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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. , NO. , 2011 1 Energy Efﬁcient Opportunistic Routing in Wireless Sensor Networks Xufei Mao, Member, IEEE, Shaojie Tang, Student Member, IEEE, Xiahua Xu, Student Member, IEEE, Xiang-Yang Li, Senior Member, IEEE, Huadong Ma, Member, IEEE, Abstract—Opportunistic routing [2], [3] has been shown to improve the network throughput, by allowing nodes that overhear the transmission and closer to the destination to participate in forwarding the packet, i.e., in forwarder list. The nodes in forwarder list are prioritized and the lower priority forwarder will discard the packet if the packet has been forwarded by a higher priority forwarder. One challenging problem is to select and prioritize forwarder list such that a certain network performance is optimized. In this paper, we focus on selecting and prioritizing forwarder list to minimize energy consumptions by all nodes. We study both cases where the transmission power of each node is ﬁxed or dynamically adjustable. We present an energy efﬁcient opportunistic routing strategy, denoted as EEOR. Our extensive simulations in TOSSIM show that our protocol EEOR performs better than the well-known ExOR protocol (when adapted in sensor networks) in terms of the energy consumption, the packet loss ratio, the average delivery delay. Index Terms—Sensor networks, opportunistic routing, energy. ✦ 1 I NTRODUCTION ExOR deals with this challenge by tying the MAC to the routing, imposing a strict scheduler on routers access to the Routing protocol design for wireless networks are often guided medium. The scheduler goes in rounds. Forwarders transmit in by two essential requirements: minimize energy cost or maxi- order such that only one forwarder is allowed to transmit at any mize network throughput. The traditional routing protocols in time. The other forwarders listen to the transmissions to learn wired networks choose the best sequence of nodes between the which packets were overheard by each node. In contrast to source and destination, and forward each packet through that ExOR’s highly structured scheduler, MORE [3] addresses this sequence. The majority routing protocols designed for multi- challenge with randomness. MORE randomly mixes packets hop wireless networks have typically followed this convention, before forwarding them. This ensures that routers which hear including those multi-path routing protocols. However, this the same transmission do not forward the same packet. As did not take advantages of the broadcast nature of wireless a result, MORE does not need a special scheduler; it runs communications: a node’s transmission could be heard by directly on top of 802.11. Both ExOR and MORE showed any node within its transmission range. On the other hand, that this kind of opportunistic routing strategy can improve the lossy and dynamic wireless links make it difﬁcult for the wireless network’s performance. traditional routing protocols to achieve stable performances. In wireless networks, various factors, like fading, interfer- ence, and multi-path effects, can lead to temporary heavy In this paper, we study how to select and prioritize the packet losses [11] in a pre-selected good path. In contrast, forwarding list to minimize the total energy cost of forwarding opportunistic routing, like ExOR [2] and MORE [3], allows data to the sink node in a wireless sensor network. Observe that any node that overhears the transmission to participate in previous protocols, i.e., ExOR and MORE, did not explore the forwarding the packet. The routing path is selected on the ﬂy beneﬁt of selecting the appropriate forwarding list to minimize and completely opportunistic based on the current link quality the energy cost. We will investigate this problem through situations. However, this new design paradigm introduces rigorous theoretical analysis as well as extensive simulations. several challenges. One challenge is that multiple nodes may We study two complementary cases (1) the transmission power hear a packet and unnecessarily forward the same packet. of each node is ﬁxed (known as non-adjustable transmission model) and (2) each node can adjust its transmission power for • The research of authors is partially supported by NSF CNS-0832120, NSF CNS-1035894, program for Zhejiang Provincial Key Innovative Research each transmission (known as adjustable transmission model). Team, program for Zhejiang Provincial Overseas High-Level Talents (One- Optimum algorithms to select and prioritize forwarder list in hundred Talents Program), the National Basic Research Program of China both cases are presented and analyzed. It is worth to mention (973 Program) under Grant No.2011CB302701, the National Natural Sci- ence Foundation of China under Grant No.60833009, the National Science that our analysis does not assume any special energy models. Funds for Distinguished Young Scientists under Grant No.60925010. We conducted extensive simulations in TOSSIM to study the • Mao and Ma are with Beijing Key Lab of Intelligent Telecommunications performance of proposed algorithms by comparing it with Software and Multimedia, Beijing University of Posts and Telecommu- nications, Beijing China. Tang, Xu, and Li are with Department of ExOR [2] and traditional routing protocols. It shows that the Computer Science, Illinois Institute of Technology, Chicago. Emails: energy consumption of routing using EEOR is signiﬁcantly maoxufei@bupt.edu.cn, stang7@iit.edu, xxu23@iit.edu, xli@cs.iit.edu, lower than ExOR with random forwarder list and traditional mhd@bupt.edu.cn distance vector routing protocols. Digital Object Indentifier 10.1109/TPDS.2011.70 1045-9219/11/$26.00 © 2011 IEEE IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. , NO. , 2011 2 2 N ETWORK M ODEL AND P RELIMINARY the forwarder list, which received the packet successfully, will We consider a