The Impact of Link Unidirectionality and Reverse Path Length on Wireless Sensor Network Lifetime

Transcription

1 IEEE ICC Ad-hoc and Sensor Networking Symposium The Impact of Link Unidirectionality and Reverse Path Length on Wireless Sensor Network Lifetime Anil Ufuk Batmaz, Bulent Tavli Electrical & Electronics Engineering Department TOBB-ETU, Ankara, Turkey {aubatmaz,btavli}@etu.edu.tr Davut Incebacak Informatics Institute METU, Ankara, Turkey davut@ii.metu.edu.tr Kemal Bicakci Computer Engineering Department TOBB-ETU, Ankara, Turkey bicakci@etu.edu.tr Abstract The occurrence of unidirectional links in wireless sensor networks (WSNs) is an inherent feature of wireless communication. Transceiver characteristics, asymmetric interference, and many other properties of the electromagnetic propagation environment result in link unidirectionality, however, transmission power heterogeneity is the dominant factor that creates unidirectional links. Most of the data transfer mechanisms designed for wireless networks work only on bidirectional links, yet, there are some mechanisms capable of utilizing unidirectional links. Employment of a multi-hop reverse path for acknowledgement delivery is the key concept and hop length of the reverse path is an important design criterion in such mechanisms. If the maximum reverse path length is allowed to take large values then the number of usable unidirectional links increases. Increasing the number of available links leads to better energy balancing and longer network lifetime. But is it necessary to keep the reverse path length large to achieve the maximum network lifetime possible? In this study, we investigate the effects of reverse path length in WSNs with unidirectional links induced by transmission power heterogeneity on network lifetime through a novel mixed integer programming framework. Our results show that reverse path length has significant impact on WSN lifetime. Index Terms wireless sensor networks, unidirectional links, mixed integer programming, energy efficiency. I. INTRODUCTION Communication links in wireless networks are, often, assumed to be bidirectional (i.e., nodes can transmit packets to and receive packets from each other). However, the assumption of link bidirectionality does not hold in many practical network deployments. In fact, a significant portion of links in various wireless network testbeds are shown to be unidirectional [1]. Link unidirectionality can be attributed to several physical factors (e.g., transceiver characteristics, unequal interference). Transmission power heterogeneity is an important paradigm that leads to unidirectionality (i.e., a high transmission power node can reach a low transmission power node, however, communication in the reverse direction is not possible) [2]. Since most Medium Access Control (MAC) layer protocols (e.g., IEEE ) are designed to operate on bidirectional links (e.g., handshaking mechanism dictates that data transmission by a transmitter should be replied back with an acknowledgement ACK transmission by the receiver), any routing protocol utilizing such a MAC protocol can use only bidirectional links for routing [3]. However, for performance optimization reasons utilization of unidirectional links in conjunction to bidirectional links is necessary. To facilitate the use of unidirectional links many MAC protocols that have the capability to utilize unidirectional links are proposed. These protocols are designed to perform handshaking over unidirectional links (i.e., ACK packets are relayed back to the transmitter in a multi-hop fashion by using one or more relay nodes) [1]. Here, an important design problem is to determine the maximum reverse path length for unidirectional links. Note that the minimum reverse path length is two hops for any unidirectional link (i.e., there is only one relay node to forward the ACK packets from the receiver to the transmitter). On the other hand the reverse path length can be arbitrarily large. However, in practical wireless sensor network (WSN) applications, maintaining a long reverse path is not desirable. One of the most important design objectives for WSNs is lifetime optimization. To avoid premature exhaustion of any sensor node s energy dissipation should be evenly shared throughout the network which can be achieved by optimally balancing the flows. Lifetime can be maximized if both bidirectional and unidirectional links are utilized