Proceedings of IC-BNMT2009
DUPLICATE-AWARE OPPORTUNISTIC ROUTING FOR MULTI-HOP WIRELESS NETWORKS Deng Qiang1, Chen Shanzhi2, Xie Dongliang1, Hu Bo1 1
State Key Lab of Switching and Networking Technology, Beijing University of Posts and Telecommunications, Beijing 2 State Key Lab of Wireless Mobile Communication, China Academy of Telecommunications Technology
[email protected],
[email protected],
[email protected],
[email protected]
Abstract Recently, opportunistic routing has been proposed to take good advantage of broadcast nature and spatial diversity to achieve high throughput, despite highly unpredictable and lossy wireless links in multi-hop wireless networks. Most previous works provide heuristic solutions to select as many candidates, and don’t take inter-candidate delivery probability into account, which might suffer acknowledgement loss and lead to duplicate forwarding, ultimately degrades network throughput. In this paper, a discrete-time Markov model is firstly presented to analyze duplicate forwarding probability at the candidates, and then simple candidates optimization algorithm and acknowledgement enhancement mechanism are proposed to eliminate the effect of duplicate forwarding. Simulations are conducted to verify our algorithm, and results show that there is a 20% gain in throughput when compared with traditional opportunistic routing protocol. Keywords: forwarding; networks
opportunistic routing; throughput; multi-hop
duplicate wireless
1 Introduction Lossy and unpredictable wireless links present a great challenge to routing protocol design in multihop wireless networks. Traditional routing protocols in wireless networks have focused on finding the best path for forwarding packets between source and destination node. While such best path is suitable for wired networks, it is not ideal for wireless networks with time varying channel qualities. On the other hand, each packet is broadcast and reception is probabilistic in wireless networks, thus overhearing the packets transmission should not be considered as interference and the broadcast nature of wireless links should be fully explored. To address above problems, opportunistic routing has been proposed as a new routing paradigm to achieve high throughput. In stead of specifying the specific next ___________________________________ 978-1-4244-4591-2/09/$25.00 ©2009 IEEE
hop forwarding node, a set of next hop forwarding candidate nodes are selected in advance, upon the receiving of the packet, the “closest” to destination that successfully received the packet becomes the actual next hop forwarding node. In this way, the number of transmissions needed for a packet is reduced, and the throughput is effectively improved. Multiple candidates unaware of others’ transmissions, however, might lead to duplicate forwarding and more overall number of transmissions to degrade network throughput, so one key issue in the design of opportunistic routing protocols is how to avoid duplicate forwarding, achieve spatial reuse. Most existing opportunistic routing protocols propose candidates selection and prioritization based on some heuristics. ExOR proposed in [1] tries to select as many candidates as possible, although it employs a batch mechanism to eliminate duplicate forwarding, it is just suitable to single-flow bulk transfer. [2] utilizes a heuristic algorithm to involve the nodes near the shortest path as candidates. MORE in [3] combines opportunistic routing and network coding to avoid transmission duplication. [4] proposes a new metric EAX to account for duplicate forwarding, but it is only appropriate for the size of candidate set is less than four. Although the proposed heuristic solutions and auxiliary technologies do make some effort on duplicate forwarding, they don’t search for the reason behind it and can’t solve the problem radically. The possibilities of duplicate forwarding at the candidates need to be further investigated, and more efficient mechanisms need to be explored. In this paper, we carefully study how intercandidate delivery probability has a significant effect on duplicate forwarding, further on throughput of wireless networks. More specifically, the acknowledgement mechanism in opportunistic routing is modeled into a discrete-time Markov model, duplicate forwarding probability at each candidate is estimated using this model. Through filtering those candidates which have high duplicate forwarding probabilities out of the candidate sets,
we propose a candidates optimization algorithm to eliminate duplicate forwarding. Furthermore, to improve the reception probability of acknowledgement, an enhancement mechanism is presented. Compared to traditional opportunistic routing, we employ fewer candidates to achieve higher network throughput. The remainder of this paper is organized as follows. In Section II, we introduce a discrete-time Markov model to analyze the duplicate forwarding probability at the candidates. In Section III, we develop simple distributed algorithms to eliminate duplicate forwarding. In Section IV, we evaluate the performance of our proposed algorithm. In Section V, we draw some conclusions.