wireless sensor network and assume that all opportunistically act as new source nodes and route the packet wireless nodes have distinctive identities, i.e., i ∈ [1, n]. In to the target node. Section 3 we ﬁrst assume that every wireless node u has In summary, the main idea of opportunistic routing are as ﬁxed transmission power W . In Section 4, we assume that follows. We let Cu (Fwd) denote the expected cost needed each node can adjust its transmission power to any value by the node u using opportunistic routing strategy to send a between 0 and W . Let w denote such adjusted transmission packet to the target node when the forwarder list chosen by u power. The multihop wireless network is then modeled by a is Fwd. For simplicity, we use Cu to denote the expected cost communication graph G = (V, E), where V is a set of n = |V | of node u if there are no confusions. Initially, the expected wireless nodes and E is a set of directed links. Each directed cost of the target node is set to be 0 and the costs of all link (u, v) has a non-negative weight, denoted by w(u, v), other nodes are set to be ∞. Using the similar mechanism which is the minimum transmission power required by node u of distance vector routing, the calculations of the expect cost to send a packet to node v successfully. It is worth to mention for each node will be carried out periodically and every node that our methods work with any weight function w(). updates its expected cost and forwarder list periodically. When Since the number of neighboring nodes of a node u may a node needs to send or relay a packet to some destination change when different transmission power is used, we deﬁne node, it will simply broadcast the packet and let some node(s) Nw (u) as the neighboring nodes of a node u when u transmits in its forwarder list (constructed according to the destination with the power w. For simplicity, when the subscript w is node) to recursively forward the data packet. In the next two not mentioned, we mean that the node is using its maximum sections, we will focus on how to compute the expect cost transmission power, i.e., N (u) = NW (u). In addition, each and choose the forwarder list for each wireless node: Section link (u, v) has an error probability, denoted by e(u, v), which 3 focuses on the ﬁxed transmission power case and Section is the probability that a transmission over link (u, v) is not 4 focuses on the case when nodes can dynamically adjust the successful, i.e., node u must consume at least w(u, v) power transmission power. to have a chance of 1 − e(u, v) to transmit a packet to node v. No transmission is possible if less power is used. 3 N ON -A DJUSTABLE P OWER M ODEL To illustrate how we can take advantage of wireless broad- We consider the case when each node uses a ﬁxed transmission cast advantage (WBA), let us consider a network example in power. One may think that the best forwarder list for a node Figure 1 (a). The error probability from the source node to u in this case is N (u). Surprisingly, this is not always true. each node vi is e and the error probability from each node vi At the end of this section, we will show an example, based to the target node is 0. Traditional routing would route all data on the Figure 1, that the best forwarder list may be a subset packets through the same node, say vi . The expected number of N (u). of transmissions will be 1−e for the intended node vi to receive 1 the packet correctly. On the other hand, by taking advantage of 3.1 Compute the expected cost WBA property, by letting every intermediate node vj to listen Now we present the main idea on calculating the expected to the transmissions, the expected number of transmissions is cost for each node and selecting the forwarder list. Consider a 1 reduced to 1−en for at least one node to receive the packet node u and its neighbors. We will compute the expected cost correctly. This difference will be more noticeable when e is of and the forwarder list of node u based on the expected cost close to 1 and n is a big number. of its neighbors whose expected cost of sending data to the given target node has already been computed. In other words, v1 v1 here we want to choose a subset of neighboring nodes N (u) v2 %, c=1 as forwarder list of node u such that the expected cost for u 50 e= source target u e=50%,c=1.5 v2 to send a packet to the target is minimized. To understand our e= method better, we introduce some deﬁnitions ﬁrst. Consider 50 %, c= 3 a ﬁxed target. Given a set of nodes S, let S ∗ denote the v3 vn increasingly sorted list of S based on the expected cost by (a) (b) each node in S to send data (via possible relay) to this given target node. Let Fwd(u) denote the forwarder list of node u. Fig. 1. (a) Wireless Broadcast Advantage. (b) Calculating To ﬁnd the expected cost at node u, we ﬁrst sort the the expected cost. forwarder list Fwd∗ (u) in increasing order by the expected cost, i.e., Fwd∗ (u) = {v1 , v2 , ..., v| Fwd(u)| }, where i < j ⇒ The advantage of WBA is more obvious in a multi-hop Cvi ≤ Cvj . Let α denote the probability that a packet sent by wireless network, especially when a source node and the node u is not received by any node in Fwd∗ (u). Clearly, destination node are far way, i.e., the packet from the source node to a target node must be routed through a multi-hop | Fwd∗ (u)| path. As proposed in ExOR [2], the source node selects α= euvi (1) a subset of its neighboring nodes as forwarder list. The i=1 forwarder list is prioritized to indicate which nodes have higher Let ρ denote the probability that a packet sent by node u is priority to forward the packet. Then one or more nodes in received by at least one node in Fwd∗ (u). Then ρ = 1 − α. IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. , NO. , 2011 3 Let Cu (Fwd∗ ) denote the expected energy that node u must h to pay an additional cost Cu (Fwd∗ ) among the forwarding c consume to send a packet to at