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Sensors & Transducers 204 by IFSA Publishing, S. L. Node Load Balance Multi-flo Opportunistic Routing in Wireless Mesh Netors Wang Tao, 2 Li Wenei, 2 He Shiming College of Information

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Sensors & Transducers 204 by IFSA Publishing, S. L. Node Load Balance Multi-flo Opportunistic Routing in Wireless Mesh Netors Wang Tao, 2 Li Wenei, 2 He Shiming College of Information Science and Engineering, Hunan City Uniersity, Yiyang, 43000,China 2 College of information science and engineering, Hunan Uniersity, Changsha, 40082, China Tel.: , fax: Receied: 23 January 204 /Accepted: 7 Marc 204 /Published: 30 April 204 Abstract: Opportunistic routing (OR) has been proposed to improe the performance of ireless netors by exploiting the multi-user diersity and broadcast nature of the ireless medium. It inoles multiple candidate forarders to relay pacets eery hop. The existing OR doesn t tae account of the traffic load and load balance, therefore some nodes may be oerloaded hile the others may not, leading to netor performance decline. In this paper, e focus on opportunities routing selection ith node load balance hich is described as a conex optimization problem. To sole the problem, by combining primal-dual and sub-gradient methods, a fully distributed Node load balance Multi-flo Opportunistic Routing algorithm (NMOR) is proposed. With node load balance constraint, NMOR allocates the flo rate iteratiely and the rate allocation decides the candidate forarder selection of opportunities routing. The simulation results sho that NMOR algorithm improes 00 %, 62 % of the aggregatie throughput than ETX and EAX, respectiely. Copyright 204 IFSA Publishing, S. L. Keyords: Wireless mesh netors, Load balance, Opportunistic routing.. Introduction Traditional ireless routing (TR) often follos the design methodology for ired netors by abstracting the ireless lins as ired lins to loo for the shortest delay or least cost path(s) for a user beteen a pair of source and destination nodes. Hoeer for unreliable ireless netors, the forarding capacity of intermediate nodes, hich oerhear pacet transmissions, can be explored to improe the performance of WMNs. This obseration motiates the emergence of a noel technique non as opportunistic routing, hich allos any node oerhearing a pacet to participate in forarding it instead of deterministically choosing the next hop before transmitting a pacet. Then opportunistic routing can effectiely combine multiple ea lins into a strong lin and tae adantage of transmissions reaching unexpectedly near or unexpectedly far. It exploits the broadcast nature and multi-user diersity of the ireless channel. And recent researches [-5] hae alidated that compared ith Traditional Routing, OR can eidently increase the reliability of pacet transmissions and promote the end to end throughput of multi-hop ireless netor, especially Wireless Mesh Netors (WMNs) [6]. The existing ORs use different route metrics to select candidate forarders, such as the transmission 62 Article number P_974 number [3, 7, 8, 9], transmission time [0, ], cost [2] or utilities [3] of all possible paths from source to destination. But these route metrics decide the route and candidate forarders ithout taing into account the distribution of flos in multi-flo ireless mesh netors. Although the distributions of flos and traffic load are different, the results of route are still same. Due to the temporal and spatial locality of flo dates, flos may tend to concentrate on a small area stemming from ignoring the space distribution hile routing. Some node on some popular paths may be oerloaded, hile the others may not. The load imbalance among candidate forarders ould preent the netor from proiding good and fair serices to its users. The heay load can exhaust prematurely a candidate forarder s resources, such as bandidth, processing poer, and memory storage. The oerload nodes may be congested and become the bottlenec of end-to-end