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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1

Green Communication in Energy RenewableWireless Mesh Networks: Routing, Rate Control,

and Power AllocationChangqing Luo, Shengyong Guo, Song Guo, Senior Member, IEEE, Laurence T. Yang, Member, IEEE,

Geyong Min, Member, IEEE, and Xia Xie

Abstract—The increasing demand for wireless services has led to a severe energy consumption problem with the rising of greenhousegas emission. While the renewable energy can somehow alleviate this problem, the routing, flow rate, and power still have to be wellinvestigated with the objective of minimizing energy consumption in multi-hop energy renewable wireless mesh networks (ER-WMNs).This paper formulates the problem of network-wide energy consumption minimization under the network throughput constraint as amixed-integer nonlinear programming problem by jointly optimizing routing, rate control, and power allocation. Moreover, the min-maxfairness model is applied to address the fairness issue because the uneven routing problem may incur the sharp reduction of networkperformance in multi-hop ER-WMNs. Due to the high computational complexity of the formulated mathematical programming problem,an energy-aware multi-path routing algorithm (EARA) is also proposed to deal with the joint control of routing, flow rate, and powerallocation in practical multi-hop WMNs. To search the optimal routing , it applies a weighted Dijkstra’s shortest path algorithm, where theweight is defined as a function of the power consumption and residual energy of a node. Extensive simulation results are presented toshow the performance of the proposed schemes and the effects of energy replennishment rate and network throughput on the networklifetime.

Index Terms—Multi-hop wireless mesh networks, renewable energy, fairness, energy consumption minimization, routing.

F

1 INTRODUCTION

The increasing demand for ubiquitous network accessleads to the rapid development of wireless access tech-nologies. The multi-hop wireless mesh network (WMN),as a promising solution for low-cost broadband Internetaccess, is being used on the last mile for the enhancementof Internet connectivity for mobile users for its provisionof high data rate [1]. A multi-hop WMN is usuallyconstructed by wireless mesh nodes that are wirelessmesh routers or gateways. One of features of WMNsis that mesh nodes are rarely mobile and powered bypower grid. Mobile users access Internet service throughgateway and information is always delivered by virtueof multi-hop relaying.

In the past years, researchers largely concentrate onthe channel assignment, routing, and rate allocationproblems in multi-hop WMNs [2], [3], [4]. Subramanianet al. [5] investigated the channel assignment problemsin multi-radio WMNs, and designed centralized anddistributed algorithms for the channel allocation withthe objective of minimizing the overall network inter-ference. Capone et al. [6] addressed the radio resource

C. Luo, S. Guo, L. T. Yang, G. Min, and X. Xia are with the School ofComputer Science and Technology, Huazhong University of Science and Tech-nology, Wuhan, China (email: [email protected], [email protected],[email protected], [email protected], and [email protected]); L. T. Yang isalso with the Department of Computer Science, St. Francis Xavier University,Antigonish, Canada, and G. Min is with the Department of Computing,School of Informatics University of Bradford, Bradford, UKS. Guo is with the School of Computer Science and Engineering, TheUniversity of Aizu, Tsuruga, Ikki-machi, Japan (email: [email protected])

assignment optimization problem in WMNs, where rout-ing, scheduling and channel assignment were jointlyconsidered. Passos and Albuquerque [7] considered therouting and rate adaptation problem in WMNs, andproposed a joint automatic rate selection and routingscheme to provide best routing and rate. In addition,since energy consumption is becoming a very importantproblem in the world for the rising of greenhouse gasemission, energy efficiency has been attracting muchattention [8], [9]. Vijayalayan et al. [10] considered theenergy efficient scheduling scheme in WMNs and anenhanced pseudo random access scheme was proposedto improve energy efficiency. The power control problemin WMNs was also investigated to reduce interferenceand energy consumption [11], [12], [13]. Although somework has been done to reduce energy consumption, thebenefit is essentially marginal.

On the other hand, the power grid infrastructure,which provides electricity to multi-hop WMNs, has beenexperiencing a dramatic change from the traditionalelectricity grid to the smart grid where renewable energyis integrated [14], [15]. Renewable energy is usuallyextracted from renewable resources (e.g., solar and wind)so that no fossil fuel is burn and thus no greenhouse gasis produced. Obviously, the use of renewable energy, tosome extent, can alleviate the greenhouse gas emissionproblem. Therefore, renewable energy will play a vitalrole in future wireless network infrastructures (e.g., wire-less mesh networks).