least one node in the forwarder nodes to prevent the scenario when multiple forwarding nodes list Fwd∗ . Cu (Fwd∗ ) can be calculated as follows: h receive the packet correctly and all decide to forward the w packet. When this additional communication is not applied, Cu (Fwd∗ ) = h (2) potentially few nodes may forward the data. This happens ρ when some receiving nodes in Fwd cannot hear from each When at least one node in the forwarder list received the other directly. Figure 2 illustrates such an example. packet successfully, we need to calculate the expected cost to forward the packet sent by node u. Here we assume that v1 only one node from the forwarder list that received the packet v4 will forward the packet. Although this assumption is very source target u v optimistic, as we will explain later, in most cases it is true. The v2 expected cost that we calculate here could be slightly lower than the actual cost when multiple nodes from forwarder list v3 could forward the data packet. (a) (b) Let Cu (Fwd∗ ) denote the expected total cost for u to for- f Fig. 2. (a) An example for expected cost calculation, (b) ward (using some nodes in the forwarder list of u) the packet to Calculating the expected cost in adjustable transmission the target. Cu (Fwd∗ ) can be calculated as follows. Assume the f power model. prioritized forwarder list is Fwd∗ = {v1 , v2 , · · · , v| Fwd∗ | }. The probability that node v1 forwards the packet is 1−e(u, v1) In Fig 2, assume v1 , v4 and v2 , v3 are the only neigh- and the expected cost by v1 is Cv1 ; then node v2 will forward boring pairs among the forwarding list. If no communications the packet with probability e(u, v1 ) · (1 − e(u, v2 )) and the are used to resolve duplicates, (i.e., Cu (Fwd∗ ) = 0) then the c cost will be Cv2 . Basically, node vi forwards the packet if it forwarding cost can be calculated as receives the packet and nodes vj , 0 < j < i did not receive the packet, and in this case, the cost will be Cvj . Hence, the Cu (Fwd∗ ) = ρ−1 · ((1 − euv1 ) · Cv1 + (1 − euv2 ) · Cv2 + f expected cost can be computed as follows: euv2 · (1 − euv3 ) · Cv3 + euv1 · (1 − euv4 ) · Cv4 ) ⎛ ⎞ ∗ | Fwd | i−1 In other words, a node vi will forward the packet only if β = (1 − euv1 )Cv1 + ⎝ euvj ⎠ · (1 − euvi ) · Cvi (3) vi received the packet, and all its neighboring nodes with i=2 j=1 higher priority did not forward the packet. Thus, the cost of forwarding is computed as follows: Since β is computed under condition that a forwarder node P| Fwd∗ | “Qi−1 ” got the packet, then we have i=1 j=1,vj ∈N(vi ) euvj · (1 − euvi ) · Cvi f Cu (Fwd∗ ) = ρ β (6) Cu (Fwd∗ ) = f (4) ρ Notice that the communication cost for obtaining agreement Due to the hardness to estimate the agreement cost and con- among nodes in Fwd on which node will forward data is sidering that most strategies need to pay the communication also a factor that affects the total cost forwarding data in cost in order to guarantee the 100% data transmission success practice. Let Cu (Fwd∗ ) denote the communication cost from c ratio, we omit the communication cost for agreement when all nodes in the forwarder list in order to reach an agreement we compute the forwarding list, i.e. formula (6) will be used on which node will ﬁnally help to relay the packet, Cu (Fwd∗ ) instead. However, we do count the number of ACK messages is computed as follows: used by each node for each packet and use this data as the communication cost in our TOSSIM simulations. We admit Cu (Fwd∗ ) = Cu (Fwd∗ ) + Cu (Fwd∗ ) + Cu (Fwd∗ ) h f c (5) that this is may be not accurate enough and we will do further analysis in our future work. Equation 5 illustrated how to compute the expected cost of a sender to broadcast a packet if the current chosen forwarder list is Fwd∗ . The cost consists of three parts. The ﬁrst part 3.2 Finding the optimal forwarder list is the expected cost for the sender to successfully transmit So far we have introduced the method to calculate the expected a packet to at least one receiver in Fwd∗ . The second part cost for a given node when the forwarder list is given. Next, we is the expected cost that there is one node in the forwarder discuss how to choose the forwarder list. Consider there are k list Fwd∗ to help to relay the packet to the ﬁnal destination nodes in N (u) for which an expected cost is already assigned, node. The third part Cu (Fwd∗ ) is the communication cost to c then there are (2k − 1) choices to select the forwarder list. reach an agreement on choosing the actual relay node. This Finding the expected cost pertaining to each forwarder list is cost Cu (Fwd∗ ) is often incurred once when the network is c not practical. Here we study the properties of the forwarder list static, while the cost of sending and forwarding depends on and the expected cost and then we explain how to efﬁciently the trafﬁc ﬂows. choose the optimal forwarder list. Without Agreement to Resolve Duplication: Observe that To simplify our arguments, let us introduce a property in our previous computation, we assume that we would like known as preﬁx. A set X is called a preﬁx of an ordered set IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. , NO. , 2011 4 Y if X are the set of ﬁrst k elements of Y . So each set Y has Algorithm 2: ExpectedCostAdjustPower(u, Cu, Fwd) (|Y | + 1) preﬁxes. Now consider node u and its neighboring 1: Set Cu = ∞, Fwd = ∅ nodes N (u). Sort the nodes in N (u) based on their expected 2: Sort nodes in N (u) based on weight in increasing order. cost in increasing order, and get N ∗ (u) = {v1 , v2 , ..., v|N (u)| } 3: Let N (u) = {v1 , v2 , ..., v|N (u)| } such that |N (u)| ≥ i > j > 0 ⇒ Cvi > Cvj . First we show 4: for (i = 1; i ≤ |N (u)|; i = i + 1) do that the optimum forwarder list of node u is a preﬁx of N ∗ (u). 