because elimination of any available link limits the options for energy balancing. However, utilization of unidirectional links are more costly than utilization of bidirectional links due to the multi-hop reverse path required for ACKs. Furthermore, the cost of unidirectional links increases as the reverse path length increases. The impact of any relevant paradigm affecting the energy dissipation characteristics of WSNs is worth investigating [4], yet, a systematic characterization of the impact of reverse path length on WSN lifetime has not been performed in the literature 1. In this study we perform an analysis on this subject by building a framework using Mixed Integer Programming (MIP). In the context of WSNs, MIP approach has been applied previously in many studies to model the unique characteristics of WSNs [5]. II. MODEL In this study, our main goal is to characterize the effects of reverse path length of unidirectional links induced by transmission power heterogeneity on WSN lifetime. In our framework, energy dissipation of sensors is dominated by communication 1 On the other hand, the impact of unidirectional links on other aspects of wireless networks such as network connectivity has been analyzed in earlier work (e.g., [1]). Due to space limitation, we cannot give a thorough overview of related work /13/$ IEEE 388

2 energy consumption rather than computation. This assumption is supported by the results of experiments in actual WSN testbeds (e.g., communication energy dissipation constitutes 91% of the total energy dissipation in Telos sensor nodes [6]). Our communication energy dissipation model is a widely accepted model introduced in [7]. In this model, the amount of energy to transmit one bit of data is E tx,ij = ρ + εd α ij and to receive one bit of data is E rx = ρ, where ρ represents the energy dissipated in the electronic circuitry, ε denotes the transmitters efficiency, α represents the path loss, and d ij is the distance between node-i (transmitting node) and node-j (receiving node). In our system model, there are N sensor nodes and a single base station. Time is organized into rounds with duration T rnd. Each sensor node-i creates the same amount of data (s i ) at each round to be conveyed to the base station (i.e., sensor nodes create CBR flows). Data generated at each node terminates at the base station either by direct transfer or through other sensors acting as relays. A directed graph G = (V, A) is used to represent the network topology. V is the set consisting of all sensor nodes and the base station (node- 1). Set W includes all the sensor nodes (i.e., W = V \ {1}). A = {(i, j) : i V, j V \ {i}} is the set of arcs (links). Note that the definition of A implies that no node sends data to itself. Total number of fixed sized data packets transmitted by node-i and received by node-j throughout the network lifetime is given by the integer variable f ij and the constant s i determines the data generated at node-i at each round in terms of number of data packets. The amount of ACK packets in reply to data flow f ji transmitted by node-k (node-i or a relay node) and received by node-l (node-j or a relay node) is represented by integer variable gij kl. The nominal maximum transmission range of nodes are denoted as R nom. Deviation from the nominal maximum transmission range leading to transmission power heterogeneity is modeled as a uniform random distribution in [ R het, R het ] range (i.e., each node-i has a maximum transmission range of R max,i = R nom + R dev,i, where R dev,i is an instance of random variable in [ R het, R het ] interval). Thus, nodei s maximum transmission range can, at most, be R max,i = R nom + R het and can, at least, be R max,i = R nom R het. This model of transmission power heterogeneity to create unidirectional links is known as the D-model [1]. Most of the studies on link unidirectionality use transmission power heterogeneity (nodes have unequal transmission ranges) to create link asymmetry [1], [2]. All system variables with their acronyms and descriptions are presented in Table I. The optimization problem is formulated as an MIP problem, presented in Figure 1. The objective is to maximize network lifetime by finding the f ij s (data flows) and gij kl s (ACK flows) that satisfy the constraints. Note that variable T gives the network lifetime in terms of number of rounds and the actual network lifetime can be expressed by