However, the problems of routing, flow rate, and


power allocation still have to be well investigated whenrenewable energy is exploited in multi-hop WMNs be-cause renewable energy replenishment of each nodein multi-hop WMNs is highly dependent on the en-vironment. Such WMNs are also denoted as energyrenewable WMNs (ER-WMNs) in this paper. Since theenergy replenishment rate dynamically changes overtime, and is affected by the weather and surroundingenvironment, new problems are thus posed. In recentyears, a few research efforts have been made to inves-tigate the problems in multi-hop ER-WMNs. Badawy,Sayegh, and Todd [16] investigated the resource as-signment problem and considered to minimize networkdeployment cost. Cai et al. [17] investigated the resourcemanagement problem in sustainable energy poweredWMNs and proposed an adaptive resource managementscheme that distributes traffic under the energy sus-tainability constraint. In particular, a G/G/1 queue isapplied to model the energy buffer of a mesh node anda diffusion approximation is then used to analyze thetransient evolution of the queue length. Zheng et al.[18] proposed an energy-aware AP placement scheme inWLAN mesh networks with renewable energy sources,where the optimal placement of APs is determined andthe power control and rate adaptation at APs are jointlyoptimized. Lin, Shroff, and Srikant [19] investigated therouting problem for multi-hop ER-WMNs, and proposedan asymptotically optimal energy-aware routing scheme,in which energy replenishment, mobility, and erroneousrouting information are jointly taken into account.

Althoug some related research work has been con-ducted on problems in ER-WMNs, the high interdepen-dency of of routing, rate, and power, and their significantinfluence on energy consumption in multi-hop WMNshave been little studied. To fill in this vacancy, thispaper proposes a scheme that jointly considers routing,rate control, and power allocation to minimize network-wide energy consumption with network throughputconstraint in multi-hop ER-WMNs. The key contribu-tions of this paper are summarized as follows.

1) The problem of network-wide energy consump-tion minimization under network throughput con-straint in multi-hop ER-WMNs is investigated. Weformulate it as a mixed-integer nonlinear program(MINLP) that is in general NP-hard. Moreover, tosolve this problem, a scheme that jointly considersthe routing, flow rate, and power allocation isproposed in this paper.

2) Fairness is also taken into account in the proposedscheme to address the uneven routing problemwhich may lead to some severe performance issues,e.g., some nodes frequently enter the sleep modedue to their low residual energy level, in multi-hop ER-WMNs compared to traditional multi-hopWMNs. The min-max fairness model is proposed toaddress the tradeoff between the power consump-tion and residual energy of each node.

3) Due to the high computational complexity to solvethe MINLP formulation, an energy-aware multi-path routing algorithm (EARA) is proposed topractically deal with the joint control of routing,rate, and power in multi-hop WMNs. This algo-rithm uses a weighted Dijkstra’s shortest path al-gorithm to search an optimal routing, in which theweight is defined as a function of the power con-sumption and residual energy of a node. Moreover,the concept of unit flow is proposed to addressthe issue that the weighted Dijkstra’s shortest pathalgorithm cannot support multi-path routing.

The remainder of this paper is organized as follows.Section 2 describes the network model, including theconsidered network scenario, session flow model, andpower and energy consumption model. The network-wide energy consumption under network throughputconstraint is formulated as an MINLP problem and fair-ness is also consider to address the uneven routing prob-lem in Section 3. Section 4 proposes an energy-awarerouting algorithm that can be used in practical multi-hop WMNs. Extensive simulation results are presentedand analysed for performance evaluation in Section 5.Finally, Section 6 concludes this paper.

2 NETWORK MODEL

This paper considers a multi-hop ER-WMN, representedby a directed graph G = {N ,L}, where N and L arethe sets of nodes and directional links, respectively. Alink between two nodes exists if and only if the two arewithin a certain communication range. The communi-cation between two nodes without a direct link needsto resort to multi-hop communication with the help ofintermediate nodes’ relaying. Orthogonal channels areused by all links so that the interference can be avoided.It is noteworthy that the number of channels is as manyas the number of active links because a channel can bereused spatially. In addition, the time-division system isconsidered here, where time is divided into slots withequal length T , and t refers to the t-th discrete timeperiod. We assume that no new session occurs duringa time slot so that the routing, rate control, and powerallocation cannot be affected.

In particular, each node is powered only by renewableenergy in multi-hop ER-WMNs and the solar is consid-ered as the energy source. A large-sized solar panel isused to obtain the solar energy that is then transformedinto electrical energy. The structure of a node is shown inFig. 1, where a solar panel connects the access point (AP).The electrical energy will be stored into the battery viaa charging controller that controls the charging process.Each node consumes the energy from the battery becauseit can supply the energy continuously. Once the energycontained in the battery is lower than a threshold, thecharging controller will immediately shut down thepower supply and the node enters sleep mode. Sincethe energy production rate is low in practical energy


Fig. 1. The structure of a node powered by solar energy.

systems, the energy replenishment rate is less than theenergy consumption rate when a session is deliveredthrough a node. Usually, the node cannot work wellwhen the residual energy of a battey is lower than athreshold Boutage and meanwhile the battery has a max-imum capacity limitation Bmax. Therefore, the residualenergy of a node varies between Boutage and Bmax.