5: Set w = w(u, vi ) Theorem 1: [1] The optimum forwarder list of node u must 6: Run Algorithm 1, be a preﬁx of N ∗ (u). ExpectedCostFixedPower(u, Nw(u), CrCost, CFwd) We further study the properties of forwarder list by in- 7: if Cu > CrCost then troducing another two theorems. The ﬁrst theorem, Theorem 8: Set Cu = CrCost and Fwd = CFwd. 2, shows that if a node, whose expected cost is less than the expected cost of a preﬁx forwarder list, is added to the forwarder list, then the expected cost of the newly created forwarder list will decrease while it will still be greater than the e(u, vi ) and ci denote the expected cost at node vi . It is expected cost of the newly added node. The second theorem, desired to calculate the expected cost at node u. First we Theorem 3, shows that if a node, whose expected cost is add node v1 to the forwarder list. The expected cost if greater than the expected cost of a preﬁx forwarder list, is Fwd(u) = {v1 } will be w+(1−e1 )·c1 = 3. The expected 1−e 1 added to the forwarder list, then the expected cost of the newly cost at node v2 is 1.5, so based on Theorem 2 adding node created forwarder list will increase. v2 will decrease the expected cost at node u. The expected Theorem 2: [1] Consider a node u, a preﬁx forwarder list cost if Fwd(u) = {v1 , v2 } will be w+(1−e1 )·c1 +e2 (1−e2 )·c2 = 1−e1 e 1 Fwd∗ , and a node vk ∈ N (u) \ Fwd∗ . If Cvk < Cu (Fwd∗ ), 2.5. The expected at node v3 is 3, so based on Theorem then Cvk < Cu (Fwd∗ {vk }) < Cu (Fwd∗ ) 3 adding node v3 will increase the expected cost at node Theorem 2 proves that the expected cost of each node is u. The expected cost if Fwd(u) = {v1 , v2 , v3 } will be w+(1−e1 )·c1 +e1 (1−e2 )·c2 +e1 e2 (1−e3 )·c3 higher than the expected cost of every node in its forwarder 1−e1 e2 e3 , which is equal to 18 > 7 list. This property enables us to take a greedy approach in 2.5. So the optimum forwarder list is {v1 , v2 } and the expected routing, which will be discussed later. cost at node u is 2.5. This would serve as a good example Theorem 3: [1] Consider a node u, a preﬁx forwarder list that an optimum forwarder list is not necessarily N (u), as Fwd∗ , and a node vk ∈ N (u) \ Fwd∗ . If Cvk > Cu (Fwd∗ ), mentioned in the beginning of this section. then Cu (Fwd∗ {vk }) > Cu (Fwd∗ ). Having these three properties, forwarder list can be selected easily. Algorithm 1 ﬁnds the optimum forwarder list and 4 A DJUSTABLE P OWER M ODEL calculates the expected cost for a wireless node. Algorithm In this section we consider the case where a node can adjust 1 works as follows. First it calculates N ∗ (u) and then adds its power to any value w ∈ [0, W ]. Note that for a given nodes in N (u) to the forwarder list as long as the cost is forwarder list, if we decrease w to the weight of the farthest decreasing. Once the cost starts to increase, it terminates. h link in Fwd(u) then Cu (see Equation 2) may decrease while Based on Theorem 2, before we add a node to the forwarder f Cu (see Equation 4) will remain the same, so using adjustable list we know this operation will increase or decrease the cost. transmission ranges will give us some marginal improvement. Note that based on the theorems we proved above, it is obvious As another example consider Figure 2. Assume node u has an that Algorithm 1 ﬁnds the optimum forwarder list. expected cost of Cu when the transmission power w is used, where W > w(u, v) > w. As can be seen in Figure 2, if node Algorithm 1: ExpectedCostFixedPower(u, N (u), Cu, Fwd) u consumes power w, node v will not receive packets sent by Input: the expected cost of all its neighboring nodes node u. Should we increase the transmission power of node Output: the cost Cu and forwarder list Fwd. u to include node v in its transmission range? If Cv > Cu , based on Theorem 3, adding node v will increase the expected 1: Set Cu = ∞, Fwd = ∅. cost of node u even if no more additional power is needed. 2: Sort the neighboring nodes N ∗ (u) = {v1 , v2 , ..., v|N (u)| } But if Cv < Cu , there is a tradeoff. On the one hand, adding based on its expected cost in increasing order. h node v increases the power Cu that node u must consume; 3: for (i = 1; i ≤ |N (u)|; i = i + 1) do f on the other hand, decreases Cu may or may not decrease the 4: if (Cu > Cvi ) then expected cost at node u. 5: Set Fwd = Fwd vi and compute Cu = Cu (Fwd) To ﬁnd the expected cost in adjustable transmission power based on Equation (5). model, we sort the nodes in N (u) based on the weight of the link that connects that node to u. Then we keep increasing Now we are ready to verify our claim that a node may not the power at node u such that the number of nodes in Nw (u) choose all its neighbors into the forwarder list as the optimum increases by one at each step until u reaches its transmission forwarder list at the beginning of this section. Consider a power limit or there is no more neighbor. Then for each w network example illustrated by Figure 1 (b). Assume node and each Nw (u), using the Algorithm 1, we calculate the u consumes one unit of energy (i.e. w = 1) to send a expected cost and pick the one that induces the minimum cost. packet and N1 (u) = {v1 , v2 , v3 }. For simplicity let ei denote Algorithm 2 summarizes our approach. IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. , NO. , 2011 5 Next, we present our method (Algorithm 3) that builds the Algorithm 4: Distributed Computing of Forwarder List forwarder list for each node in the graph. We will calculate the and Expected Cost by Opportunistic Routing expected cost for each node u to send a packet to the target Input: target node t, source node s, power w(u, v) and node t. Let Cu,t denote this expected cost and assume that the link reliability for each link uv. cost for a node to send a packet to itself is zero (i.e., Ct,t = 0). Output: the expected cost Cu,t from node u to node t Given a set V of nodes, a source node s, and a target node using opportunistic routing and the forwarder list of each t, Algorithm 3 computes the expected energy cost needed to node u. relay a packet from any node to the target node t using our 1: ∀u ∈ V , set Cu,t = ∞. Let Ct,t = 0. opportunistic routing strategy. 