the product T T rnd. Equation 1 and Equation 2 state that all flows are nonnegative. Equation 3 is used for flow balancing at the sensor nodes. The difference of incoming flows (from other sensor) TABLE I TERMINOLOGY FOR MIP FORMULATION Variable Description T Network lifetime in terms of rounds N Number of sensor nodes f ij Data flow from node-i to node-j (in terms of number of packets - integer variable) gij kl ACK flow from node-i to node-j transmitted by nodek and received by node-l (in terms of number of ACK packets - integer variable) b k ij ACK flow indicator which is unity if node-k is a relay node for ACK flow gij kl (binary variable) M A large integer L data Data packet size (bits) L ACK ACK packet size (bits) s i Amount of data generated at each round by node-i (in terms of number of packets) E rx Energy consumption for receiving one bit of data (J/bit) E tx,ij Energy consumption for transmitting one bit of data from node-i to node-j (J/bit) d ij Distance between node-i and node-j (m) ρ Energy dissipated in the electronic circuitry (J/bit) ε Transmitters efficiency (J/bit/m 2 ) α Path loss exponent e i Energy stored at each sensor node (J) ξ Battery energy (J) G = (V, A) Directed graph that represents network topology V Set of nodes, including the base station as node-1 W Set of nodes except the base station (node-1) A Set of arcs (links) T rnd Duration of one round (seconds) R nom Nominal maximum transmission range (m) R het Maximum deviation from R nom (m) R max,i Actual maximum transmission range of node-i (m) R dev,i Deviation of node-i s actual maximum transmission range from the nominal maximum transmission range (m) L RP HD Maximum value of reverse path hop distance and outgoing flows (to other sensors acting as relays or to the base station) is equal to the amount of generated data. Note that T s i gives the total amount of data packets generated at sensor node-i (s i is the number of fixed sized data packets generated at sensor node-i in each round which is a constant). Equation 4 guarantees that all data generated at the sensor nodes terminate at the base station. Equation 5 ensures that there are no outgoing flows from the base station. In many WSN applications sensor nodes acquire data periodically and captured data have a predetermined constant size [4], [7]. Equation 6 is used to model data routing on both unidirectional and bidirectional links. Flow f ij is zero if the distance between a transmitter and a receiver (d ij ) is larger than the maximum transmission range of node-i (R max,i ). Equation 7 states that the total number of ACKs received at node-i for its data transmissions to node-j is equal to the total number of data packets it sent to node-j (either directly or by relaying through other sensor nodes as relays). Note that Equation 7 is used for end-to-end data and ACK flow balancing. Equation 8 is used to equate the number of ACKs sent from node-j to its single hop neighbors destined for node-i to the number of data packets node-j receives from node-i. Equation 9 and Equation 10 prevent any ACK flows out of sender nodei and any ACK flows into destination node-j, respectively. 389

3 Equation 11 is used to balance ACK flows at relay nodes. Equation 12 is used to determine the value of binary variable b k ij (i.e., showing whether node-k is a relay for the ACK flow gij kl or not). Equation 13 is used to set the ACK flow to zero if the separation between the transmitter node-k and receiver node-l is more than the maximum range of node-k. Maximize T Subject to: l V f ij 0 (i, j) A (1) gij kl 0 (i, j) A k V l W (2) f ji + T s i = f ij i W (3) j W f j1 f 1j = T s i (4) j W j W i W f 1j = 0 (5) f ij = 0 if R max,i < d ij (i, j) A (6) f ij = f ij = g ki ji i W j V (7) g jk ji i W j V (8) g ki ij = 0 i V j V (9) g jk ij = 0 i V j V (10) gij kl gij lm = 0 i V j V m V l V \ {i, j} (11) g kl ij Mb k ij i V j V k V \ {j} (12) gij kl = 0 if R max,k < d kl i V j V \ {i} k V l V \ {k} (13) b k ij L RP HD i V j V (14) L data E tx,ij f ij + L ACK E tx,ij gij kl l V +E rx L data f ji + E rx L ACK j W Fig. 1. l V g kl ji e i i W (15) e i = ξ i W (16) MIP framework Equation 14 limits the maximum value of the reverse path hop distance (e.g., L RP HD = 1 means only bidirectional links can be used). Equation 15 states that for all nodes except the base station energy dissipation for data communication is bounded by the energy stored in batteries (e i ). Equation 