2 The proposed model The efficacy of opportunistic routing depends on inter-candidate delivery probability to ensure that only the highest priority candidate that received the packet forwards it. To improve the acknowledgement reception probability and avoid duplicate forwarding, opportunistic routing protocol lets all the candidates relay the acknowledgement of higher priority candidate, which makes deriving the duplicate forwarding probability at the candidate not a trivial thing. This is because, theoretically, the candidate can receive the acknowledgement from any higher priority candidate. It becomes extremely difficult when a large number of candidates participate in relaying the acknowledgement. 2.1 The system model We use a discrete-time finite-state Markov chain to model acknowledgement transmissions in opportunistic routing. Consider a network composed of the source node s and its candidates set Cs {C1 ,", Cn } , in which the priority order is Cn ! " ! C1 . To derive the system state model, we first define the state vector as follows. DEFINITION 1. The system state X n is a bit vector of acknowledgement reception status for all the possible receivers (the candidates) after n transmissions with one (1) means a reception and zero (0) means a miss of the acknowledgement. The reception or loss of the acknowledgement at the candidate Ci is corresponding to the ( N i ) -th bit in the vector. X n (Ci )
1 Ci received Cn ' ACK after n transmissions ® ¯0 else
Ci (C1 ," , Cn )
(1)
To formulate the lowest priority forwarding C1 ' acknowledgement reception candidate probability, we will define the sink state of that candidate. Note that, the acknowledgement
reception probability of the other candidates can be modeled as the same way. DEFINITION 2. States with the ( N 1) -th bit set are the sink states of candidate C1 and they are compacted into one single state. The sink state is described as (0 / 1,",0 / 1,1) . Now we derive a 2n1 1 state discrete-time Markov model, in which the initial state vector is X 0 S0 (0,",0) and the sink state vector is X n S2n1 (0 / 1,",0 / 1,1) . Intuitively speaking, the initial state vector represents that Cn is attempting to acknowledge its reception, and the sink state vector corresponds to the candidate C1 ' reception of the acknowledgement. Every state transition is a relay of the acknowledgement. The goal of our model is to formulate the acknowledgement reception probability after n transmissions. Fig. 1 gives the system state transition diagram described above.
Figure 1. System state transition diagram. To deduce the system state transition probability, we prove the following related theorems first. THEOREM 1. The transition probability matrix is a higher triangular matrix with several zero elements appearing above the main diagonal. PROOF. According to the definitions on the initial state and the sink state, and the procedure of acknowledgement transmissions, a state transition is impossible between Si and S j if i t j , so the transition probability matrix is a higher triangular matrix; on the other hand, once received the acknowledgement, the candidate will always keep it, that means, once a bit in the state vector is set 1, the bit will always hold it after that. Therefore, some transitions between Si and S j (i d j ) is not reachable. THEOREM 2. The number of transitions relies on the number of candidates, i.e., if the source node has n candidates, n transitions are needed at most. PROOF. Considering that even if the candidate C1 has not received the acknowledgement directly form the highest priority candidate, it may receive it form other higher priority candidates in the following acknowledgement transmissions. In the worst case, the acknowledgement is only received by the candidate whose priority is just lower than itself, such that n transitions are needed until the candidate C1 receives the acknowledgement.
We define the state transition probability matrix as P {Pi , j } , in which Pi , j indicates the transition probability from state Si to state S j (0 d i d j d 2n 1 ) . 2.2 Duplicate forwarding probability analysis In this section, we will formulate the expression of the state transition probability Pi , j and conclude the duplicate forwarding probability at the candidate C1 . Assume that the delivery probability between candidate i and candidate j is pij , we discuss the transition probability in three cases according to different conditions.
Among which, i(bit 1) and i(bit 0) indicate the candidate corresponding to the bit that is 1 and 0 respectively. Specifically, the transition probability of the sink state S2n1 is P2n1 ,2n1 1 . Having derived the expressions of transition probability, we now use them to analyze the duplicate forwarding probability at the candidate C1 . At the beginning of the acknowledgement process, no candidate receives the acknowledgement, so the state vector X 0 S0 , and the initial state probability matrix is
1) The state transition probability P0,i from state S0
Pr (0)
n 1
to state Si (0 i d 2 ) . All the bits in state vector S0 are 0, which indicates that there is no candidate receives the acknowledgement; on the other hand, there must be some bits set by 1 in the state vector Si (0 d i d 2n 1 ) , which means the candidate corresponding to this bit has received the acknowledgement. Therefore, the state transition probability can be formulated as P0,i
pi ( bit
1) n
(1 pi ( bit
0) n
) (0 i d 2n 1 )
Si (0 i d 2n 1 ) to state S j (0 j d 2n 1 ) .
