Opportunistic Routing in Wireless Mesh Networks

Opportunistic Routing in Wireless Mesh Networks Amir arehshoorzadeh amir@ac.upc.edu Llorenç Cerdá-Alabern llorenc@ac.upc.edu Vicent Pla vpla@dcom.upv.es August 31, 2012 Opportunistic Routing in Wireless Mesh Networks 1 / 37

Outline 1 Introduction to Opportunistic Routing (OR). 2 Research directions in OR. 3 Routing metrics in OR. 4 Coordination methods in OR. 5 Candidate selection algorithms. 6 Performance evaluation. 7 Conclusions. Opportunistic Routing in Wireless Mesh Networks 2 / 37

Introduction to Opportunistic Routing (OR). Traditional Uni-path Routing 30% 10% 90% 90% 90% S A B Node S A B Next Hop for A B Opportunistic Routing in Wireless Mesh Networks 3 / 37

Introduction to Opportunistic Routing (OR). Traditional Uni-path Routing 30% 10% 90% 90% 90% S A B Node S A B Next Hop for A B For each destination selects a single next-hop forwarder. End-to-End delivery probability: 0.9 0.9 0.9 0.72 Opportunistic Routing in Wireless Mesh Networks 3 / 37

Introduction to Opportunistic Routing (OR). Traditional Uni-path Routing 30% 10% 90% 90% 90% S A B Node S A B Next Hop for A B For each destination selects a single next-hop forwarder. End-to-End delivery probability: 0.9 0.9 0.9 0.72 Lot of retransmissions. Opportunistic Routing in Wireless Mesh Networks 3 / 37

Introduction to Opportunistic Routing (OR). Traditional Uni-path Routing 30% 10% 90% 90% 90% S A B Node S A B Next Hop for A B For each destination selects a single next-hop forwarder. End-to-End delivery probability: 0.9 0.9 0.9 0.72 Lot of retransmissions. Waste of network resources. Opportunistic Routing in Wireless Mesh Networks 3 / 37

Introduction to Opportunistic Routing (OR). What is Opportunistic Routing (OR)? For each destination selects an ordered set of nodes (Candidate Set). CandSet(S)={, B, A} 10% 30% 90% 90% 90% S A B Opportunistic Routing in Wireless Mesh Networks 4 / 37

Introduction to Opportunistic Routing (OR). What is Opportunistic Routing (OR)? For each destination selects an ordered set of nodes (Candidate Set). CandSet(S)={, B, A} The candidates that receive the packet will coordinate to determine the best one to actually forward the packet. 10% 30% 90% 90% 90% S A B Opportunistic Routing in Wireless Mesh Networks 4 / 37

Introduction to Opportunistic Routing (OR). What is Opportunistic Routing? S 20% 20% C 1 C 2 20% C 3 100% 20% 20% C 4 100% 100% 100% 100% End-to-End elivery Probability Uni-path Routing 20% C 5 Opportunistic Routing in Wireless Mesh Networks 5 / 37

Introduction to Opportunistic Routing (OR). What is Opportunistic Routing? S 20% 20% C 1 C 2 20% C 3 100% 20% 20% C 4 100% 100% 100% 100% End-to-End elivery Probability Uni-path Routing 20% OR 1 (1 20%) 5 67% C 5 OR Combines weak physical links into one stronger virtual link. Opportunistic Routing in Wireless Mesh Networks 5 / 37

Issues in Opportunistic Routing Issues in Opportunistic Routing Candidate selection in OR. OR metric. Candidate coordination in OR. Opportunistic Routing in Wireless Mesh Networks 6 / 37