16 is used to assign equal battery energy to all sensor nodes. The time when the first node runs out of energy lifetime of the network ends. This definition should be interpreted correctly. If the framework is examined carefully it can be seen that all nodes are forced to dissipate their energies in a balanced fashion to maximize the lifetime, as a result, sensor nodes in the network collaborate altogether to avoid premature death of any sensor node due to overutilization of its energy source. We also remind that MIP framework we present in this study provides the optimal results by using global network information. The design of network protocols with the objective of having performance figures close to the optimal results while requiring only local routing information is beyond our scope and left as a future work. WSNs are assumed to be consisting of stationary sensor nodes and unlike mobile networks topology changes are not frequent. Thus, topology discovery and route creation are one-time operations for substantial amount of time (rounds/epochs) these functions are not repeated [7]. If the network reorganization period is long enough then, the energy costs of these operations constitute a small fraction (less than 1%) of the total network energy dissipation [8]. Hence, routing overhead can be neglected in stationary WSNs without leading to significant underestimation of total energy dissipation. III. ANALYSIS We use General Algebraic Modeling System (GAMS) [9] for the numerical analysis of the developed MIP model. In our analysis, each sensor node generates one data packet per round (s i = 1) to be conveyed to the base station. Data and ACK packet sizes are 256 Bytes and 20 Bytes, respectively (L data = 2048 bits and L ACK = 160 bits). The communication parameters are chosen as ε = 100 pj/bit/m 2, ρ = 50 nj/bit and α = 2 same as the ones in [7]. Each node is assumed to be equipped with two AA batteries (ξ = 25.0 KJ). To illustrate the effects of limiting the maximum value of the reverse path length, graphically, we solve the optimization problem for the small scale topology (N = 5) presented in Figure 2. The optimal routes for R nom are shown in Figure 2(b). The effects of limiting the transmission range without any transmission power heterogeneity (R het = 0 m) is presented in Figure 2(c). Note that limiting the transmission ranges eliminates some optimal routes for maximal network lifetime which leads to a 2 % decrease in network lifetime (i.e., normalized network lifetimes for R nom and R nom = 125 m with R het = 0 m are 1.02 and 1.00, respectively). Network lifetimes obtained for configurations with transmission power heterogeneity (R het = 125 m) are 0.71, 0.88, and 0.90 for L RP HD = 1, L RP HD = 2, and L RP HD = 3, respectively. Network lifetimes obtained for L RP HD > 3 are the same with the network lifetime obtained 390

4 (a) R nom = R het = 125, flow=0 (dashed line), flow 0 (solid) (b) R nom, R het = 0, L RP HD = 1, LT=1.02 (c) R nom = 125, R het = 0, L RP HD = 1, LT=1.00 (d) R nom = R het = 125, L RP HD = 1, LT=0.71 (e) R nom = R het = 125, L RP HD = 2, LT=0.88 (f) R nom = R het = 125, L RP HD = 3, LT=0.90 Fig. 2. Illustration of optimal routes for maximal lifetime using the parameter sets indicated. For each relevant configuration the amount of data generated by sensor nodes are normalized to unity and the numbers on each arc shows the amount of data flow. The base station is designated as node-1. Figure 2(a) illustrates the network topology where usable links (source node transmission range is larger than the distance between the source and the destination) are shown by solid lines (R nom = R het = 125 m). Lifetimes (LT) values are normalized with the lifetime obtained in Figure 2(c) (Best viewed in colors). with L RP HD = 3. Utilization of unidirectional links allows the network to balance the energy dissipation efficiently and improves the network lifetime significantly, however, most of this improvement can be achieved by employing a single relay node in the reverse path. For example, for L RP HD = 1, node- 3 carries the burden of relaying the data of all the other senor nodes by itself which makes node-3 the bottleneck, however, for L RP HD = 2, the burden of relaying is shared by both node-3 and node-4 and premature death of node-3 is avoided. Further increase of L RP HD does not improve the network lifetime significantly For L RP HD = 3, node-2 can transmit only a small fraction (0.18) of its data directly to node-1 and most of node-2 s data (0.82) is relayed by other sensor nodes due to two factors: (i) ACK flow from node-1 to node-2 traverses three hops and creates an extra energy burden on the network and (ii) distance between node-2 and node-1 is large and direct transmission dissipates more energy than relaying. To analyze the effect of reverse path length on network lifetime for larger topologies, we used a network consisting of regularly placed sensors 2 and a base station at the center. 