2.1 Session Flow Model

Suppose a set of F active unicast sessions in the con-sidered network scenario. Let s(f) and d(f) denote thesource and destination nodes of session f (f ∈ F),respectively. Moreover, r(f) represents the data rate ofsession f . Therefore, for the network with |F| activesession flows, network throughput U is the sum of datarate of all sessions, i.e.,

U =∑f∈F

r(f). (1)

To achieve data transmission between a source nodeand its corresponding destination node, the multi-pathrouting scheme is applied in this study. Hence, eachsession can be split into multiple flows, and traffic isdelivered through multiple paths. Let rl(f) denote theflow rate attributed to session f (f ∈ F) on link l. We useLIni and LOuti to represent the set of potential incomingand outgoing links at node i, respectively. Since the rateof all incoming flows and the rate of all outgoing flowsat a node satisfy the flow conservation, the followingequations can then be obtained. If node i is the sourcenode of session f , i.e., i = s(f), then∑

l∈LOuti

rl(f) = r(f). (2)

If node i is the destination node of session f , i.e., i =d(f), then ∑

l∈LIni

rl(f) = r(f). (3)

If node i is an intermediate node of session f , i.e., i 6=

s(f) and i 6= d(f), then

l 6=(i,s(f))∑l∈LOuti

rl(f) =

l′ 6=(d(f),i)∑l′∈LIni

rl′(f). (4)

Since the quality of service (QoS) for each user needsto be guaranteed in multi-hop ER-WMNs, the data rateof each session should be met in the design of the jointrouting, rate control, and power allocation scheme.

2.2 Power and Energy Consumption ModelIn general, when a session is delivered on a link in multi-hop ER-WMNs, the energy is mainly consumed due todata transmission and reception. The receiving poweris denoted by Prec, which is considered as a constantin this paper. The transmission power is represented byPl when link l is active. It is obvious that transmissionpower is a variable parameter that is related to thequality of the link and rate allocation.

Let Xl be a binary variable indicating whether link lis active or not, i.e.,

Xl =

{1, if link l ∈ L is active,0, otherwise. (5)

Hence, the energy consumption for link l is (Pl+Xl·Prec).The maximum transmission power for each node is

defined as Pmax and the transmission power cannotexceed the maximum transmission power

0 ≤ Pl ≤ Xl · Pmax, l ∈ L. (6)

Since there are several potential outgoing links at nodei, the transmission power constraint can be expressed asfollows

0 ≤∑

l∈LOuti

Pl ≤ Pmax, l ∈ L, i ∈ N . (7)

Let Ei denote the total energy consumption at node iduring a time slot, and it is expressed as follows

Ei = (∑

l∈LOuti

Pl +∑l∈LIni

Xl · Prec) · T, l ∈ L, i ∈ N . (8)

The data rate allocated to a link l cannot exceed thecapacity of this link denoted as cl, that is∑

f∈F

rl(f) ≤ cl, l ∈ L. (9)

The data rate of a link is constrained by its theoreticalcapacity that can be obtained through Shannon formula,i.e.,

cl = Wl log2(1 +PlGlσ2

), l ∈ L, (10)

where cl, Wl, and Gl are the achievable capacity, band-width, and channel gain of link l, respectively; σ2 is theambient Gaussian noise power. Accordingly, when max-imum transmission power is used, the correspondingmaximum capacity cmaxl is

cmaxl = Wl log2(1 +PmaxGlσ2

), l ∈ L. (11)


In multi-hop ER-WMNs, the residual energy of a nodeat the end of a time slot depends on the replenishedand consumed energy during this time slot. Denote Bi(t)and Bi(t + 1) as the residual energy of node i at thebeginning and the end of time slot t and Bi(t + 1) isthus the residual energy of node i at the end of timeslot t, respectively. Let Ri(t) represent the correspondingreplenished energy that is highly related to geographicallocation, environment, climate and other natural factors[20]. Because the energy level of a battery is constrainedbetween Boutage and Bmax, the residual energy of nodei at the end of time slot t is

Bi(t+1) = min{Bmax,max[Boutage, Bi(t)+Ri(t)−Ei(t)]},(12)

where Ri(t) = ri(t) · T , and ri(t) is the energy re-plenishment rate that changes dynamically. The residualenergy for each node in multi-hop ER-WMNs is updatedthrough (12).