Research irections in Opportunistic Routing Research irections in Opportunistic Routing Protocol Year Type Topic Metric Coord. Cand. Sel. SF 2001 S Candid. Coord ETX Ack Topology GeRaF 2003 A/S Cand. Coord Geo. RTS-CTS Location ExOR ver-1 2004 S Cand. Sel ETX Ack Topology ExOR ver-2 2005 E Cand. Coord ETX Timer Topology NA 2005 A/S Sensor networks Geo. RTS-CTS Location COPE 2005 E Network coding ETX Net. coding Topology OAPF 2006 S Cand. Sel ETX/EAX Ack Topology LCOR 2007 S Cand. Sel EAX NA Topology MORE 2007 E Network coding ETX Net. coding Topology GOR 2007 S Cand. Sel Geo. Timer Location NA 2008 A Analytical Geo. NA Location NA 2008 A/S Analytical Geo. NA Location NA 2008 E Cand. Sel ETX Ack Topology CORE 2008 S Network coding Geo. Timer Location MTS 2009 S Cand. Sel EAX Timer Topology Opportunistic Routing in Wireless Mesh Networks 7 / 37

Research irections in Opportunistic Routing Research irections in Opportunistic Routing Protocol Year Type Topic Metric Coord. Cand. Sel. POR 2009 S Cand. Sel Geo. Timer Location SOAR 2009 S/E Cand. Sel ETX Timer Topology Pacifier 2009 S Multicast ETX Net. coding Topology NA 2010 A Maximum performance EAX NA Location MSTOR 2010 S Multicast EAX/ETX Ack Topology MORP 2011 S Multicast ETX Ack Topology NA 2011 A Analytical/Cand. Sel ETX/EAX NA Topology Opportunistic Routing in Wireless Mesh Networks 8 / 37

Routing metrics in OR. Usual routing metric in OR Hop Count geographic-distance (Geo-istance) Expected Transmission Count ETX [ouglas 2003]: The average number of transmissions required to reliably send a packet across a link or route including retransmissions. p ij is the delivery probability between nodes i and j then ETX= 1 p ij Using the ETX does not give an accurate metric for OR. Expected Any-path Transmission EAX: [Zhong 2006]: is an extension of ETX and can capture the expected number of transmissions taking into account the multiple paths that can be used under OR. Opportunistic Routing in Wireless Mesh Networks 9 / 37

Routing metrics in OR. What is EAX? source destination q 13 = 0.3 1 3 q 12 = 0.7 2 q 23 = 0.7 node candidates to 3 1 3, 2 2 3 q ij is the delivery probabilities from node i to node j Opportunistic Routing in Wireless Mesh Networks 10 / 37

Routing metrics in OR. What is EAX? source destination q 13 = 0.3 1 3 q 12 = 0.7 2 q 23 = 0.7 node candidates to 3 1 3, 2 2 3 q ij is the delivery probabilities from node i to node j What is the expected number of transmissions from node 1 to the destination using OR (E1 OR)? E1 OR= 1 + 3 i=1 p i E i p i is the probability of node i being the next forwarder. E i is the expected number of transmissions from node i to the destination. Opportunistic Routing in Wireless Mesh Networks 10 / 37

Routing metrics in OR. What is EAX? source destination q 13 = 0.3 1 3 q 12 = 0.7 2 q 23 = 0.7 node candidates to 3 1 3, 2 2 3 q ij is the delivery probabilities from node i to node j What is the expected number of transmissions from node 1 to the destination using OR (E1 OR)? E1 OR= 1 + 3 i=1 p i E i p i is the probability of node i being the next forwarder. E i is the expected number of transmissions from node i to the destination. E 1 = (1 + p 2 E 2 )/(p 2 + p 3 ) = (1 + (1 q 13 )q 12 1/q 23 )/((1 q 13 )q 12 + q 13 ) 2.15 Opportunistic Routing in Wireless Mesh Networks 10 / 37

Coordination methods in OR. Coordination methods in OR. Acknowledgment-based coordination Timer-based coordination Network coding coordination (NC) RTS-CTS coordination Opportunistic Routing in Wireless Mesh Networks 11 / 37

