore, the equilibrium point calculated in (16) depends on the number of neighbors Nk and v. It is essential to determine the range of v and Nk , such that the following conditions are satisfied: i) the number of player nodes is greater than or equal to two, and ii) network connectivity is maintained with minimum routing overhead. Previous studies in [32] and [33] shown that the required number of neighbors to maintain overall connectivity is four. When the value of v is low, then the probability in (16) will be low, which might result in network disconnectivity. However, for a high reward value, the nodes increase their forwarding probability and when v → ∞ all nodes will forward the received packets causing redundant transmissions. By using (16) with δ = 51 milliwatts where a node transmits with 3 dBm, the value of v will be in the range of 6.15×δ 6 v 6 30.16×δ. Fig. 3 shows the Nash equilibrium forwarding probability q ∗ versus the neighboring number of nodes in forwarding sub-regions. When v is 30.16 × δ both previous conditions are satisfied. Once the nodes in a selected forwarding region k receive a packet, these nodes will start the Nk -player non-cooperative game. Each of these nodes calculates its own forwarding probability pi,k given by (17) in order to make its forwarding decision. The received packet will be forwarded only when the value of the forwarding probability is less than the Nash equilibrium q ∗ . This forwarding probability is calculated based on the following three factors: i) the ideal share of packets that must be forwarded by every node in a selected forwarding ´ region,( (CiC−iCi ) ), ii) the ratio of the residual energy in a ´
i forwarding node, ( E Ei ) and iii) the share of packets that is assigned to a selected forwarding sub-region by a sender, ´ ( (λkλ−kλk ) ). Ci is given by λk /Nk and represents the number of packets that must ideally be forwarded by the node i in the selected sub-region. C´i is the number of packets that have already been forwarded by the node i and is tracked by the node. Ei is the initial energy of the node i and E´i is the residual energy of the node. λk is the proportion of the packets assigned by the sender for the region k and λ´k is the number of packets which have been forwarded by the region k out of λk . Ci , C´i , λk , λ´k , Nk and E´i are dynamic and EGT utilizes these values to capture the dynamic change in the energy of the networks. Hence the forwarding probability is given by
pi,k = 1 − [(
(Ci − C´i ) E´i (λk − λ´k ) )( )( )]. Ci Ei λk
(17)
Any node, which decides to forward a packet based on the Nk -player non-cooperative forwarding game, will play its own evolutionary game to balance the energy in its surrounding sub-regions. Fig. 4 shows that the node forwarding probability, pi,k , increases as the number of forwarded packets by the node increases. A node will not forward a packet when its
TABLE I: THE PAYOFF MATRIX OF Nk -PLAYER NONCOOPERATIVE GAME. aa
Nk − 1 Players 1 − (1 − q)Nk −1 aa aa aa T Player A a a
(1 − q)Nk −1 T¯
q
T
−δ − ∆,−δ − ∆
v − δ,0
1−q
T¯
0,v − δ
0,0
forwarding probability is greater than its Nash equilibrium and will wait for a round trip time (RTT) or until it overhears the forwarded packet by any other nodes. If the node does not overhear the packet, it will gradually decrease its forwarding probability until the packet is forwarded either by itself or by another node. A node is considered dead when its remaining energy drops below Etx + Etr . When the node is about to die, it notifies its neighbors. IV. RESULTS AND DISCUSSION The performance of the proposed protocol, GTEB, was analyzed for network lifetime, average energy consumption per packet and packet delivery ratio. Network lifetime is defined as the duration until any sensor node in the network becomes inoperative due to the depletion of energy [5], [12]. Energy consumption per packet is defined as the average energy that is required to transmit a packet successfully. The packet delivery ratio is defined as the ratio between the number of delivered packets and the total number of generated packets in a given duration. The proposed routing protocol has been evaluated using OMNeT++ 4.2.2 network simulator with MiXiM framework [34]. The simulation parameters are given in Table II. A converge-cast traffic pattern was used and the sensors were uniformly randomly deployed in a two-dimensional (2D) terrain of 100 × 100 m2 . The performance of GTEB was evaluated in two experimental setups. In the first experimental setup, the effectiveness of combined evolutionary and CGT was tested against three other random test cases. These three random test cases are labeled as: Random-Random, RandomCGT and EGT-Random. In these labellings, the first part of the label indicates the decision making mechanism at the region level and the second part of the label indicates the decision making mechanism at the node level. These test cases identify the effectiveness of employing the combination of game theory in two levels of decision making on the network performance. In the Random-Random test, the region and node selections are random. In the Random-CGT test, the forwarding region is selected at random but the forwarding node selection in this region is based on a Nk -player non-cooperative game. In the EGT-Random test case, a sender distributes a packet population over a set of sub-regions based on EGT while a forwarding node in this region will be chosen randomly. In the second experimental setup, the performance of GTEB is compared with three competing GRPs, which are RTLD [4], RPAR [15] and probabilistic forwarding routing protocol (gossiping).The probabilistic forwarding protocol was used to
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TABLE II: SIMULATION PARAMETERS. Value IEEE802.15.4 Log-normal Shadowing 2.5 128 bytes 200 kbps 3.3J 2mW CBR
verify if the proposed GT approach was better than the random forwarding approach, in which every node forwards or discards the received packet with a certain probability.