3 PROBLEM FORMULATION

This section studies how to jointly control the routing,rate, and power so as to achieve the network-wideenergy consumption minimization under the networkthroughput constraint in multi-hop ER-WMNs. Thisproblem is motivated by the scenario where users havestrict network throughput limit. Hence, given the net-work throughput constraint, the optimization problemis to minimize network-wide energy consumption byvirtue of jointly controlling the multi-path routing, ratefor each session, and power on each link.

Mathematically, this problem can be formulated asfollows:

OPT: min Σi∈NEi

s.t. (1)− (4), and (6)− (10)

xl ∈ {0, 1}, Pl, rl(f) ≥ 0.

OPT is a mixed-integer nonlinear program (MINLP),which is in general NP-hard [21]. The solution to thisproblem is to seek a feasible routing vector for sessionf (f ∈ F) along with the corresponding rate vector oneach link l ∈ L and power vector for each node i ∈ Nsuch that the network-wide energy consumption of thetriples vector (i.e., routing, rate, and power) is minimumamong all feasible vectors. Therefore, based on the re-sults of solving this formulation, the optimal routing,rate control, and power allocation can be obtained.

However, simply minimizing the network-wide en-ergy consumption can lead to a severe bias. That is, somewireless mesh nodes are starved for no opportunity todeliver sessions while some other nodes are always se-lected to deliver sessions for their high-quality outgoingor incoming links. It is well known that this phenomenonwill result in some severe performance problems inmulti-hop WMNs, such as unbalanced traffic load andnetwork access collision [22], [23]. Because the energyreplenished from solar at each node is very limited, this

problem may be much severe in multi-hop ER-WMNs.For instance, a node with low residual energy may fre-quently enter sleep mode due to the alterntive processesof energy consumption and replenishment. Therefore,fairness should be considered when the scheme of jointlycontrolling routing, rate, and power is designed in multi-hop ER-WMNs.

This paper addresses the fairness issue based on asimple min-max fairness model, which can lead to theminimum network-wide energy consumption with guar-anteed minimum maximum power allocation of eachnode according to its residual energy. The goal of ap-plying this min-max fairness model in this paper is thatthe lower power is allocated to deliver information at anode with lower residual energy, while the higher poweris allocated at a node with higher residual energy. Thefairness constraint factor is a value that is used to limitthe transmission power of each node. Let

α = maxi∈N

{αi}, and

αi =Pi/

∑i∈N Pi

Bi/∑i∈N Bi

denote the fairness constraint factor. Through the trans-formation, the power constraint can be obtained

Pi ≤Bi∑i∈N Bi

·∑i∈N

Pi · α, i ∈ N , l ∈ L, (13)

where Pi =∑l∈LOuti

Pl is transmission power of node i.As shown in (13), the transmission power of each

node is constrained by its residual energy, network-wideresidual energy, and network-wide power consumption.Therefore, the network-wide power consumption is bal-anced by leveraging the residual energy. In particular,the maximum allowed transmission power is propor-tional to the residual energy of the transmitting node.The fairness constraint factor α can be derived throughsolving MIN-MAX, and then is used for solving OPT-Fto obtain routing, rate control, power allocation.

MIN-MAX min α

s.t. (1)− (4), (6)− (10), and (13)

xl ∈ {0, 1}, Pl, rl(f) ≥ 0.

OPT-F: min Σi∈NEi

s.t. (1)− (4), (6)− (10), and (13)

xl ∈ {0, 1}, Pl, rl(f) ≥ 0.

The result of solving MIN-MAX is consistent withthat of solving OPT when all nodes have same residualenergy. Compared with OPT, the objective of OPT-Fis to minimize the network-wide energy consumptionwhile making sure that each node i has a minimumpower allocation among all maximum allowed power.Therefore, solving MIN-MAX firstly to obtain α and


0 x1 x2 x3 x4

ln(1

+x)

Fig. 2. An illustration of piece-wise linear approximation.

then solving OPT-F can provide a min-max guaranteedpower, and corresponding routing and rate.

It is obvious that MIN-MAX and OPT-F are alsoMINLP. So far, some techniques have been proposedto address general MINLP problems, e.g., branch-and-bound [24], outer approximation method [25]. However,these can only handle small-sized problems. In addition,as shown in OPT, MIN-MAX, and OPT-F, only (10)involving log function is a nonlinear equation. In gen-eral, solving a mixed-integer linear programming (MILP)problem is much easier than solving a MINLP problem.This motivates the efforts to transform the log functioninto linear functions as conducted in the literature [26].The idea is to use a series of piece-wise linear functionsto approximate the log function and replace it as shownin Fig. 2.