Coordination methods in OR. Acknowledgment-based coordination [Biswas 2004] Propose modifying 802.11 for OR coordination. S (source) C data frame B A (destination) Node S A B C Candidates for A, B, C, A, A source S A B C ata frame candidate C candidate B candidate A destination Opportunistic Routing in Wireless Mesh Networks 12 / 37

Coordination methods in OR. Acknowledgment-based coordination [Biswas 2004] Propose modifying 802.11 for OR coordination. S (source) C ack B A (destination) Node S A B C Candidates for A, B, C, A, A source S A B C ata frame candidate C candidate B candidate A ack A destination SIFS Opportunistic Routing in Wireless Mesh Networks 12 / 37

Coordination methods in OR. Acknowledgment-based coordination [Biswas 2004] Propose modifying 802.11 for OR coordination. S (source) ack C B A (destination) Node S A B C Candidates for A, B, C, A, A source S A B C ata frame candidate C candidate B candidate A destination SIFS ack A SIFS ack B Opportunistic Routing in Wireless Mesh Networks 12 / 37

Coordination methods in OR. Acknowledgment-based coordination [Biswas 2004] Propose modifying 802.11 for OR coordination. S (source) ack C B A (destination) Node S A B C Candidates for A, B, C, A, A source S A B C ata frame candidate C ack A candidate B ack B SIFS candidate A ack A SIFS destination SIFS Opportunistic Routing in Wireless Mesh Networks 12 / 37

Coordination methods in OR. Acknowledgment-based coordination [Biswas 2004] Propose modifying 802.11 for OR coordination. S (source) C source S A B C ata frame candidate C candidate B candidate A destination B SIFS ack A A data frame SIFS ack B (destination) SIFS ack A IFS+backoff ata frame Node S A B C Candidates for A, B, C, A, A Opportunistic Routing in Wireless Mesh Networks 12 / 37

Coordination methods in OR. Timer-based coordination {B,A} is the candidate set of S to reach. S A B Opportunistic Routing in Wireless Mesh Networks 13 / 37

Coordination methods in OR. Timer-based coordination {B,A} is the candidate set of S to reach. Candidates A and B receive the packet. S A B Opportunistic Routing in Wireless Mesh Networks 13 / 37

Coordination methods in OR. Timer-based coordination {B,A} is the candidate set of S to reach. Candidates A and B receive the packet. Candidate B forwards the packet. S A B Opportunistic Routing in Wireless Mesh Networks 13 / 37

Coordination methods in OR. Timer-based coordination {B,A} is the candidate set of S to reach. Candidates A and B receive the packet. Candidate B forwards the packet. If A hears B s transmissions, it simply discard the packet. S A B Opportunistic Routing in Wireless Mesh Networks 13 / 37

Coordination methods in OR. Network coding coordination (NC) [Michele 2003] {C 1,C 2 } is the candidates set of S to reach. C 1 a b S C 2 Opportunistic Routing in Wireless Mesh Networks 14 / 37

Coordination methods in OR. Network coding coordination (NC) [Michele 2003] {C 1,C 2 } is the candidates set of S to reach. S generates two coded packet. C 1 a b S p 1 p 2 a+b a b C 2 Opportunistic Routing in Wireless Mesh Networks 14 / 37

Coordination methods in OR. Network coding coordination (NC) [Michele 2003] {C 1,C 2 } is the candidates set of S to reach. S generates two coded packet. C 2 receives both packets while C 1 receives only one. a+b C 1 a b S p 1 p 2 a+b a b C 2 a+b a-b Opportunistic Routing in Wireless Mesh Networks 14 / 37

Coordination methods in OR. Network coding coordination (NC) [Michele 2003] {C 1,C 2 } is the candidates set of S to reach. S generates two coded packet. C 2 receives both packets while C 1 receives only one. Both candidates generate coded packet and broadcast them. a+b C 1 p 3 2a+2b a b S p 1 p 2 a+b a b p 4 2a C 2 a+b a-b Opportunistic Routing in Wireless Mesh Networks 14 / 37