As the state transition probability matrix is a higher triangular matrix, we will only discuss the cases in which i j . There must be some bits set by 1 in the state vector Si and S j , and the state transition just happens between the candidates both have 1 at the same bit as well as 0 in the state vector Si and 1 in the vector S j . Therefore, the state transition probability can be formulated as ¦ pi (bit 1)[ j (bit 1)|i (bit 0)] (1 pi (bit 1)[ j (bit 0)|i (bit 0)] ) (1 d i j d 2n 1 ) Among which, i(bit 1) indicates the candidate Pi , j
(3)
corresponding to the bit that is 1, j (bit 1) | i (bit 0) indicates the candidate corresponding to the bit that is 0 in Si and 1 in S j , and j (bit 0) | i(bit 0) indicates the candidate corresponding to the bit that is 0 in both Si and S j . 3)
The
state
transition
probability
Pi ,i
of
n 1
state Si (1 d i d 2 ) . This case means that the acknowledgement is not received by the candidate corresponding to the bit that is 0 in Si . Therefore, the state transition probability can be formulated as Pi ,i
(1 pi ( bit
1) i ( bit 0)
) (0 d i d 2n 1 )
(4)
T
ª1 º «0 » « » « #» « » ¬0 ¼
T
(5)
After the n transitions of the acknowledgement, the state probability matrix is
Pr ( n )
(2)
Among which, i(bit 1) indicates the candidate corresponding to the bit that is 1, i(bit 0) indicates the candidate corresponding to the bit that is 0. 2) The state transition probability Pi , j from state
ª Pr( X 0 S0 ) º « Pr( X S1 ) »» 0 « « » # « » «¬ Pr( X 0 S2n1 ) »¼
ª Pr( X n S0 ) º « Pr( X S1 ) »» n « « » # « » X S Pr( ) n 2n1 » ¬« ¼
T
Pr (0) P ( n )
(6)
From the above formulation, we can derive the acknowledgement reception probability is Prrec
Pr(C1 received ACK )
Pr( X n
S2n1 )
(7)
And immediately we get the duplicate forwarding probability at the candidate C1 is 1 Prrec
(8) The duplicate forwarding probability Prd plays an important role in the throughput of the network. The larger the Prd is, the more unnecessary transmissions are needed, and the lower the throughput is. Prd
3 Distributed implementation Increasing the number of candidates can’t radically eliminate duplicate forwarding, in this section, we will propose a candidate optimization algorithm based on the duplicate forwarding probability we have discussed in the previous section. In addition, to increase the acknowledgement reception probability at candidates, we also propose an acknowledgement enhancement mechanism. 3.1 Forwarding Algorithm
Candidates
Optimization
At the beginning of the proposed algorithm, we still use the ETX[5] as a metric to determine the original candidates and their priorities. For each candidate, we use the model presented to analyze the duplicate forwarding probability at each candidate, if the calculated probability is larger than some threshold, the candidate will be filtered out. In this way, the
candidates we get are approximately optimized. The whole algorithm can be divided into three stages: selecting the initial candidates, calculating the duplicate forwarding probability, and filtering the candidates. The algorithm detail is described as follows.
Put all s ' Neighbors into Set N ( s) ; For all N i N ( s ) do If ETX ( N i ) ETX ( s ) , then Put N i into C ( s ) ; For all Ci C ( s) do Ci Compute Prd ; For each Prd do If Prd ! threshold , then Remove Ci from C ( s ) ; Else Put Ci into F ( s) ; End Compared to the traditional opportunistic routing, the proposed algorithm effectively eliminates duplicate forwarding through filtering out the potential harmful candidates. The complexity of the algorithm is O(n 2 ) in case of n candidates, and there is no additional communication overhead. The efficacy of the algorithm will be verified in the next section. 3.2 Acknowledgement Mechanism
Enhancement
Besides optimizing the candidates, another way to decrease duplicate forwarding is to increase the reception probability for each packet forwarding. In this section, we propose an acknowledgement enhancement mechanism like a robust acknowledgement to avoid the unnecessary duplicate forwarding. By increasing the number of acknowledgement in the data packet, the reception probability significantly raise up. Assume the reception probability of data packet is D , if there are m acknowledgements in the data packet, the reception probability becomes 1 (1 D ) m , it is clear that if the value of m is large enough, the probability is close to 1.