Recall that (10) can be written as

cl =Wl

ln 2ln(1 +

PlGlσ2

), l ∈ L. (14)

For simplicity of the presentation, by letting xl = PlGlσ2 ,

it can be rewritten as

cl =Wl

ln 2ln(1 + xl), l ∈ L. (15)

Variable xl is in the range [0, xmaxl ], which is evenlydivided into several segments with

xmaxl =PmaxGlσ2

.

Therefore, the piece-wise linear approximation ex-presstion can be obtained

cl =Wl

ln 2{m(k)

l [PlGlσ2

−x(k−1)l ] + ln[1 + x(k−1)l ]}, (16)

k = 1, ...,Kl, l ∈ L,

where Kl represents the total number of segments andthe slope of the k-th linear segment is denoted as

m(k)l =

ln(1 + x(k)l )− ln(1 + x

(k−1)l )

x(k)l − x

(k−1)l

.

If the number of linear segments is enough, the linearapproximation error will be very small, but the resultingcomputational complexity would be very high. Theoret-ically, the number of segments can be obtained when anapproximation error of each linear segment is prescribed.By using (16) to replace the nonlinear constraints in (10),the three MINLP problems, OPT, MIN-MAX, and OPT-F, can be transformed into MILP problems that can beefficiently solved by an off-the-self solver such as CPLEX[27]. Hence, after obtaining the results, the routing, flowrate, and power can be determined accordingly.

4 AN ENERGY-AWARE ROUTING ALGORITHMDESIGN

Although routing, rate, and power can be determinedthrough solving MINLP problems, much time is stillneeded to solve large-scale problems [28]. This sectionpresents an Energy-Aware Routing Algorithm (EARA)with the consideration of flow rate and power allocation.This algorithm can achieve the joint control of routing,rate, and power with no need of solving MINLP prob-lems. The computational complexity of the proposedEARA is controllable, and can be adjusted according tothe accuracy requirements. As a result, the algorithm canbe well applied in the practical multi-hop ER-WMNs.Moreover, the consumed energy and residual energyare simultaneously considered and a balance betweenthem can be attained. It is noteworthy that a multi-pathrouting is considered here and the split flows meet therate balance.

In this algorithm, a weighed Dijkstra’s shortest pathalgorithm is exploited to find the optimal routing. Sincethe energy consumption and residual energy should bejointly considered, the weight should have the follow-ing properties: 1) it can reflect the energy consumptionrelating to the flow rate and channel quality, and 2) itshould be inversely proportional to the residual energyof the transmission node and receiving node. The weightof link l, represented by wl, is defined as follows

wl =(Pl + Prec) · T

AiAj, (17)

where Ai = Bi/∑j∈N Bj indicates the energy level of

node i.As shown in (17), the power consumption and residual

energy are contributed to the weight. Since the value ofwl can reflect the consumed energy and residual energy,the energy-aware routing problem with the objective ofminimizing network-wide energy consumption undernetwork throughput constraint can be transformed intofinding a weighed shortest routing problem in multi-hopER-WMNs.

However, the weighted Dijkstra’s shortest path canonly support single-path routing rather than multi-pathrouting. Thus, this problem should be addressed to makethis algorithm support multi-path routing. In order todeal with this problem, the concept of unit flow is


Algorithm 1 The Energy-aware Routing Algorithm(EARA)Initialization:

Initialize unit flow rate δ, link rate rl = 0, the raterl(f) = 0 allocated to link l by flow f , and Bi(t)(i ∈ N , l ∈ L, f ∈ F). The number of allocatedunit flows num(f) is inialized num(f) = 0. Theflag flag(f) = true indicates that there are unitflows to be allocated. According to (18), N(f) isobtained. Based on Bi(t), a new network topologyGt is constructed through removing all sleep nodesand the maximum channel capacity cmaxl for eachlink is calculated according to (11).

Main Loop:1: If flag(f) == false (∀f ∈ F), go to Step (6).2: If rl+δ > cmaxl (l ∈ L), link l is removed and network

topology Gt is updated.3: According to (20), the weight wl for each link in

network Gt is calculated.4: The weighted Dijkstra’s shortest path algorithm is

used to find a shortest path for each active sessionand choose the session (e.g., f ) whose shortest pathhas the minimum weight to allocate a unit flow.

5: Update rl, num(f) = num(f) + 1. If num(f) >=N(f), flag(f) = false.

6: Merge all unit flows and compute the power con-sumption through (10) for each node.

proposed in this algorithm. The unit flow is an atomicflow with a constant flow rate, and cannot be splitfurther when it is delivered in ER-WMNs. The selectionof constant flow rate depends on the accuracy andcomputational complexity requirements. Let δ denotethe unit flow rate and a session is usually composed ofseveral unit flows. For session f with N(f) unit flows,its flow rate r(f) is

r(f) = δ ·N(f). (18)

By introducing the concept of unit flow, the multi-pathrouting problem for a session has become a single-pathrouting problem for multiple unit flows. The weightedDijkstra’s shortest path algorithm will be executed tofind a routing for a unit flow. Therefore, for session fwith N(f) unit flows, the weighted Dijkstra’s shortestpath algorithm should be executed N(f) times.