Coordination methods in OR. Network coding coordination (NC) [Michele 2003] {C 1,C 2 } is the candidates set of S to reach. S generates two coded packet. C 2 receives both packets while C 1 receives only one. Both candidates generate coded packet and broadcast them. can decode and restore the original packets. a+b C 1 p 3 2a+2b a b S p 1 p 2 a+b a b a b p 4 2a C 2 a+b a-b Opportunistic Routing in Wireless Mesh Networks 14 / 37

Coordination methods in OR. RTS-CTS coordination [Szymon 2007] An explicit control packet(s) exchanged immediately before sending a data packet. CandSet={a, b, c} s c b a a b c RTS t Opportunistic Routing in Wireless Mesh Networks 15 / 37

Coordination methods in OR. RTS-CTS coordination [Szymon 2007] An explicit control packet(s) exchanged immediately before sending a data packet. CandSet={a, b, c} Candidates send CTS in time in order of their priorities. s c b a a b c RTS SIFS CTS a t Opportunistic Routing in Wireless Mesh Networks 15 / 37

Coordination methods in OR. RTS-CTS coordination [Szymon 2007] An explicit control packet(s) exchanged immediately before sending a data packet. CandSet={a, b, c} Candidates send CTS in time in order of their priorities. s c b a a b c RTS 2*SIFS CTS b SIFS CTS a t Opportunistic Routing in Wireless Mesh Networks 15 / 37

Coordination methods in OR. RTS-CTS coordination [Szymon 2007] An explicit control packet(s) exchanged immediately before sending a data packet. CandSet={a, b, c} Candidates send CTS in time in order of their priorities. Sender sends data to the candidate that sent CTS and is received. s a b c RTS SIFS ata t c b a 2*SIFS CTS b SIFS CTS a Opportunistic Routing in Wireless Mesh Networks 15 / 37

Coordination methods in OR. RTS-CTS coordination [Szymon 2007] An explicit control packet(s) exchanged immediately before sending a data packet. CandSet={a, b, c} Candidates send CTS in time in order of their priorities. Sender sends data to the candidate that sent CTS and is received. s c b a a b c RTS 2*SIFS CTS b SIFS CTS a SIFS ata NAV ata SIFS ACK NAV ata t Opportunistic Routing in Wireless Mesh Networks 15 / 37

Candidate selection algorithms. General Aim of OR To Minimize the expected number of transmissions from the source to the destination. Candidate Selection Algorithms How to select the forwarders from the neighbors? How to prioritize the selected candidates. Opportunistic Routing in Wireless Mesh Networks 16 / 37

Candidate selection algorithms. Extremely Opportunistic Routing (ExOR) [Biswas 2004] One of the first and most referenced OR protocols. It uses ETX metric. Shortest Path First (SPF) algorithm is used. Simple to implement. How does ExOR work? S is the source and is the destination. 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 17 / 37

Candidate selection algorithms. Extremely Opportunistic Routing (ExOR) [Biswas 2004] One of the first and most referenced OR protocols. It uses ETX metric. Shortest Path First (SPF) algorithm is used. Simple to implement. How does ExOR work? SPF from S to is S-A- and A is selected as the candidate. 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 17 / 37

Candidate selection algorithms. Extremely Opportunistic Routing (ExOR) [Biswas 2004] One of the first and most referenced OR protocols. It uses ETX metric. Shortest Path First (SPF) algorithm is used. Simple to implement. How does ExOR work? The edge between S and A is removed. 0.85 B 0.64 0.31 S A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 17 / 37

Candidate selection algorithms. Extremely Opportunistic Routing (ExOR) [Biswas 2004] One of the first and most referenced OR protocols. It uses ETX metric. Shortest Path First (SPF) algorithm is used. Simple to implement. How does ExOR work? The new SPF is S-B- and B is selected as the candidate. 0.85 B 0.64 0.31 S A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 17 / 37