2: ∀u ∈ N (t) run Algorithm 1 or 2 to compute Cu,t ⇐ Cu . Algorithm 3 works as follows. First, the set of nodes V is 3: repeat divided into two sets S1 and S2 . Initially set S1 = V − {t} 4: For each u, run Algorithm 1 or 2 to compute Cu,t and and S2 = {t}. Then we ﬁnd the node u in S1 that has the update its forwarder list, depending on the power least expected cost (denoted as Cu,t ). We remove that node model. from S1 and add it to Set S2 . The algorithm continues till all 5: Node u sends the new cost Cu,t to all its neighboring node are in the set S2 . nodes. Let Expected Cost Graph denote the directed subgraph that 6: until no node updated the forwarder list and cost Cu,t . includes a directed edge uv from the original communication graph if v is in the forwarder list of u. We have the following Theorem 4: [1] Expected Cost Graph is loop free and Algorithm 3 assigns the optimum expected cost to each node. nodes in the forwarder list of a node must agree on next opera- tion, i.e., based on the priorities coming with the packet, which Algorithm 3: Expected Cost by Opportunistic Routing one(s) will ﬁnally act as the relay node(s) in order to save energy and increase the throughput. Since agreement involves Input: target node t, source node s, power w(u, v) and communication and thus increases the overhead of the wireless link reliability for each link uv. network, we must guarantee the increased overhead will not Output: the expected cost Cu,t from node u to node t overwhelm the performance gain brought by EEOR. Secondly, using opportunistic routing and the forwarder list of each the EEOR protocol should be able to handle the network trafﬁc node u. efﬁciently, i.e., be able to handle with congestion, to avoid 1: ∀u ∈ V , set Cu,t = ∞. Let Ct,t = 0. bottleneck in order to decrease packet loss ratio and save the 2: ∀u ∈ N (t) run Algorithm 1 or 2 to compute Cu,t ⇐ Cu . energy cost at the same time. To solve this issue, we need to 3: repeat consider many aspects. For example, the ongoing trafﬁc ﬂows 4: Let v be the node in S1 that has the minimum cost. from all source nodes should not exceed the capacity bound 5: Let S1 = S1 − {v} and S2 = S2 ∪ {v}. of the wireless networks. In other words, all source nodes 6: For each u ∈ N (v) ∩ S1 , run Algorithm 1 or 2 to should be able to dynamically adjust their network ﬂows such compute Cu,t , depending on the power model. that the ongoing ﬂows in the wireless network are stable, e.g., 7: until no node updated the forwarder list and cost Cu,t . push more ﬂow to the network if the network does not reach its capacity; Otherwise, decrease its ﬂow. Thirdly, a single Observe that the unmarked node u with the minimum cost packet could arrive at the destination through multiple pathes, among all unmarked nodes can be found using a distributed thus involves more wireless nodes, consumes more energy approach. However, the cost may be prohibitive. We thus and increases the trafﬁc burden of wireless networks. Thus, design a method (Algorithm 4) that is similar to the Bellman- it is necessary to introduce certain penalty scheme in order to Ford algorithm, a distributed computing method of the shortest punish those selﬁsh nodes, e.g., some node chooses too many path. The basic idea of Algorithm 4 is to let each node nodes as potential forwarders. This is because when a wireless continuously update its expected cost to the target node t. node ﬁnds that the packets from its neighbor contain too many When the network does not change, the expected cost Cu,t nodes in the forwarder list, it could increase its expected cost to will not be reduced. The algorithm terminates when no node quit the forwarder list next time or drop this packet. Fourthly, can reduce its expected cost Cu,t . It is easy to show that a node can utilize overheard messages to reduce the needs of Algorithm 4 can terminate in constant rounds and ﬁnd the ACK messages. Actually, to utilize these snooped information correct optimum forwarder list and the cost Cu,t . to avoid duplication is one important strategy in our design and simulation results indicate that this strategy can improve the system performance. 5 P ERFORMANCE S TUDY IN WSN S We implemented our protocol EEOR on TOSSIM, TinyOS In this section, we present the design details of our Energy 2.0.2. on Ubuntu 7.0.4. and conducted extensive tests based on Efﬁcient Opportunistic Routing (EEOR) protocol in TinyOS- different network environment. We compared our simulation based wireless sensor network (WSN) simulation environment. results with ExOR [2] for unicast case in terms of energy In our simulation, we consider the case where there are consumption, packet loss ratio, end-to-end delay and packet multiple source/destination pair nodes in a randomly deployed duplication ratio. The experimental results showed that the WSN. Our design faces several key challenges. Firstly, all performance of our protocol is better than ExOR’s. IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. , NO. , 2011 6 5.1 Network Description EEOR, AdjustablePower-EEOR and ExOR when we let the We randomly place 100 wireless nodes with transmission data size of each source node change from 200 to 500. As range 50 feet in a 300 × 300 f eet2 square region. A node we can see, the total energy consumption for each protocol is uses default CSMA MAC protocol in TinyOS. increased with the data size of each source node. And for each From 100 wireless nodes we randomly pick 18 pairs case, the performance of our protocols is better than ExOR’s. of wireless node as source/destination pairs and for each To compare the packet loss rate, we set the data size of each source/destination pair nodes u and v, u will generate a source node equal to 500 and compared 18 source/destination new packet per second, which is heading for v by one- or pairs one