3500 3000 2500 2000 1500 1000 500 0 120
160
200 240 280 320 360 400 440 Number of nodes in deployment space
480
520
Fig. 5: Lifetime in GTEB and three test cases with different densities. 1400
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A. Network lifetime In this experiment, the packet generation rate was chosen to be two packets per second whereas the number of sensor nodes was varied from 120 to 520 nodes. Fig. 5 shows the network lifetime versus the number of nodes in deployment space. GTEB provided 9% to 38% longer network operation compared to other three random test cases. This superior performance is because of the balancing of energy consumption in nodes surrounding the sender node using evolutionary game and eliminating redundant transmissions in the forwarding sub-region using a Nk -player non-cooperative game. However, the EGT-Random curve shows a similar trend as GTEB but with a relatively lower lifetime, since at the node level, random node selection cases do not perform as good as GT approach. On the other hand, for the other two approaches, namely Random-CGT and Random-Random, the packets are randomly distributed to the regions and lifetime is significantly reduced as a result. That result confirms that unfair packet distribution over forwarding regions significantly shortens the WSN lifetime. Although the increased node density may cause more redundant transmissions, GTEB effectively managed forwarding decisions to distribute the packets among the nodes and achieved the best results. Fig. 6 illustrates the performance of GTEB with an increasing packet generation rate in a fixed network size of 120 nodes. This figure shows that the GTEB protocol performance is better than the other three random cases even with increased traffic load by 30% to 78%, due to intelligent forwarding decision making. Fig. 7 presents a comparison of the lifetime of GTEB and probabilistic forwarding. This figure proves that using forwarding probability provided by the Nash equilibrium condition and fitness function in GT approaches allow better utilization of energy in each sensor network compared to probabilistic forwarding. GTEB integrates the accumulated energy in various sub-regions and the remaining energy in each individual node in a sub-region in forwarding decisions while the gossiping approach does not consider the energy factor in its forwarding decision and only forwards based on a fixed probability. GTEB prolongs the lifetime by 33% to 58% compared to probabilistic forwarding. In Fig. 8, the network lifetime of RTLD and GTEB are compared using the same network scenario. This figure shows
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Fig. 6: Lifetime in GTEB and probabilistic forwarding. that GTEB prolongs the lifetime by 30% to 40%. This longer lifetime in GTEB is due to balancing traffic load over a set of forwarding regions around every sensor node and among the nodes belonging to the same forwarding sub-region. In Fig. 9, we compare the results between GTEB, selfish one level CGT based routing protocol, and two level Random-CGT protocol. The figure shows that the performance of GTEB is better than the selfish CGT by 32% to 44%. However, network lifetime in selfish CGT is better than Random-CGT by 33% to 59%, which reveals that selfish behavior in CGT performed better than random region selection and CGT combination. It is also interesting to note that EGT-Random outperforms selfish CGT performance slightly, which reveals that RLEB with EGT is an important factor to extend the network lifetime. B. Average energy consumption per packet The energy that is required for successfully delivering a packet to the destination is evaluated in this section. In this scenario, GTEB is evaluated with three random test cases and two other competing protocols. Fig. 10 shows that the average energy consumed per packet in GTEB is better than the other three test cases by up to 60%. In this figure, the results are obtained based on different network densities with a packet generation rate of two packets per second. The figure shows
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Fig. 8: Lifetime in GTEB versus RTLD. that the increase in the number of sensor nodes increases the energy consumed per packet because test cases do not consider residual energy and the ideal number of packets to be forwarded by each node. Fig. 11 shows the energy consumption per packet in GTEB and three other test cases with different packet generation rates. The figure shows that increased traffic in the network impacts the average energy consumed per packet. Despite this traffic increase, GTEB still has better performance because every node makes ideal forwarding decisions based on a combination of Nash equilibrium and its residual energy, and its share of the packet forwarding. Besides that, the GTEB traffic distribution mechanism prevents the traffic load from condensing in some parts of the network. The energy consumption per packet in GTEB is less than in the other test cases by 2% to 64%. On the contrary, the randomness of forwarding tasks and unfair traffic distribution in other test cases cause this difference in energy depletion as compared to the GTEB protocol. GTEB’s energy consumption per packet is compared with RTLD [4] and RPAR [15]. Energy consumption per packet of GTEB is 26% to 65% less than RTLD and 35% to 70% less than RPAR in similar network scenarios. It is also observed that in a typical experiment, with 121 sensor nodes, the average
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Fig. 10: Energy per packet in GTEB and three test cases with different densities. latency for a packet in GTEB is 68 milliseconds (ms) while it is 61 ms in RTLD.