Candidate selection algorithms. Extremely Opportunistic Routing (ExOR) [Biswas 2004] One of the first and most referenced OR protocols. It uses ETX metric. Shortest Path First (SPF) algorithm is used. Simple to implement. How does ExOR work? Prioritization:ETX of each candidate to the destination. 0.85 B 0.64 0.31 S A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 17 / 37

Candidate selection algorithms. Extremely Opportunistic Routing (ExOR) [Biswas 2004] One of the first and most referenced OR protocols. It uses ETX metric. Shortest Path First (SPF) algorithm is used. Simple to implement. How does ExOR work? CandSet(S)= {A, B} 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 17 / 37

Candidate selection algorithms. Opportunistic Any-Path Forwarding OAPF [Zhong 2006] It uses EAX. It does not select the optimum candidate set. It finds a candidate which improves the EAX of the node. Opportunistic Routing in Wireless Mesh Networks 18 / 37

Opportunistic Any-Path Forwarding OAPF How does OAPF work? InitCandSet(S)={A, B, } A and B must select their candidates sets before S 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 19 / 37

Opportunistic Any-Path Forwarding OAPF How does OAPF work? InitCandSet(S)={A, B, } A and B must select their candidates sets before S CandSet(S)={B} Iteration Selection 1 EAX({A}, S, )=3.99, EAX({B}, S, )=3.97, EAX({}, S, )=6.66 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 19 / 37

Opportunistic Any-Path Forwarding OAPF How does OAPF work? InitCandSet(S)={A, B, } A and B must select their candidates sets before S CandSet(S)={B} CandSet(S)={,A} Iteration Selection 1 EAX({A}, S, )=3.99, EAX({B}, S, )=3.97, EAX({}, S, )=6.66 2 EAX({A, B}, S, )= 3.64, EAX({,B}, S, )= 3.46 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 19 / 37

Candidate selection algorithms. Least-Cost Opportunistic Routing LCOR [ubois 2007] EAX is used. LCOR is a generalization of the well-known Bellman-Ford algorithm. It selects the optimum candidates. Exhaustive search. CandSet(S)= {, A}. 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 20 / 37

Candidate selection algorithms. Minimum Transmission Selection MTS [Yanhua 2009] It uses EAX. Like LCOR, it selects the optimum candidates. Adding the candidates of the node with smallest EAX to the neighbors of that node. It is simpler than LCOR. Opportunistic Routing in Wireless Mesh Networks 21 / 37

Minimum Transmission Selection (MTS) How does MTS work? S = {S,A,B} Iteration S A B 0 {}, 6.66 {}, 2.5 {}, 3.22 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 22 / 37

Minimum Transmission Selection (MTS) How does MTS work? S = {S,A,B} A has the minimum EAX Iteration S A B 0 {}, 6.66 {}, 2.5 {}, 3.22 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 22 / 37

Minimum Transmission Selection (MTS) How does MTS work? S = {S,A,B} A has the minimum EAX Iteration S A B 0 {}, 6.66 {}, 2.5 {}, 3.22 1 {,A}, 3.36 - {,A}, 2.79 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 22 / 37

Minimum Transmission Selection (MTS) How does MTS work? S = {S,A,B} B has the minimum EAX Iteration S A B 0 {}, 6.66 {}, 2.5 {}, 3.22 1 {,A}, 3.36 - {,A}, 2.79 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 22 / 37

Minimum Transmission Selection (MTS) How does MTS work? S = {S,A,B} B has the minimum EAX Iteration S A B 0 {}, 6.66 {}, 2.5 {}, 3.22 1 {,A}, 3.36 - {,A}, 2.79 2 {,A,B}, 3.22 - - 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 22 / 37