2 We use the best known disk packing geometries reported in [10] to form the constellation for N nodes in a 1000 m diameter disk. 391

5 (a) N = 20 MIP problem is solved for 20 randomly selected maximum transmission ranges for each node and we present the average results in the figures. Lifetime values cannot be presented for the whole range of R het because for larger values of R het /R nom we cannot get any connected topologies with L RP HD = 1 (e.g., for N = 20 and R nom = 800 m, all topologies are disconnected for R het > 400 m). As the level of transmission power heterogeneity increases, normalized network lifetime decreases for L RP HD = 1. In other words, exclusion of unidirectional links prevents the network to reach the maximal lifetime possible with inclusion of unidirectional links especially for high heterogeneity levels. The decrease in normalized network lifetime is less than 2.0 % throughout the whole parameter space (not shown in the figures) for L RP HD 2 (when unidirectional links with at least one relay node in the reverse path are allowed). IV. CONCLUSION We investigate the impact of limiting the reverse path length of unidirectional links on WSN lifetime through a novel MIP framework. Our results show that if the reverse path length is limited by one, then the lifetime can decrease more than 70 % in comparison to a network with no limit on the reverse path length. However, if the reverse path length is limited by at least two then the decrease in network lifetime is negligible (at most 2 %). We conclude that utilizing unidirectional links with only one relay node in the reverse path leads to near-optimal network lifetime values and employment of unidirectional links that necessitate reverse paths with more than one relay nodes does not provide any significant lifetime gains. Fig. 3. (b) N = 25 (c) N = 30 Normalized lifetime with L RP HD = 1 for different network sizes. Figure 3 presents the normalized 3 network lifetime with L RP HD = 1 for different values of N, R nom and R het. The 3 Normalization is achieved by dividing all network lifetime values of each configuration with the lifetime obtained with L RP HD. REFERENCES [1] V. Ramasubramanian and D. Mosse, BRA: a bidirectional routing abstraction for asymmetric mobile ad hoc networks, IEEE/ACM Transactions on Networking, vol. 16, pp , [2] G. Wang, D. Turgut, L. Boloni, Y. Ji, and D. C. Marinescu, A MAC layer protocol for wireless networks with asymmetric links, Ad Hoc Networks, vol. 6, pp , [3] B. B. Chen, S. Hao, M. Zhang, M. C. Chan, and A. L. Ananda, DEAL: discover and exploit asymmetric links in dense wireless sensor networks, in Proceedings of the IEEE Conference on Sensor, Mesh and Ad Hoc Communications and Networks (SECON), 2009, pp [4] J. Yick, B. Mukherjee, and D. Ghosal, Wireless sensor network survey, Computer Networks, vol. 52, pp , [5] F. Ishmanov, A. S. Malik, and S. M. Kim, Energy consumption balancing (ECB) issues and mechanisms in wireless sensor networks (WSNs): a comprehensive overview, European Transactions on Telecommunications, vol. 22, pp , [6] M. Rahimi, R. Baer, O. Iroezi, J. Garcia, J. Warrior, D. Estrin, and M.Srivastava, Cyclops: in situ image sensing and interpretation in wireless sensor networks, in Proceedings of the ACM Conference on Embedded Networked Sensor Systems (SenSys), 2005, pp [7] W. Heinzelman, A. Chandrakasan, and H. Balakrishnan, An application specific protocol architecture for wireless microsensor networks, IEEE Transactions on Wireless Communications, vol. 1, pp , [8] K. Bicakci, H. Gultekin, and B. Tavli, The impact of one-time energy costs on network lifetime in wireless sensor networks, IEEE Communications Letters, vol. 13, pp , [9] General Algebraic Modeling System (GAMS). [Online]. Available: [10] E. Specht. (2010) The best known packings of equal circles in the unit circle. [Online]. Available: 392