by one for both protocols. The comparison results multi-hop. Notice that the frequency of generating new packet are shown in Fig. 7. could change when the source node ﬁnd congestion in the As we can see, the average packet loss rate of each pair network. We call the number of sending packets as data size. increases as the hop count increases between a source and a Considering the limited storage capacity of wireless sensor destination node. For pairs with same hop numbers, the packet nodes, we set the buffer size to 20. After the buffer of a node loss rate ﬂuctuates due to the different unreliability of links is full, it will either drop new packet or replace old packet and real-time trafﬁc situation. In addition, in most cases, the with new one according to different priorities of packets. packet loss rate is less than ExOR’s. The next comparison property is the end-to-end delay. We still let each source node send up to 500 packets towards 5.2 Performance Evaluations its destination at the same time. We measure both average We compared our protocol with ExOR with respect to the and max end-to-end delay time for each source/destination total energy consumption, packet loss rate, end-to-end delay pair. Here, the deﬁnition of end-to-end delay of a packet is and packet duplication ratio. We implement ExOR following the time duration from a source node sent a packet to a the descriptions in [2]. To compare two protocols fairly, we destination received this packet. The average delay of each use same max forwarder list size for both protocols and we pair is illustrated in Fig.8 and the maximum delay for each let the each batch contain one packet in ExOR. pair is described in Fig. 9. Due to different operations have different energy consump- As we can see, the end-to-end delay of EEOR is smaller tion parameters, we ﬁrst considered and compared several than EXOR’s. This is mainly because in ExOR, a wireless operations of nodes which dominates the energy consumption, node u sorts the neighbors nodes only by ETX (expected like sending and receiving. The Fig. 3 and 4 show the total transmission count) when it chooses the forwarder list for a transmission times and receiving times (including receiving, packet. However, the computation of ETX is not real time, snooping intercepting) of all wireless nodes for both EEOR when a node on some deliver path changed its ETX, other and ExOR. nodes may need to update their ETX one hop by one hop As we can see from the ﬁgures, both transmission times based on the new ETX value of this node. and receiving times of ExOR are larger than EEOR’s. This is In EEOR, for a wireless node u, we considered both the due to the following reasons. First, for a node u in ExOR, it expected cost of a neighbor node v and the link error rate will always choose more neighbors (ExOR includes nodes that (which could be considered as real time) between u and v. make on average at least 10% of the total expected number The last property we compared our protocol with ExOR of transmissions [24]) into forwarder list for a packet under is the packet duplication ratio. Here the main motivation to the constraint of penalty. However, in EEOR, when a node u test the packet duplication ratio is that both our algorithm and chooses forwarder list for a packet, it will not only consider ExOR are multi-path routing protocols. In most of cases, same the expected cost of sorted neighbors, but also consider the packets will be relayed to the destination node through differ- increment cost by adding a node to the forwarder list such ent pathes, thus increases the overhead of wireless networks. that u will not add a new neighbor to the forwarder list if Even using other tricks like Clique Method or Double ACK doing so will increase the expected cost. Second, in ExOR Method, we still cannot guarantee that the packet will only protocol, a wireless node u’s expected cost only depends on arrive at the destination node at most once due to the unreliable the neighbor which has smallest ETX value. However, the links. Thus, multi-path property for unicast on the one hand expected cost of a wireless node u is determined by the current decrease the packet loss ratio and energy consumption to selected forwarder list and link error rates between u and some extend, on the other hand increase the overhead of the nodes in the forwarder list, which is more reasonable. These whole network. Fortunately, through our simulation results, the two differences between EEOR and ExOR make the average overhead increased by multi-path property is not much and forwarder list size of the former is smaller than latter’s in most the total energy consumption is decreasing as our conjecture. of cases, thus EEOR involves fewer intermediate nodes. The reason is that for both protocols, a forwarder list for each Next, we measure the total energy consumption for both engaging node constraints the area in which a packet can travel protocols based on the energy consumption parameters of in the network, and eventually these multi-pathes will converge TmoteSky sensor node. For example, the energy consumption to some nodes or at least cross with each other. The result of for one time transmission and receiving for TmoteSky sensor duplication packet ratio is shown in Fig.6. Here, the deﬁnition node is 17.4mA and 19.7mA respectively. Given a ﬁxed of repeat times is the average times that a wireless node is randomly topology, we randomly chosen 18 source/destination required to forward how many duplicated packets for each pairs, the Fig. 5 illustrates the total energy consumption for source/destination pair. IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. , NO. , 2011 7 4 5 7 x 10 x 10 x 10 9 8 1.5 30 ExOR ExOR ExOR ExOR EEOR EEOR EEOR EEOR # of Total Transmission Times 8 A−EEOR 7 A−EEOR A−EEOR A−EEOR # of Average Repeat Times Energy−Consumption (mA) # of Total Receiving Times 25 7 6 6 5 1 20 5 4 15 4 3 3 2 0.5 10 200 250 300 350 400 450 500 200 250 300 350 400 450 500 200 250 300 350 400 450 500 200 250 300 350 400 450 500 # of Packets per Source # of Packets per Source # of Packets per Source # of Packets per Source Fig. 3. Total transmis- Fig. 4. Total received Fig. 5. Energy con- Fig. 6. Duplicated sions. packets. sumption. Packets. 