Minimum Transmission Selection (MTS) How does MTS work? S = {S,A,B} o the exhaustive search over founded candidates sets. Iteration S A B 0 {}, 6.66 {}, 2.5 {}, 3.22 1 {,A}, 3.36 - {,A}, 2.79 2 {,A,B}, 3.22 - - 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 22 / 37

Minimum Transmission Selection (MTS) How does MTS work? S = {S,A,B} CandSet(S)= {, A}. Iteration S A B 0 {}, 6.66 {}, 2.5 {}, 3.22 1 {,A}, 3.36 - {,A}, 2.79 2 {,A,B}, 3.22 - - 0.85 B 0.64 0.31 S 0.67 A 0.4 0.15 Opportunistic Routing in Wireless Mesh Networks 22 / 37

Performance evaluation. Assumptions There is only one active connection. Perfect coordination. Independent delivery probabilities. Linear topology with evenly spaced nodes: d [m] vs 1 2 3 N v d [m] Opportunistic Routing in Wireless Mesh Networks 23 / 37

Performance evaluation. Basic Model Assume that OR is used with a list of 2 candidates. We can model OR with an absorbing discrete time Markov chain, where the state is the node forwarding the packet: p 3 p p 3 p 1 p 3 1 p 1 1 vs p 2 p 2 p 2 1 2 3 4 5 N-1 N v d p 2 p 2 p p p 1 3 p p1 3 p 1 3 Let p(d) be the probability of successfully delivering a packet to a node located at a distance d. Then: p 1 = p(2d) p 1 = p(d) p 2 = p(d)(1 p 1 ) p 3 = 1 p 1 p 3 = 1 (p 1 + p 2 ) Opportunistic Routing in Wireless Mesh Networks 24 / 37

Performance evaluation. Solution of the model The model yields a discrete phase-type distribution, for which there exists a simple equation for the distribution and moments of the first time until absorption. In our model this is the number of transmissions since the source first transmits the packet, until it is received by the destination. Extension of the model A similar chain can be easily derived for any number of candidates and arbitrary topology: With 1 candidate is equivalent to uni-path routing. We shall refer to it as c 1. We shall refer as infinite candidates, c, to the case when all possible nodes are candidates. Opportunistic Routing in Wireless Mesh Networks 25 / 37

Performance evaluation. Summing up: The only ingredients needed to build the transition probability matrix are: The delivery probabilities. The ordered list of candidates of each node. Propagation model We assess the delivery probability at a distance d, p(d), with a shadowing propagation model, with path loss exponent β and standard deviation σ db. We assume that a link exists only if p(d) min.dp. Opportunistic Routing in Wireless Mesh Networks 26 / 37

Numerical results. Evaluation Methodology Area: A square field with diagonal = 300 m Random topology. Source and destination are placed at the end points of one of the diagonals. Number of nodes is equal to 10 N 50. The delivery probabilities o the links are obtained with shadowing propagation model. min.dp = 0.1 Opportunistic Routing in Wireless Mesh Networks 27 / 37

Numerical results. Measures of interest Expected number of transmissions Variance of the expected number transmissions. Probability of the number of transmissions. Execution Time. Opportunistic Routing in Wireless Mesh Networks 28 / 37

Numerical results. Expected number of transmissions and Mean number of candidates Expected number of transmissions 5.6 5.2 4.8 4.4 4 3.6 3.2 2.8 LCOR and MTS have exactly the same results. OAPF is only slightly larger than optimum algorithms. EAX Opt( ) < EAX Opt(3) EAX Unipath but a large number of candidates are used. =300m, β=2.7, σdb=6, min.dp=0.1 Uni-path ExOR(3) OAPF(3) LCOR(3) MTS(3) Opt( ) Mean number of candidates 25 22 19 16 13 10 7 ExOR( ) OAPF( ) Opt( ) =300m, β=2.7, σdb=6, min.dp=0.1 2.4 10 15 20 25 30 35 40 45 50 Number of nodes 4 10 15 20 25 30 35 40 45 50 Number of nodes Opportunistic Routing in Wireless Mesh Networks 29 / 37

