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Energy Efficient Opportunistic Routing

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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

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                                                                                                                                                                                                        94

                                                                                                                                                                                                        89

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                                                                                                                                                                                                        91

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                                                                                                                                                                                                        95

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                                                                                                                                                                                                                                                                                                                                                             96

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                                                                                                                                                                                                                                                                                                                                                             86

                                                                                                                                                                                                                                                                                                                                                             87

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                              3

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                              0

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                       |<--------1 hop-------->| |<------2 hops------>| |<---3 hops-->| |<-----------more than 3 hops---------->|                                                                     |<--------1 hop-------->| |<------2 hops------>| |<---3 hops-->| |<-----------more than 3 hops---------->|




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                                                                                                                                                                                                                                                                                                                                                                  0

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                                                                                                                                                                                                                                                                                                                                                                  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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