4.1 Evaluation Environment We develop a trace-based module to replace the theoretical wireless propagation and error models in ns-2[6]. The trace-based module is initialized with link-level trace data from real wireless networks MIT Roofnet[7]. Roofnet is a multi-hop wireless networks with 38 nodes. The measurement trace records packet delivery over each link of the network for totally 90 seconds with transmitting 1 Mbit/s. We use the average delivery ratio over 90 seconds for a link as its link-level delivery probability, and compute the ETX using that value. Our algorithm is implemented in an ns-2 version (v2.29) incorporated with our trace-based module. The detailed simulation parameters are described as Table 1. Table 1 Simulation Parameters Parameter Value Node Number (N) 38 Bandwidth (B) 1Mbps Packet Size (Z) 1500 Node Pairs 100 Delivery Probability (P) Roofnet link-level Measurement EACK Size 1, 10, 20 4.2 Evaluation results In this section we present the results conducted on our simulation setting. Specifically, we investigate the throughput improvement the proposed algorithm can achieve over traditional opportunistic routing, the number of candidates used by the proposed algorithm, and how acknowledgement size affects the throughput performance. We randomly choose 100 pairs of nodes from the network, for each pair, we use the proposed algorithm and traditional algorithm to select candidates respectively, and compute the throughput. For simplicity, we use OR and OOR (optimized OR) to indicate the traditional opportunistic routing and optimized opportunistic routing.
In the proposed mechanism, m is determined by the actual link condition of the network. We can use a larger m if the condition is worse. As the acknowledgement is relatively small, there is no much more overhead than the original data packet.
4 Evaluation This section we will validate the efficiency of our candidates optimization algorithm and acknowledgement enhancement mechanism using simulation.
Figure 2. CDFs of throughput achieved by OR vs. OOR between 100 node pairs
Figure 3. Difference in candidates selection in OR and OOR Fig. 3 compares the throughput CDFs of OR and OOR. In this figure each plot presents the results of 100 simulation runs with transmitting rate of 1 Mbit/s. It can be seen that OOR performs better than OR and the improvement is significant. The average throughput for each node pair is 16 Kbytes/sec in OR, and it achieves 20 Kbytes/sec in OOR. Our proposed algorithm achieves 20% higher throughput than traditional opportunistic routing. The reason is that, OOR filter out the potential harmful candidates using our proposed algorithm and effectively eliminates the duplicate forwarding to improve the throughput. Fig. 4 shows the distribution of candidates selected in OR and OOR respectively. In OOR, most of node pairs have small candidates set with size less than 8. Specifically, only 14% of node pairs have more than 7 candidates in OOR, while the corresponding fraction of node pairs in OR is 37%, in which 18% of node pairs have more than 10 candidates. Fewer candidates in opportunistic routing effectively mitigate node load and is favorable to multiple flows transmission in the network. Now we investigate how acknowledgement size affects throughput performance. On the one hand, the enhanced acknowledgement ensures robust delivery of acknowledgement and improves its reception; on the other hand, a larger acknowledgement size could incur higher packet delivery delay and thus degrade network throughput. To determine the proper acknowledgement size, we vary it as 10 and 20. The simulation results are presented in Fig. 5. It shows that, acknowledgement enhancement mechanism always performs better than traditional opportunistic routing, especially for the low throughput node in the network. Note that, the throughput is slightly worse along with delivery probability becoming higher. This is because that it is enough to deliver acknowledgement robustly with size 10 when the delivery probability is high, but with a size of 20, the delay in packet delivery becomes prominent and thus degrade the overall throughput performance. The simulation results ensure that in a wireless environment like Roofnet, a median acknowledgement size around 10 is favorable for opportunistic routing to achieve high throughput.
Figure 4. CDFs of OR throughput for three different acknowledgement sizes
5 Conclusions In this paper, we present a discrete-time Markov model to analyze the duplicate forwarding probability at candidate, and find out the potential candidates that may cause duplicate forwarding in the network. Through filtering out the harmful candidates, we propose a candidates optimization algorithm and acknowledgement enhancement mechanism to eliminate the effect of duplicate forwarding. Simulations show that, with fewer candidates, we achieve a 20% gain in throughput when compared with traditional opportunistic routing protocol.
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