transmission, consequently resulting in longer end-to-end delay and significant throughput reduction stemming from pacet loss and buffer oerflo. The use of underutilized paths and nodes can enhance the oerall system throughput. In addition, a node can sere for multiple flos concurrently. And ho much resources the node should be assigned to different flos in order to obtain higher throughput are still open problems. These to problems can be resoled by introducing a joint candidate forarder selection and rate allocation opportunistic routing scheme. With multiple flos, some ors maximize the netor throughput or utility ia allocating the sending rate, channel resource or gateay [4-9]. But they pre-select route before allocating resource hich isn t included the node resource. The route playing an important role in netor performance, e need to allocate node and select route in reason ith multi-flo. Compared ith traditional routing, opportunistic routing has multiple candidate forarders resulting in the nodes of flos crossing more frequently. According to the distribution of flo, ho to allocate node resources in order to maximize the netor throughput and eep fairness is an urgent need to be resoled. In this paper, e address the problem of choosing OR route and allocating rate for multi-flo ith load balance of nodes in lossy WMNs. Opportunities routing selection ith node load balance is described as a conex optimization problem. In order to sole the problem, by combining primal-dual and subgradient methods, a fully distributed joint candidate forarders selection and rate allocation Node load balance Multi-flo Opportunistic Routing algorithm (NMOR) is proposed. NMOR allocates the flo rate iteratiely and the rate allocation decides the candidate forarder selection of opportunities routing. The simulation results sho that NMOR algorithm improes 00 %, 62 % of the aggregatie throughput than expected number of transmissions (ETX) [9] and expected any path number of transmissions (EAX [7]), respectiely. The rest of this paper is organized as follos. The motiation is introduced in Section 2. After analyzing the constraint of the problem, e gie the problem formulation in Section 3. Section 4 proposes the distributed algorithm. Details on the simulation to ealuate the proposed algorithm are proided in Section 5. Section 6 summarizes and concludes the paper. 2. Motiation In this section, an example is used to present the motiation as shon in Fig.. A ireless mesh netor consists of to concurrent flos from s 0 to d 0 and from s to d. s and d present the sources and destinations of flos, R present the other nodes hich can be selected as candidate forarders. The sources, destinations and candidate forarders of each flo are mared by a dashed rectangle. Because the source and destination of the to flos are nearby, they choose all most same nodes as candidate forarders by ETX or EAX route metrics. For example, R 2, R 4, R 7 are the candidate forarder of flo (s 0,, d 0 ) and flo (s,d ); R 5 is the candidate forarder of (s,d ); R, R 3, R 6 and R 8 are candidate forarders of none flo. Some node may be oerloaded hile the others may not. (a) Opportunistic routing selection ignoring the flo distribution. (b) Opportunistic routing selection ith the flo distribution. Fig.. Opportunistic routing selection. 63 Fig. (b) is the opportunistic routing selection result ith the flo distribution. The to flos mae full use of nodes as candidate forarders. Additionally, nodes sering for multiple flos (such as R 4 ) suitably allocate rate for each flo can produce better netor throughputs. Ho to assign candidate forarders and nodes rates to multiple flos in order to maximize the throughput is our problem. 