Numerical results. Expected number of transmissions Vs Number of candidates For ncand= all algorithms have almost the same results. Limiting the maximum number of candidates makes the selection of the candidates sets more critical. =300m, beta=2.7, sigmadb=6, min.sp=0.1 =300m, beta=2.7, sigmadb=6, min.sp=0.1 Expected number of transmissions 5.6 4.8 4 3.2 ExOR OAPF LCOR MTS Expected number of transmissions 5.6 4.8 4 3.2 ExOR OAPF LCOR MTS 2.4 2.4 1 2 3 4 5 1 2 3 4 5 ncand ncand Number of Nodes = 10 Number of Nodes = 50 Opportunistic Routing in Wireless Mesh Networks 30 / 37

Numerical results. Variance of expected number of transmissions The variance of the expected number of transmissions using OR is significantly reduced compared with uni-path routing. 2 or 3 is enough to attain a significant part of the potential reduction. =300m, beta=2.7, sigmadb=6, min.sp=0.1 =300m, beta=2.7, sigmadb=6, min.sp=0.1 Variance of the expected number of transmissions 5.6 4.8 4 3.2 2.4 1.6 0.8 0 ExOR OAPF LCOR MTS Variance of the expected number of transmissions 5.6 4.8 4 3.2 2.4 1.6 0.8 0 ExOR OAPF LCOR MTS 1 2 3 4 5 1 2 3 4 5 ncand ncand Number of Nodes = 10 Number of Nodes = 50 Opportunistic Routing in Wireless Mesh Networks 31 / 37

Numerical results. Probability distribution of the number of transmissions The number of transmissions needed to reach the destination is significantly reduced by using OR with respect to the uni-path routing. = 300 m, β= 2.7, σdb= 6, min.dp= 0.1 = 300 m, β= 2.7, σdb= 6, min.dp= 0.1 0.6 0.6 Probability 0.5 0.4 0.3 Uni-path ExOR(3) OAPF(3) LCOR(3) MTS(3) Opt( ) Probability 0.5 0.4 0.3 Uni-path ExOR(3) OAPF(3) LCOR(3) MTS(3) Opt( ) 0.2 0.2 0.1 0.1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Number of transmissions Number of transmissions Number of Nodes = 10 Number of Nodes = 50 Opportunistic Routing in Wireless Mesh Networks 32 / 37

Numerical results. Execution Time The fastest algorithm is ExOR whereas LCOR is the slowest. OAPF is between the optimal algorithms and ExOR. MTS outperforms LCOR in terms of the execution time. 12000 5000 Execution time in log scale (second) 500 100 10 1 0.1 0.05 50 50 50 45 40 35 30 25 =300m, β=2.7, σdb=6, min.dp=0.1 20 15 50 N=10 N=10 N=10 ExOR(3) OAPF(3) MTS(3) LCOR(3) 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 Expected number of transmissions N=10 Opportunistic Routing in Wireless Mesh Networks 33 / 37

Conclusions and Future Research irections Conclusions We describe the meaning of Opportunistic Routing (OR). Research directions in OR. ifferent metrics in OR. Coordination in OR. Candidate selection algorithms in OR. A discrete time Markov chain to analyze the performance of OR. We have compared different candidate selection algorithms. Opportunistic Routing in Wireless Mesh Networks 34 / 37

Conclusions and Future Research irections Future Research irections An efficient candidate selection algorithm. A link layer implementation of the candidate coordination. Ad hoc, sensor, Vehicular ad hoc networks using Opportunistic Routing. Using Opportunistic Routing for broadcasting messages. Using Opportunistic Routing in Multi-channel multi-radio networks. Opportunistic Routing in Wireless Mesh Networks 35 / 37

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