1 6000 12000 EEOR EEOR EEOR EXOR EXOR EXOR 5000 10000 0.8 Average End to end delay (ms) 4000 8000 End to end delay (ms) 0.6 Loss Ratio 3000 6000 0.4 2000 4000 0.2 1000 2000 0 0 0 83 84 93 96 85 86 87 88 97 81 94 89 90 91 92 95 98 82 83 84 93 96 85 86 87 88 97 81 94 89 90 91 92 95 98 82 -3 -4 -1 -1 -5 -6 -7 -8 -1 -1 -1 -9 -1 -1 -1 -1 -1 -2 -3 -4 -1 -1 -5 -6 -7 -8 -1 -1 -1 -9 -1 -1 -1 -1 -1 -2 83 84 93 96 85 86 87 88 97 81 94 89 90 91 92 95 98 82 3 6 7 4 0 1 2 5 8 3 6 7 4 0 1 2 5 8 -3 -4 -1 -1 -5 -6 -7 -8 -1 -1 -1 -9 -1 -1 -1 -1 -1 -2 |<--------1 hop-------->| |<------2 hops------>| |<---3 hops-->| |<-----------more than 3 hops---------->| |<--------1 hop-------->| |<------2 hops------>| |<---3 hops-->| |<-----------more than 3 hops---------->| 3 6 7 4 0 1 2 5 8 Source-Destination Pair Source-Destination Pair |<--------1 hop-------->| |<------2 hops------>| |<---3 hops-->| |<-----------more than 3 hops---------->| Source-Destination Pair Fig. 7. Packet loss ratio. Fig. 8. Average delay for each pair. Fig. 9. Max delay for each pair. 6 R ELATED WORK median unicast throughput is 22% higher than ExOR, and A number of energy efﬁcient routing protocols [5], [12] have the gains rise to 45% over ExOR when there is a chance been proposed recently combining with a variety techniques. of spatial reuse. In addition to EXOR, [21] propose another Most existing power aware protocols did not consider the opportunistic any-path forwarding protocol. Notice that ExOR packet losses of the wireless links. They assumed that the and MORE were designed for large ﬁle transferring in wireless wireless links are reliable and then tried to theoretically static mesh networks where energy saving is not a concern. provide performance guarantees [7], [16], [17]. Our protocol focused on minimizing the energy consumption There are some other protocols proposed recently to remedy of data forwarding in wireless sensor networks. the unreliability of the wireless channels such as using multi- Recently [19] proposed a local metric, expected packet ad- path routing [9], [10], building reliable backbone [17], [8], and vancement (EPA) for GOR to achieve efﬁcient packet forward- using energy efﬁcient reliable routing structure [4], [23]. In [4], ing. EPA for GOR is a generalization of EPA for traditional Dong and Banerjee addressed the problem of energy-efﬁcient routing. Later, [18] proposed a new method of constructing reliable wireless communication in the presence of unreliable transmission conﬂict graphs and proposed transmitter based or lossy wireless link layers in multi-hop wireless networks. conﬂict graph in contrast to link conﬂict graph. Their main focus is on single path routing. Banerjee and Misra For geographic routing, [13] proposed a novel online routing [23] explored the effect of lossy links on energy efﬁcient scheme to provide loop-free, fully stateless, energy-efﬁcient routing and solved the problem of ﬁnding the minimum energy sensor-to-sink routing at a low communication overhead with- paths in the hop-by-hop retransmission model. out the help of prior neighborhood knowledge. [20] studied However, they all followed a conventional design principle contention-based geo-routing with guaranteed delivery and in network layer of wired networks: after the best path(s) minimal communication overhead. [15] discussed the case of between a source and destination is calculated, all data ﬂows adjustable transmission radii for geo-routing. from source and destination follow the selected path(s) until the path is updated after certain routing update period. ExOR [2] challenges this conventional design principle in network 7 C ONCLUSION layer. MORE [3] presents a MAC-independent opportunistic Several interesting and challenging problems are left unsolved routing protocol. MORE randomly mixes packets before for- here. An interesting question is to design efﬁcient protocols for warding them. MORE needs no special scheduler to coordinate selecting optimum forwarder list for multicast and broadcast. routers and can run directly on top of 802.11. Experimental A challenge is to compute the expected cost accurately when results from a 20-node wireless testbed show that MORE’s we need to consider the additional overhead by sensor nodes IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. , NO. , 2011 8 for agreeing a unique node in the forwarder list to forward Dr. Xufei Mao is an Assistant Professor in Com- the data when multiple nodes could have potentially received puter Science Department, Beijing University of Posts and Telecommunications. He’s also a re- the data correctly. It is interesting to design protocols using searcher of Beijing Key Laboratory of Intelligent opportunistic routing that deliver the data most reliably, or Telecommunications Software and Multimedia. deliver the data with the minimum delay. He hold PhD(2010) degree at Computer Science from Illinois Institute of Technology. He received MS(2003) and Bachelor degree(1999) at North- R EFERENCES eastern University and Shenyang University of Technology respectively. His research interests [1] X.-F. Mao, X.-Y. Li, W.