As shown in (17), in order to get the weight of eachlink l, transmission power Pl should be calculated firstly.Through transforming (10), Pl can be obtained as

Pl ≥ (2r′lWl − 1)

σ2

Gl, (19)

where r′

l = rl+δ indicates the expected rate when a unitflow is allocated to link l with rate rl. By the combination

of (17) and (19), the weight can be obtained

wl =((2

rl+δ

Wl − 1)σ2

Gl+ Prec) · T

AiAj. (20)

In addition to the routing and flow rate, the powerconsumption can also be obtained due to the relationshipbetween power consumption and data rate. Therefore,once the routing of each unit flow is determined, therouting, flow rate, and power consumption will be alldetermined.

At the beginning of each time slot, any node whoseresidual energy is lower than Boutage enters the sleepmode. A new network topology is then formed byremoving all such nodes. Since the weight dependson the link rate and residual energy, the weight of alink changes as a unit flow is allocated to this link.Accordingly, the weight should be updated according to(20) before a weighted Dijkstra’s shortest path algorithmis executed. After the weighted Dijkstra’s shortest pathalgorithm is executed, the shortest path for each sessioncan be found, such as, Path1, Path2, ..., Pathf , ..., f ∈ F .Among the whole searched paths for all sessions, a pathwith the lowest weight is identified and a unit flowis assigned to it. Then, the rate for all links along thepath is updated and a new loop starts. In the process ofexecuting this algorithm, if the sum of data rate of a linkl and δ exceeds the maximum capacity cmaxl , link l willbe removed from the network. That is, link l is no longerallocated a unit flow. It is noteworthy that a unit flow isallocated in each loop. This process does not cease untilall unit flows of all sessions have been assigned or thenetwork cannot accommodate more sessions. If all unitflows for all sessions are assigned to paths in multi-hopER-WMNs, the unit flows from same session are merged.In other words, the multi-path routing is achieved whilethe rate control and power allocation are also completed.

The energy-aware routing algorithm for each time slotis summarized in Algorithm 1.

5 SIMULATION RESULTS AND PERFORMANCEANALYSIS

This section aims to investigate the performance ofthe proposed algorithms, including OPT, OPT-F, andEARA, in multi-hop ER-WMNs by virtue of simulationexperiments. The considered network scenario is that arandomly generated multi-hop ER-WMN is deployed ina 1000m × 1000m square area. The maximum transmis-sion power is Pmax = 2w and the receiving power isPrec = 0.2w. Since the multi-hop WMN is considered asa time-division system, the energy consumption can beseen as the allocated power. Hence, the outage energythreshold is prescribed as the output power, Boutage =10w and the maximum output power is Bmax = 100w.The initial energy of each node in mult-hop WMNsis random number among [0, 100] when a networkscenario is generated. The energy replenishment rate


TABLE 1Each flow’s source node, destination node, rate requirement, and unit flow rate.

Session f Source node s(f) Destination node d(f) Rate requirement r(f) Unit flow rate δ1 1 12 3.0 0.012 2 15 4.0 0.01

Fig.3(a) OPT Fig.3(b) OPT-F Fig.3(c) EARA

Fig. 3. Comparison of routing and flow rate for OPT, OPT-F, and EARA in a 15-node multi-hop wireless mesh network.

is r(t) = 0.02w/(slot), and identical for all nodes. Thechannel bandwidth is Wl = 1MHz for all links andchannel gain varies between 5dB and 30dB. Within thisnetwork scenario, there are several sessions and thesource node and destination node of each session arechosen randomly.

5.1 The Routing and Flow Rate Allocation

This subsection shows the routing and rate allocationfor OPT, OPT-F, and EARA in the network scenario asdecribed in Fig. 3, where a 15-node multi-hop WMN israndomly generated. The initial residual energy is set asB = [80, 40, 70, 30, 80, 60, 35, 60, 20, 60, 70, 60, 40, 60, 90].There are two sessions in the network and relativeparameters are set as shown in Table 1.

Figs. 3(a), 3(b), and 3(c) compare the routing andflow rate allocation for OPT, OPT-F, and EARA. Theroutings and flow rates of session 1 and 2 are shownin each subfigures. Fig. 3 shows that flow routing forsession 1 and 2 are all multi-path and multi-hop. It canbe validated easily that the rate of all incoming flowsand the rate of all outgoing flows at a node satisfythe rate conservation. In addition, it can be seen thatsessions 1 and 2 always choose the path with minimalenergy consumption as long as flow rate does not exceedthe maximum capacity in OPT algorithm, OPT-F algo-rithm and EARA algorithm. This figure shows that theproposed scheme is effective, and can achieve efficientrouting and rate allocation.