C. Packet delivery ratio In this set of experiments the packet delivery ratio of GTEB is evaluated against three random test cases with different packet generation rates varying from 1 to 14 packets per second, as shown in Fig. 12. GTEB shows improved packet delivery rate by 2% to 52% in comparison with the other random test cases. Fig. 13 shows the packet delivery ratio in GTEB in comparison to RTLD and RPAR. RTLD experiences a lower packet delivery ratio as traffic condenses in one region, while RPAR uses a set of pre-defined routes to deliver the packets and excludes other sensors that do not belong to any routes. The increase of traffic over a limited number of routes elevates the congestion and lowers the number of delivered packets. However, in RTLD and RPAR protocols, the congestion and collisions are the main reasons for packets to miss their deadlines and eventually be dropped.
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Fig. 12: Packet delivery ratio in GTEB and three test cases. D. Energy distribution In these sets of experiments, the energy distribution was studied to evaluate the energy consumption pattern in the network. Fig. 14 shows the energy distribution in the network in four different snapshots. The left upper subplot illustrates the initial energy of sensor nodes. The right lower subplot presents the remaining energy in the network after 1150 hours of running with the GTEB protocol. It is observed that the protocol evenly dissipates the network energy over time and does not cause the energy hole problem. V. CONCLUSION This paper proposes a fully distributed routing protocol, called game theoretic energy balance (GTEB), for maximizing the lifetime of WSNs. GTEB utilizes evolutionary game to capture dynamic changes on a macro scale, classical game theoretic to capture selfish behavior of the sensor node, and the geographical routing protocol to minimize routing overhead in the network. The combination of evolutionary and classical game theoretics with geographical routing is shown to be effective in improving lifetime of the network. The simulation
Fig. 14: Energy distribution in the network. results showed that GTEB provides significant improvement in extending network lifetime and delivery ratio over other test protocols and competing geographical protocols. The obtained results showed that GTEB provides excellent adaptation to factors in the network, such as the network density, traffic load and asymmetric energy use. The proposed low overhead protocol can make WSNs operate longer for a given energy resource. GTEB does not currently support mobility. As common to all GRPs, GTEB needs positioning hardware in sensor nodes or alternatively, the pre-programming of node locations. ACKNOWLEDGMENT This work was supported in part by the NSERC Discovery Grant program (grant no. 262323-2011). The authors would like to thank the anonymous reviewers for their insightful comments. R EFERENCES ´ et environnement (France), [1] J. Galliard, J. Guarini, F. Gaill, and I. E. Sensors for Ecology: Towards Integrated Knowledge of Ecosystems. CNRS-[Institut e´ cologie et environnement], 2012. [2] C. Efthymiou, S. Nikoletseas, and J. Rolim, “Energy balanced data propagation in wireless sensor networks,” in Proc. 18th Int. Parallel and Distributed Processing Symposium, April 2004, pp. 225–232.
