Optimal Energy Efficient Routing in Wireless Sensor Networks with Link Asymmetry Sibel T. Ozyer(Corresponding author) 1,* ,Bulent Tavli 2 , and Murat Koyuncu 3 1 Cankaya University, Department of Computer Engineering, Ankara, Turkey 2 TOBB University, Department of Electrical & Electronics Engineering, Ankara, Turkey 3 Atilim University, Department of Information Systems Engineering, Ankara, Turkey * Corresponding author (E-mail : tariyan@cankaya.edu.tr) Abstract—In Wireless Sensor Networks (WSNs), link uni- directionality is an unavoidable phenomenon. The existence of unidirectional links can be attributed to several physical factors induced by the transceiver characteristics as well as other environmental phenomena. Transmission power heterogeneity is the dominant paradigm that leads to unidirectionality. In this study, we investigate the effects of transmission power heterogeneity on the lifetime of WSNs through a novel Linear Programming (LP) framework both for networks that utilize only bidirectional links and for those that can use unidirectional links in addition to bidirectional links. Our results show that transmission power heterogeneity can lead to more than 25 % decrease in network lifetime for protocols that can operate only on bidirectional links when compared to a network without any heterogeneity. However, if the use of unidirectional links is also enabled then, the decrease in network lifetime is at most 12 %. Keywords - wireless sensor networks, link asymmetry, unidi- rectional links, linear programming, energy efficiency. I. I NTRODUCTION In wireless communications electromagnetic propagation medium between a transceiver pair is, often, abstracted as a bidirectional link, which implies that both entities share a symmetric direct path for their mutual data communication op- erations. However, in many practical network deployments the assumption of link symmetry is questionable. The existence of unidirectional links can be attributed to several physical factors induced by the transceiver characteristics as well as other environmental phenomena. Hardware components of wireless radios (e.g., antenna, RF circuits) determine the maximum transmission range of the radios [1]. Unavoidable variations in individual component characteristics lead to non-homogeneous maximum transmission ranges for different nodes. Trans- mission power heterogeneity is the most 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 feasible). Since most Medium Access Control (MAC) layer protocols (e.g., IEEE 802.11 in unicast mode) 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 transmission by the receiver), any routing protocol utilizing such a MAC protocol has no other option but to use only bidirectional links in the routing operations [2]. However, if the MAC protocol is used in broadcast mode then, a node can transmit over a unidirectional link, hence, it is possible to employ a routing protocol that can use unidirectional links on top of a MAC protocol operating in broadcast mode [3]. Yet, it is highly desirable to have a MAC layer that can perform handshaking over unidirectional links in unicast flows both for performance optimization and for avoiding network partitioning (i.e., it is possible that some nodes can only be reached by unidirectional links). Indeed, there are several MAC protocols designed to perform handshaking over unidirectional links (i.e., acknowledgement packets are relayed back to the transmitter in a multi-hop fashion by using one or more relay nodes) [4]. The effects of the level of link asymmetry on the perfor- mance of wireless networks are investigated and characterized in several studies [4], [1], [5]. However, performance analysis presented in these studies are focused on Mobile Ad Hoc Networks (MANETs) and they do not include a characteri- zation of the energy overhead incurred by unidirectional links in Wireless Sensor Networks (WSNs). In WSNs, nodes share the burden of relaying data from sen- sor nodes to the base station. To avoid premature exhaustion of the any sensor nodes batteries relaying energy dissipation should be evenly shared throughout the network which can be achieved by optimally balancing the flows. Transmission power heterogeneity and induced link unidirectionality limits the options available for balancing energy dissipation when compared to a network without heterogeneity. In this study, we built a novel Linear Programming (LP) framework to model energy dissipation of data transfer in WSNs with unidirectional links. To the best of our knowledge, there is no previous study that investigates the energy cost of link asymmetry in WSNs within an LP framework. The novel contribution of this study is to analyze the impact of unidirectionality induced by transmission power heterogeneity on the lifetime of WSNs. II. MODEL In this study, our main goal is to characterize the effects of unidirectional links induced by transmission power hetero- geneity on the network lifetime. In this section we define our system model, clarify the assumptions, and formulate the optimization problem. The system model is presented in the following subsection. 978-1-4577-0058-3/12/$26.00 '2012 IEEE 185