0 200 400 600 800 1000 1200 1400500

600

700

800

900

1000

1100

1200

1300

1400

1500

Time (slots)

Ne

two

rk R

esid

ua

l E

ne

rgy (

w.s

lot)

EARA

OPT−F

OPT

Fig. 4. The change of the total residual energy along thetime.

5.2 Dynamics of Total Residual Energy and TheNumber of Sleep Nodes

Figs. 4 and 5 depict the changes of total residual energyand the number of sleep nodes along the time in OPT,OPT-F, and EARA algorithms. A 15-node multi-hopWMN is considered in these two examples and severalsessions are perpetually delivered over the network. Inorder to avoid the selected source node and destinationnode entering into sleep mode, the sessions occur ran-domly and periodically change.

Fig. 4 shows that the total residual energy is con-tinually degrading along the time. The reason is thatthe energy is consumed to deliver two sessions whilethe energy replenishment rate is much less than the


0 200 400 600 800 1000 12000

2

4OPT

0 200 400 600 800 1000 12000

2

4OPT−F

0 200 400 600 800 1000 12000

2

4EARA

Time (Slots)

Th

e N

um

be

r o

f S

lee

p N

od

es

Fig. 5. The change of the number of sleep nodes alongthe time.

energy consumption rate. In addition, the OPT algo-rithm has the highest residual energy among thesethree algorithms. This is because the OPT algorithmcan achieve the minimal energy consumption whereasOPT-F and EARA can obtain the balance between theresidual energy and energy consumption owing to thefairness constraint factor. Moreover, it can be seen thatthe two curves of OPT-F and EARA are much close. Itmeans that the similar performance can be achieved bythe proposed algorithm, EARA, compared with OPT-F.This phenomenon shows the effectiveness of the EARAalgorithm.

Fig. 5 illustrates that the number of sleep nodes isincreasing along the time. Meanwhile, the number ofsleep nodes of the OPT algorithm is more than that ofthe OPT-F algorithm and the EARA algorithm at thefirst stage. This is because OPT can achieve the optimalenergy consumption. Moreover, the network lifetime,i.e., the duration of delivering sessions, if using the OPT-F algorithm or the EARA algorithm is less than thatusing the OPT algorithm. In this paper, the lifetime isdefined as the network operation time until the residualenergy of the whole network is less than 30%. The reasonis that much more energy is consumed by the OPT-F andEARA algorithms, so some nodes can easily enter sleepmode after a duration.

5.3 Effect of Energy Replenishment Rate on Net-work LifetimeFig. 6 illustrates the effect of the energy replenishmentrate on network lifetime in multi-hop ER-WMNs. Theenergy replenishment rate varies in this simulation ex-periment and other parameters are set the same asdescribed above.

Fig. 6 depicts the change of the network lifetime withthe increasing of the energy replenishment rate, andcompares the network lifetime with different algorithms.As shown in this figure, the network lifetime is increas-ing when the energy replenishment rate grows. Owing

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

The Energy Replenishment Rate (w/slot)

Ne

two

rk L

ife

tim

e (

Slo

ts)

OPT

EARA

OPT−F

Fig. 6. The effect of energy replenishment rate on net-work lifetime.

0 2 4 6 8 10 120

1000

2000

3000

4000

5000

6000

Network Throughput (Mbps)

Ne

two

rk L

ife

tim

e (

slo

ts)

OPT

EARA

OPT−F

Fig. 7. The effect of throughput on network lifetime.

to the increasement of the energy replenishment rate,the residual energy of each node increases so that thenetwork lifetime can be extended. In addition, OPT canachieve the highest network lifetime because the energyconsumption of OPT is the lowest among these threealgorithms. It can also be seen that the curve of EARAis close to OPT-F, indicating that the proposed algorithmcan work very well.

5.4 Effect of Throughput on Network LifetimeFig. 7 reveals the effect of the throughput required byusers on network lifetime in multi-hop ER-WMNs. Inthis simulation experiment, the throughput requirementvaries and other parameters are set the same as describedabove.

It can be observed from Fig. 7 that the network lifetimeis gradually decreasing with the increase of the through-put. This is because more energy will be consumed todeliver the information over multi-hop ER-WMNs whenthe throughput required by users is increasing, resultingin that more nodes will enter into sleep mode and thenetwork lifetime will be reduced. In addition, among


OPT, OPT-F, and EARA, OPT algorithm can achievethe highest network throughput. The reason is that theenergy consumption by applying the OPT algorithm islowest due to no consideration of the balance of energyconsumption and residual energy. Moreover, this figureshows that the curve of EARA is close to OPT-F as well.