3. System Model We use a undirected graph G(V,E) to model the ireless mesh netor in hich V is the set of n nodes, and E is the set of m lins. p(u,) is pacet deliery ratio (PDR) of lin l(u,) according to the propagation model. If u can correctly decode the pacets from at least ith the possibility P 0 (P 0 ), that is p(u,) is greater than P 0, node u is a neighbor of node. The neighbor set of node is denoted by R(u). In this WMNs, there are K concurrent flos hose sources and destinations are {(s, d ), =..K}. We should allocate reasonable candidate forarders and forarders rate for these flos in order to maximize the total netor throughput at the same time eeping the fairness. In this section, e firstly analyze the constraint of problem. Then the object of netor performance is proposed, and e transform the problem in order to sole it coneniently according to the dependence of ariables. 3.. Variables and Constrains on OR In order to describe the opportunistic routing, firstly seeral ariables are defined. Then e mainly use the model introduced in [7] to formulate the basic properties of opportunistic routing, hich has been shon to be sufficiently effectie and tractable for netor analysis. We define a binary ariable βu denoted hether or not node u is the candidate forarder of session, yes and 0 no, defined as follos:, node u is the candidate forarder βu = of session () 0, otherise We define a binary ariable α u, hich has alue if the lin from u to is actie in the session in the routing solution, and alue 0 otherise, defined as follos:, the lin from u to is actie in the session αu = (2) 0, otherise Note that only if both node u and are the candidate forarder of session and node is the neighbor of node u, the lin from u to is actie in session. α = β * β * BH, [, K], ( u, ) E, (3) u u u here BH u presents hether or not node is the neighbor of node u, yes and 0 no. ) Multipath flo conseration constraint. For a unicast session here the source s ants to send data ith rate λ to d, by the flo conseration condition, e hae: here αur ( u, ) αur (, u) = h ( u),, (4) [, K], λ,if u = s h ( u) = λ,if u = d 0, otherise and r ( u, ) is the information flo rate of session from node u to, hich is the aerage injection rate of innoatie pacets on lin (u,). For session, the equation represents the flo conseration constraint that the source node's net transmission rate is λ, the destination node's net transmission rate is -λ, and any intermediate node's net transmission rate is 0. Moreoer, only if the lin from u to is actie in session, the information flo rate of session on lin (u,) has alue non zero and alue 0 otherise. The constraint can be expressed as follo: α r ( u, ) = r ( u, ), [, K], ( u, ) E (5) u 2) MAC broadcasting rate constraint. We use the broadcast MAC model of Zhang and Li [7], hich extends the unicast MAC model to obtain a necessary condition for feasible broadcast schedules. In this model, the transmission range and the interference range are considered to be the same, and the reception probability beyond this range can be ignored. Specifically, the ireless netor is modeled as an ideal time-slotted broadcast MAC here competing transmitters can optimally multiplex the channel ithout any collisions. Since the transmission range is defined as the distance here the reception probability falls belo a small threshold, it is fair to assume that the interference range equals to the transmission range [7]. The neighbor set R(u) is equal to the set of nodes hose transmission range (interference t range) node u is located in. Let B ( u) denote a binary decision ariable indicating hether node u is transmitting session s data in slot t. Thus, according to the aboe definition of collision, a schedule is collision free: 64 β B ( u) + β B ( ), u s t t u [, K] [, K] R( u) (6) This equation indicates that any receier u allos the broadcast transmission from at most one transmitter ithin its range at each time slot. Note that for session the source node s is excluded, since s does not need to receie information from other t nodes for this user. B ( u ) indicates hether node u is transmitting session s data in slot t. If node u isn t the candidate forarder of session hich means t that β is zero, the alue of B ( u) must be zero, u because the node u don t send any pacet for session. Assuming that the schedule length is T, according to (6) e hae W t W t βub( u) + βb( ) T t [, T] [, K] T t [, T] [, K] R( u) W, u s, (7) here W is the MAC layer capacity, hich is the maximum broadcast rate of a node hen no interferer presents. The aerage broadcast rate of node u for session can be computed by W t b( u) = lim B( u). Apply to (7), e must hae: T T t [, T] β b ( u) + β b ( ) W, u s u [, K] [, K] R( u) (8) t We transformed an integer ariable B ( u ) into a continuous one b ( u ) by aeraging. Moreoer, t according the relationship beteen B ( u ) and β u, e can obtain the relationship beteen b ( u ) and β u. Only if the node u is the candidate forarder of session, the broadcast rate of node u for session has alue non zero and alue 0 otherise. The constraint can be expressed as follo: β b ( u) = b ( u), [, K], u V (9) u 3) Coding constraint. In our paper opportunistic routing ith netor code (e.g. MORE[3]) is considered, here the forard rate of node is unaffected by the order of forarding, only affected by the quality of lins. Therefore the information flo rate of session on lin (u,) must not exceed the corresponding unicast transmission rate, hich is the folloing straightforard netor coding model. b( u)* pu (, ) r( u, ), [, K], ( u, ) E, (0) here p(u,) is the pacet deliery ratio of lin (u,). As discussed in [7, 8], although it is not a tight bound, it inoles approximations to the behaior of an actual WMN, and includes all the tractable information that users can use to induce a better payoff. Other coding models hich mae an exact characterization ith an exponential number of constraints mae the problem intractable. 4) Node load balance constraint. We define a load balance area (i.e. a set of nodes) for each node. Let A( u) present that is in u s load balance area. That is to say, bu ( ) b ( ) θ( u, ), θ( u, ) 0, Au ( ) bu ( ) = b( u),, () [, K] here b(u) is Node max load of u, θ(u,) is a parameter set by node u. We introduce A(u) and θ(u,) to help u hae a controllable balanced load ith other nodes. In this paper, e consider a symmetric definition (i.e. A( u) u A( ), and θ(u,) = θ(,u)). In practice, the required load balance constraint could be asymmetric Problem Formulation The soling problem is selecting opportunistic route for the K flos in order to maximize the total netor throughput at the same time eeping the fairness. Therefore the objectie of this problem can be designed to maximize the product of all flos rate ia optimal multi-hop flo routing. It is defined as maximize λ equaled to maximize ln( λ ). [, K] [, K] With the aboe constrains, e can formulate the problem as the folloing system: maximize ln( λ ) [, K] subject to αu = βu * β * BHu, [, K], ( u, ) αur ( u, ) αur (, u) = h ( u), [, K], αur ( u, ) = r ( u, ), [, K], ( u, ) βub( u) + βb( ) W, u s [, K] [, K] R( u) βub( u) = b( u), [, K], b( u)* pu (, ) r( u, ), [, K], ( u, ) b( u) b( ) θ ( u, ), u, A( u) [, K] [, K] oer: αu = 0or, [, K], ( u, ) βu = 0or, [, K], u V 0 r ( u, ) W, [, K], ( u, ) 0 b ( u) W, [, K], (2) here the ariables are α, β, rb,, and λ,if u = s h( u) = λ,if u = d 0, otherise. 65 The nonlinear constrains mae the problem hard to be soled, therefore e transform it according to the relationship of ariables. The constraints in (4) (5) contain the product of to ariables α u and r ( u, ) hich is in non-linear form. According to property in (5), e can rerite the constraints (4) (5) as follos. If the information flo rate of session on lin (u,) has alue non zero, the lin from u to must be actie in session. r( u, ) r(, u) = h( u), [, K],, (3) (, ) 0, r u αu =, [, K ], ( u, ), (4) 0, r ( u, ) = 0 Similarly e can reformulate (8), (9) into linear constraints as follos. If the broadcast rate of node u for session has alue non zero, the node u must be the candidate forarder of session. b ( u) + b ( ) W, u s, [, K] [, K] R( u) (5), ( ) 0 b u βu =, [, K ], (6) 0, otherise After conerting the nonlinear constrains, the alue of α, β are only dependent on r and b and don t need to be included in our final formulation. No all of our constraints are linear. Using the