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[3] H. Zhang and H. Shen, “Balancing energy consumption to maximize network lifetime in data-gathering sensor networks,” IEEE Trans. on Parallel and Distributed Systems, vol. 20, no. 10, pp. 1526–1539, Oct 2009. [4] A. A. Ahmed and N. Fisal, “A real-time routing protocol with load distribution in wireless sensor networks,” Elsevier Computer Communications, vol. 31, no. 14, pp. 3190 – 3203, 2008. [5] Y. Chen and Q. Zhao, “On the lifetime of wireless sensor networks,” J. IEEE Communications Letters, vol. 9, no. 11, pp. 976–978, Nov 2005. [6] N. Pantazis, S. Nikolidakis, and D. Vergados, “Energy-efficient routing protocols in wireless sensor networks: A survey,” IEEE Communications Surveys Tutorials, vol. 15, no. 2, pp. 551–591, Sept 2013. [7] Y. Hou, Y. Shi, J. Pan, and S. Midkiff, “Maximizing the lifetime of wireless sensor networks through optimal single-session flow routing,” IEEE Tran. on Mobile Computing, vol. 5, no. 9, pp. 1255–1266, Sept 2006. [8] D. Zhang, G. Li, K. Zheng, X. Ming, and Z.-H. Pan, “An energybalanced routing method based on forward-aware factor for wireless sensor networks,” IEEE Trans. on Industrial Informatics, vol. 10, no. 1, pp. 766–773, Feb 2014. [9] G. Iyer, P. Agrawal, E. Monnerie, and R. Cardozo, “Performance analysis of wireless mesh routing protocols for smart utility networks,” in Proc. IEEE Int. Conf. Smart Grid Communications, Oct 2011, pp. 114–119. [10] M. Abd, B. Singh, S. Al Rubeaai, K. Tepe, and R. Benlamri, “Game theoretic energy balanced (gteb) routing protocol for wireless sensor networks,” in Wireless Communications and Networking Conference (WCNC), 2014 IEEE, April 2014, pp. 2564–2569. [11] J. Gao, F. Li, and Y. Wang, “Distributed load balancing mechanism for detouring routing holes in sensor networks,” in Proc. IEEE Vehicular Technology Conf., Sept 2012, pp. 1–5. [12] G. Anastasi, M. Conti, M. Di Francesco, and A. Passarella, “Energy conservation in wireless sensor networks: A survey,” Elsevier Ad Hoc Network, vol. 7, no. 3, pp. 537–568, May 2009. [13] F. Cadger, K. Curran, J. Santos, and S. Moffett, “A survey of geographical routing in wireless ad-hoc networks,” J. of IEEE Communications Surveys Tutorials, vol. 15, no. 2, pp. 621–653, July 2013. [14] C. Petrioli, M. Nati, P. Casari, M. Zorzi, and S. Basagni, “Alba-r: Load-balancing geographic routing around connectivity holes in wireless sensor networks,” IEEE Trans. on Parallel and Distributed Systems, vol. 25, no. 3, pp. 529–539, March 2014. [15] O. Chipara, Z. He, G. Xing, Q. Chen, X. Wang, C. Lu, J. Stankovic, and T. Abdelzaher, “Real-time power-aware routing in sensor networks,” in Proc. 14th IEEE Int. Workshop on Quality of Service, June 2006, pp. 83–92. [16] M. Khan, H. Tembine, and A. Vasilakos, “Evolutionary coalitional games: design and challenges in wireless networks,” IEEE J. of Wireless Communications, vol. 19, no. 2, pp. 50–56, April 2012. [17] H.-Y. Shi, W.-L. Wang, N.-M. Kwok, and S.-Y. Chen, “Game theory for wireless sensor networks: A survey,” MDPI Sensors, vol. 12, no. 7, pp. 9055–9097, 2012. [18] R. Machado and S. Tekinay, “A survey of game-theoretic approaches in wireless sensor networks,” Elsevier Computer Networks, vol. 52, no. 16, pp. 3047 – 3061, 2008. [19] N. Edalat, C.-K. Tham, and W. Xiao, “An auction-based strategy for distributed task allocation in wireless sensor networks,” Elsevier Computer Communications, vol. 35, no. 8, pp. 916 – 928, Sept 2012. [20] A. Behzadan, A. Anpalagan, and B. Ma, “Prolonging network lifetime via nodal energy balancing in heterogeneous wireless sensor networks,” in Proc. of IEEE Int. Conf. on Communications, June 2011, pp. 1–5. [21] C. Kamhoua, N. Pissinou, and S. Makki, “Game theoretic analysis of cooperation in autonomous multi hop networks: The consequences of unequal traffic load,” in Proc. of IEEE GLOBECOM Workshops, Dec 2010, pp. 1973–1978. [22] M. Naserian and K. Tepe, “Game theoretic approach in routing protocol for wireless ad hoc networks,” Elsevier Ad Hoc Networks, vol. 7, no. 3, pp. 569–578, Sept 2009. [23] X.-H. Lin and H. Wang, “On using game theory to balance energy consumption in heterogeneous wireless sensor networks,” in Local Computer Networks (LCN), 2012 IEEE 37th Conference on, Oct 2012, pp. 568–576. [24] T. Hui, J. Fan, and C. Weijun, “A game theory based load-balancing routing with cooperation stimulation for wireless ad hoc networks,” in High Performance Computing and Communications, 2009. HPCC ’09. 11th IEEE International Conference on, June 2009, pp. 266–272.