6 CONCLUSION

In this paper, the routing, rate control, and power allo-cation are investigated in multi-hop energy renewablewireless mesh networks and the problem of network-wide energy consumption minimization under networkthroughput constraint is formulated in a form of MINLP.To address the uneven routing problem which may incursome severe performance issues, fairness is taken intoaccount and the min-max fairness model is applied toaddress this problem. In addition, solving the MINLPproblem would time prohibitive, an energy-aware rout-ing algorithm EARA is proposed to deal with the jointcontrol of routing, rate, and power in practical multi-hop ER-WMNs. A weighted Dijkstra’s shortest pathalgorithm is applied to search an optimal routing. Fur-thermore, the concept of unit flow is proposed suchthat our Dijkstra-based algorithm can support the multi-path routing. Extensive simulation results are presentedand analysed to show the performance of the proposedschemes.

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Changqing Luo is an Assistant Professor atSchool of Computer Science and Technology,Huazhong University of Science and Technol-ogy, China. He received his Ph.D. degree inElectrical Engineering from Beijing University ofPosts and Telecommunications in 2011. Duringhis Ph.D. study, he worked as a visiting studentin Dept. of Electrical and Computer Engineer-ing at University of British Columbia (UBC) forhalf year, and also in Dept. of Systems andComputer Engineering at Carleton University for

half year. His current research focuses on algorithm and optimizationfor wireless networks, green communication, resouce management inheterogeneous wireless networks, and mobile cloud computing. He hasserved on the Technical Program Committee (TPC) of several confer-ences, such as IEEE ISWTA’13, ICCC’13-GMCN, ICC’12, PIMRC’12.He was the recipient of the Best Paper Award from IEEE GreenCom’13.

Shengyong Guo received the B.S. degree inInformation and Computing Science from South-central University for Nationalities in 2011. Heis now pursuing his M.S. degree at School ofComputer Science and Technology, HuazhongUniversity of Science and Technology, China.His research interests include the green commu-nication and wireless networks.

Song Guo received the PhD degree in computerscience from the University of Ottawa, Canadain 2005. He is currently a Senior AssociateProfessor at School of Computer Science andEngineering, the University of Aizu, Japan. Hisresearch interests are mainly in the areas ofprotocol design and performance analysis forreliable, energy-efficient, and cost effective com-munications in wireless networks. Dr. Guo is anassociate editor of the IEEE Transactions onParallel and Distributed Systems and an editor

of Wireless Communications and Mobile Computing. He is a seniormember of the IEEE and the ACM.

Laurence T. Yang (M’97) received the BE de-gree in Computer Science and Technology fromTsinghua University, China and the PhD degreein Computer Science from University of Victoria,Canada. He is a professor in the School ofComputer Science and Technology at HuazhongUniversity of Science and Technology, China,and in the Department of Computer Science,St. Francis Xavier University, Canada. His re-search interests include parallel and distributedcomputing, embedded and ubiquitous/pervasive

computing, Big Data, Cyber-Physical-Social Systems. His research hasbeen supported by the National Sciences and Engineering ResearchCouncil, and the Canada Foundation for Innovation.

Geyong Min (M’01) is a Professor of ComputerScience in the Department of Computing at theUniversity of Bradford, United Kingdom. He re-ceived the PhD degree in Computing Sciencefrom the University of Glasgow, United Kingdom,in 2003, and the B.Sc. degree in Computer Sci-ence from Huazhong University of Science andTechnology, China, in 1995. His research inter-ests include Next Generation Internet, WirelessCommunications, Multimedia Systems, Informa-tion Security, Ubiquitous Computing, Modelling

and Performance Engineering. His recent research has been supportedby UK EPSRC, Royal Society, Nuffield Foundation, and EuropeanFP. Prof. Min has published over 200 research papers in prestigiousinternational journals and reputable international conferences. He is anEditorial Board member of 9 international journals. He served as theGuest Editor for 17 International Journals and was the Chair or Vice-Chair of 30 international conferences/workshops. He was awarded theOutstanding Leadership Awards from IEEE International conferencesCIT2010/ScalCom2010/ICESS2010, ScalCom2009, HPCC2008.

Xia Xie is an Associate Professor at School ofComputer Science and Technology, HuazhongUniversity of Science and Technology, China.She got her Ph.D. degree in Computer Sciencefrom Huazhong University of Science and Tech-nology, China. Her current research includesdata mining, performance evaluation, and paral-lel and distributed computing.

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