aboe definition of objectie function, e represent the problem formulation as follos. maximize ln( λ ) [, K] subject to b( u)* pu (, ) r( u, ), [, K], ( u, ) r( u, ) r(, u) = h( u), [, K], b( u) + b( ) W, u s [, K] [, K] R( u) b( u) b( ) θ ( u, ), u, A( u) [, K] [, K] 0 r ( u, ) W, [, K], ( u, ) E 0 b ( u) W, [, K],, (7) here rbare, the optimization ariables. A node decides hether or not to forard pacet for a flo according to the flo rate, unlie [7, 8] hich perform a node selection procedure beforehand, then allocate the flo rate. Since the objectie function is strictly conex and the constraints are linear, the problem (7) represents a strictly conex optimization problem. We conert (7) into a standard form of conex optimization problem (8). Though the problem (8) can be readily soled by standard conex programming algorithm, it is desirable to proide a decentralized solution in WMNs. We deelop a distributed algorithm to sole the problem (8) in section 5. minimize ln( λ ) [, K] subject to r( u, ) b( u)* pu (, ) 0, [, K], ( u, ) r ( u, ) r (, u) = h ( u), [, K], b( u) b( ) θ ( u, ) 0, u A u [, K] [, K] 0 r ( u, ) W, [, K], ( u, ) 0 b ( u) W, [, K], b( u) + b( ) W 0, u s [, K] [, K] R( u), ( ) 4. Distributed Algorithm (8) In this section, e propose a decentralized algorithm for the problem (8) based on decomposition techniques [20]. Specifically, e decompose the original problem into to separate sub-problems ith decoupled ariables based on the dual decomposition. Then e sole the sub-problems independently, and finally sole the master dual problem by updating dual ariables. 4.. The Dual Decomposition Method Solution By introducing dual ariables x ( u), y ( u, ), z ( u, ) to relax the three sets of constraints in (8) respectiely, e hae the Lagrangian function of the primal problem (8) subject to constraint (3) as (9). Lrbxyz (,,,,) = ln( λ ) [, K] u V [, K], u s [, K] R( u), u s [, K] ( u, ) u, V, Au ( ) [, K] [, K] = ln( λ ) + y [, K] [, K]( u, ) + x ub u + [, ], [, ] ( ), + zu (, )( b( u) b( )) u, V, Au ( ) [, K] y( ub, ) ( u) pu (, ) [, K] ( u, ) xuw ( ) θ ( u, ) zu (, ) + xu ( )( b( u) + b( ) W) + y( u, )( r( u, ) b( u) pu (, )) + zu (, )( b( u) b( ) θ ( u, )) u, V, A( u) ( u, ) r ( u, ) ( ) ( ) xb ( ) ( u) K u V u s K u V R u s u V (9) Thus, the minimization operation of L(r,b,x,y,z) oer (r,b) can be decomposed as to sub-problems as follos: SUB: the information flo rate problem of session 66 minimize ln( λ ) + y ( u, ) r ( u, ) ( u, ) subject to r( u, ) r(, u) = h( u), 0 r ( u, ) W, ( u, ) SUB2: the broadcast rate problem of node u minimize b ( u)( x( u) u s + x( ) R( u), s ( u, ) Au ( ) Au ( ) (20) y( u, ) pu (, ) + zu (, ) zu (, )) (2) subject to 0 b ( u) W, [, K] The Lagrange dual function is the minimum alue of the Lagrangian function as folloing. rb, Gxy (, ) = inf{ Lrbxyz (,,,, )} (22) The dual problem of problem (8) is formulated as maximize Gxyz. (,, ) We use the subgradient method to sole the Lagrange dual problem. In the i th iteration, the dual ariables are updated as (23) here the subgradients of dual ariables are M, H and C. here ϕ min min minimize ln( Γ ) + ϕ Γ, (25) subject to 0 Γ W π ( u, ) π = min y ( u, ) is the cost of the mincost path. Since the objectie function is an increasing, strictly conex and continuously differentiable function, (25) can be easily soled and min Γ = / ϕ is the solution. r ( u, ) is set to the solution to (24), if lin (u,) is on this min-cost path. Otherise the result of r ( u, ) in (24) is zero. Therefore, each session can use a distributed shortest path algorithm to compute its r. 2)The broadcast rate problem of node u (SUB2). Since the objectie of the problem SUB2 (2) is linear, the Lagrange multiplier method may not necessarily generate the optimal solution. To handle this difficulty, e adopt the proximal method and add 2 a small regularization term ε b ( u) b ( u) to mae it strictly conex. ε is positie constant scalar. When ε is sufficiently small, the term 2 ε b ( u) b ( u) is

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