-Z. Song, P. Xu and K. Moaveni-Nejad Energy include design and analysis of algorithms con- Efﬁcient Opportunistic Routing in Wireless Networks In ACM MSWIM’ cerning wireless networks, network security, Internet of Things etc. 09 Topics include Coverage problems in sensor network, Routing, Top-k [2] Sanjit Biswas and Robert Morris. Exor: opportunistic multi-hop routing Query, Capacity (Throughput) study, Diagnosis of WSN and so on. for wireless networks. In SIGCOMM, pages 133–144, 2005. [3] S. Chachulski, M. Jennings, S. Katti, and D. Katabi. Trading structure Shaojie Tang is a Computer Science PhD stu- for randomness in wireless opportunistic routing. In ACM SIGCOMM, dent at Illinois Institute of Technology. He re- 2007. ceived B.S. at Radio Engineering, Southeast [4] Qunfeng Dong, Suman Banerjee, Micah Adler, and Archan Misra. University, P.R.China, 2006. His research ﬁeld Minimum energy reliable paths using unreliable wireless links. In ACM is on algorithm design, optimization, security MobiHoc, 449–459, 2005. of wireless networks, electronic commerce as [5] Robin Kravets and P. Krishnan. Power management techniques for well as online social network. He is a student mobile communication. In ACM MobiCom, 1998. member of IEEE. [6] Johnson Kuruvila, Amiya Nayak, Ivan Stojmenovic. Hop count optimal position-based packet routing algorithms for ad hoc wireless networks with a realistic physical layer. IEEE JSAC, Vol. 23, No. 6, June 2005, 1267-1275. Xiaohua Xu received the BS degree from [7] Xiang-Yang Li, Wen-Zhan Song, and Weizhao Wang. A uniﬁed energy- ChuKochen Honors College at Zhejiang Univer- efﬁcient topology for unicast and broadcast. In MobiCom, 1–15, 2005. sity, P.R. China, in 2007. He is currently working [8] Manki Min, Feng Wang, Ding-Zhu Du, and Panos M. Pardalos. A toward the PhD degree in Computer Science reliable virtual backbone scheme in mobile ad-hoc networks. In IEEE at Illinois Institute of Technology. His research MASS, 2004. interests and experience span a wide range [9] A. Nasipuri, R. Castaneda, and S. R. Das. Performance of multipath of topics from theoretical analysis to practical routing for on-demand protocols in ad hoc networks. ACM/Kluwer design in wireless networks. He is a student Mobile Networks and Applications (MONET), 6(4):339–349, 2001. member of the IEEE. [10] J. Raju and J. Garcia-Luna-Aceves. A new approach to on-demand loop-free multipath routing. In ICCCN, pages 522–527, 1999. [11] T.S. Rappaport. Wireless Communications: Principles and Practices. Dr. Xiang-Yang Li (M’99, SM’08) has been an Prentice Hall, 1996. Associate Professor since 2006 and Assistant [12] Volkan Rodoplu and Teresa H. Meng. Minimum energy mobile wireless Professor of Computer Science at the Illinois networks. In IEEE ICC, volume 3, 1998. Institute of Technology from 2000 to 2006. He [13] Stephan Ruehrup, Ivan Stojmenovic. Contention-based georouting with hold MS (2000) and PhD (2001) degree at Com- guaranteed delivery and minimal communication overhead in wireless puter Science from UIUC. He received B.Eng. ad hoc and sensor networks. IEEE IPDPS, 2010 at Computer Science and Bachelor degree at [14] Anand Srinivas and Eytan Modiano. Minimum energy disjoint path Business Management from Tsinghua Univer- routing in wireless ad-hoc networks. In MobiCom, pages 122–133. 2003. sity, P.R. China in 1995. His research interests [15] I. Stojmenovic, A. Nayak, J. Kuruvila, F. Ovalle-Martinez, E. span wireless sensor networks, computational Villanueva-Pena. Physical layer impact on the design and performance geometry, and algorithms, and has published of routing and broadcasting protocols in ad hoc and sensor networks. over 200 papers and 4 books on these ﬁelds. He is an editor of IEEE Computer Communications, Vol. 28, Issue 10, June 2005, 1138-1151. TPDS, Networks: An International Journal, and was a guest editor [16] P.-J. Wan, G. Calinescu, X.-Y. Li, and O. Frieder. Minimum-energy of several journals, such as ACM MONET, IEEE JSAC. In 2008, he broadcast routing in static ad hoc wireless networks. ACM Wireless published a monograph “Wireless Ad Hoc and Sensor Networks: Theory Networks, 2002. and Applications”. He is a senior member of the IEEE and a member of [17] Y. Wang, W.-Z. Wang, and X.-Y. Li, Distributed low-cost backbone ACM. formation for wireless ad hoc networks. In ACM MobiHoc, 2005. [18] K. Zeng, W. Lou, and H, Zhai. On End-to-end Throughput of Oppor- Dr. Huadong Ma (M’99) received the B.S. de- tunistic Routing in Multirate and Multihop Wireless Networks. In IEEE gree in Mathematics from Henan Normal Uni- InfoCom 2008 versity in 1984, the M.S. degree in Computer [19] K. Zeng, W. Lou, J. Yang, D. III. On geographic collaborative Science from Shenyang Institute of Computing forwarding in wireless ad hoc and sensor networks. In WASA 2007 Technology, Chinese Academy of Science in [20] H. Zhang, H. Shen, Energy-Efﬁcient Beaconless Geographic Routing in 1990 and the Ph.D. degree in Computer Sci- Wireless Sensor Networks IEEE TPDS, June 2010 pp. 881-896. ence from Institute of Computing Technology, [21] Z. Zhong, J. Wang, and S. Nelakuditi. Opportunistic any-path forwarding Chinese Academy of Science in 1995. He is in multi-hop wireless mesh networks. In USC-CSE, Technical Report currently a Professor and Director of Beijing Key TR-2006-015 Lab of Intelligent Telecommunications Software [22] H. Dubois-Ferriere, D. Estrin and M. Vetterli. Packet Combining in and Multimedia, Dean of School of Computer Sensor Networks In ACM SenSys, 2005. Science, Beijing University of Posts and Telecommunications, China. [23] S. Banerjee and A. Misra. Minimum energy paths for reliable commu- He visited UNU/IIST as research fellow in 1998 and 1999. From 1999 nication in multi-hop wireless networks. In ACM MobiHoc 2002. to 2000, he held a visiting position in the Department of EECS, The [24] D. De Couto, D. Aguayo, J. Bicket, and R. Morris. A high-throughput University of Michigan. He was a visiting Professor at The University of path metric for multi-hop wireless routing. In ACM MobiCom, 2003. Texas at Arlington from July to September 2004, and a visiting Professor at HKUST from Dec. 2006 to Feb. 2007. His current research focuses on multimedia system and networking, Internet of things and sensor networks, and he has published over 100 papers and 4 books on these ﬁelds. He is member of IEEE and ACM.

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