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Dr. Mehmmood A. Abd received B.Sc. degree in computer science from the University of Baghdad, Iraq, 1992 and M.Sc. in information technology from the University of Liverpool, UK in 2006, and received his Ph.D. in 2015 from the Department of Electrical and Computer Engineering of University of Windsor, ON, Canada. His research interests include energy balance in wireless sensor network, image processing, resource allocation and game theory applications.
Sarab F. Majed Al-Rubeaai received her B.Sc. and M.Sc. in mathematics from the University of Baghdad in 1992 and 1997, respectively and received M.Sc in mathematics from the University of Western Ontario, ON, Canada in 2009. She is currently a Ph.D. candidate at the Department of Electrical and Computer Engineering of University of Windsor, ON, Canada. Her research interests include real-time data communication for wireless sensor network, cryptography, number theory, image processing, resource allocation and game theory applications.
Dr. Brajendra Kumar Singh Brajendra Kumar Singh (S09) received the B.E. degree in electronics from Jiwaji University, India, M.E. degree in communication control and networking from Rajiv Gandhi Technical University, India, and the Ph.D. degree in Electrical Engineering from the University of Windsor, Canada, in 1996, 2001, and 2010, respectively. He is currently working as post-doctoral research associate in the WiCIP lab at the University of Windsor since 2012. He worked as senior engineer at the Space Applications Centre, Indian Space Research Organization (ISRO), India for nine and half years since 1998. His research interest includes MAC layer design, real-time data communication, wireless sensor networks, and FPGA design and verification.
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Dr. Kemal Tepe received his B.Sc. from Hacettepe University, Ankara, Turkey in 1992; and M.Sc. and Ph.D. degrees from Rensselaer Polytechnic Institute, Troy, NY in 1996 and 2001, respectively, all in Electrical Engineering. He worked as research scientist at Telcordia Technologies in Red Bank, NJ and post-doctorate researcher at Rutgers University between 2001 and 2002. He joined to the University of Windsor in 2002 and founded Wireless Communication and Information Processing Research Laboratory (WiCIP) in 2004. His research area focuses on wireless communication systems, wireless sensor networking, communication networks and network protocols. He is particularly interested in real-time wireless communication protocols in sensor networks, applications of sensor networking in smart grid applications, vehicular ad hoc networks for safety/emergency messaging, and vehicular internet access protocols. His research projects are sponsored by Canada Foundation for Innovation (CFI), Natural Sciences and Engineering Research Council of Canada (NSERC), Canada Federal Development Research Fund (FedDev). He is area editor for Elsevier Journal of Ad Hoc Networks.
Dr. Rachid Benlamri is a Professor at the Software Engineering Department at Lakehead University, Canada. He obtained his Master and PhD from the University of Manchester - UK in 1987 and 1990 respectively. Prof. Benlamri is the head of the Mobile Computing and Semantic Web Technologies Lab. at Lakehead University. His research interests are in the area of Semantic Web, Context-Aware Computing, Ubiquitous Computing, Mobile Knowledge Management, and Semantic Video Analysis. His research is supported by many funding institutions such as the Natural Sciences and Engineering Research Council of Canada (NSERC), Ontario Center of Excellence (OCE) and the Ontario Partnership for Innovations and Commercialization (OPIC). He supervised over 70 students and postdoctoral fellows. He served as keynote speaker for many international conferences. Prof. Benlamri is an Associate Editor for the International Journal of Ubiquitous Learning, and member of the editorial board of many other journals such as the International Journal of Learning Technologies, the International Journal of Mobile Communications, the International Journal of Emerging Technologies in Web Intelligence, the International Journal of Electronic Government, and the International Journal of Multimedia and Computer Systems.
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