2012 IEEE fifth International Conference on Advanced Computational Intelligence(ICACI)October 18-20,2012 Nanjing, Jiangsu, China

Energy-aware Resource Allocation Algorithm for Mobile Ad HocNetworks

Bingqing Han, Linyuan Liu

Abstract-Energy efficiency is a key factor in the design of adhoc networks. In this paper, we adopt the network utilitymaximization framework for joint power and rate optimizationat both transport and physical layer. Then, we propose a novelenergy-aware resource allocation algorithm by integrating thepower cost into the objective function. The proposed algorithmhas been implemented in a distributed manner. Simulationresults show that the proposed algorithm not only has goodconvergence, but also improve the energy efficiency of thenetwork significantly.

I. INTRODUCTION

M OBILE ad hoc networks (MANETs) representautonomous distributed systems that areinfrastructure-less, fully distributed, and multi-hop in

nature. There is considerable interest in designing andimplementing such networks to provide services in a varietyof diverse applications, e.g., disaster relief and temporarymeetings. Recently, due to increasing popularity ofmultimedia applications, QoS (Quality of Service) support inmobile ad hoc networks has become an important yetchallenging objective. However, due to the limited bandwidthand scarce energy, the conflict between the wireless resourceand QoS requirements of multimedia service growsincreasingly. How to use the energy as efficiently as possibleis the main challenge in designing ad hoc networks.

The energy efficiency is a key factor in the design ofad hocnetworks. With the scarce energy constraints in the ad hocnetworks, the energy consumption for data transmission,routing establishment and maintenance should be kept as lowas possible. Therefore, the goal is to maximize the flow rate ofthe network subject to some kind of energy constraints, i.e.,the sum of all the transmission power should be below acertain threshold. During the past few years, there has beensignificant effort in the design of energy efficient protocolsfor ad hoc networks. From the users' perspective,energy-saving communications will enlarge the autonomy ofbattery powered devices. The great challenge in ad hocnetworks is how to allocate the scarce energy resources,which are more significantly limited in wireless networksthan in wired networks.

This work was supported in part by the Jiangsu Provincial Natural ScienceFoundation of China (Grant No. BK2011692), and the Natural ScienceFoundation of Jiangsu Higher Education Institutions of China (GrantNo. 1OKJB520008)

B Han, corresponding author, is with the Department of InformationScience, Nanjing Audit University, Nanjing, 210029 China, (phone:025-86550352; e-mail: hbqsky@163.com).

L Liu is with the Department of Information Science, Nanjing AuditUniversity, Nanjing, 210029 China, (e-mail: liulinyuan@163.com).

978-1-4673-1744-3/12/$31.00 ©20 12 IEEE 10

Thus far, various techniques [1]-[4] have been proposed toreduce the energy consumption for the transmission nodes inmobile ad hoc networks. In [5], the authors propose alow-complexity and low-energy consumption modulation forwireless sensor networks (WSNs). This algorithm is based onthe use of Luby Transform (LT) codes along with a MultipleFrequency-Shift Keying (MFSK) modulation. A differentapproach has been followed in [6] where joint power and rateproblem is addressed as a trade off to be balanced. The mainpoint of the scheme is that each node determines itstransmission power and rate as a fictitious game to attainglobal utility. This is similar to the utility-based algorithmconsidered by [7]. The policy can adjust power and rateadaptively with both consideration of channel conditions andchanges. In [8], a rate control policy is proposed to minimizethe total transmission energy while satisfying the QoSconstraints. In [9], the authors consider a wirelessenergy-harvesting node for which they find the minimumtransmission completion time in two situations. However, theauthors of [9] assume that the battery capacity of the node isinfinite. A different path is taken in [10], where the authorsintroduce a pricing function to maximize the user's individualinterest without much attention to other users' utility. Most ofthese algorithms are based on the network utilitymaximization (NUM) framework [3] which is formulated as afunction of power and rate control strategy. In the aboveschemes, engineers have tried to develop designs thatconsume as little energy as possible. However, energyefficiency has not traditionally been the target of the designbut just a constraint. Also, most of the algorithms do not havethe energy-aware capability and can not reduce unnecessaryinterference in the network.

In this paper, we propose a new solution for energyefficient network operations in ad hoc networks. We use thenetwork utility maximization (NUM) framework for jointpower and rate optimization at both transport and physicallayer. Power control is conducted at each link to achieve highenergy efficiency, while rate control is done at the transportlayer, aiming to support high network throughput. The majordifference of our algorithm compared with previous schemesis that we propose the energy-aware utility by integrating thepower cost into the objective function, rather than as aconstraint. Compared with previous works, this algorithm cansignificantly improve the energy efficiency of the network.

The rest of this paper is organized as follows. In Section 2,we introduce the mathematical model and explain theterminology used in this paper. Section 3 develops anenergy-aware resource allocation algorithm with utility

(3)

constraints. Section 4 reports our experimental results, and isfollowed by some discussions. Finally, we conclude the paperin Section 5.

II. MATHEMATICAL MODEL

A. Network ModelA wireless ad hoc network is modeled as a directed graph

G == (V,E) , where V is the set of nodes and E is the set ofwireless links. Each node v E V has transmission range d.;and interference range dint. A transmission link (u, v) E E ifnode v is in the transmission range of node u. These links areshared by a set of N flows, where flow f uses the set ofEfeE of links (f == 1,2, ... ,N). Also we denote the set of

links comprising flow f as E (f) . If either the source or thedestination of one subflow is within the interference range dintof another flow, the link flows are said to contend.

Then we will derive our node interference model. First weconvert the connectivity graph G into a link contention graphGc = (~,Ee) based on the contention relationship betweendifferent link flows. Gc is an undirected graph. The vertex setVc contains all the link flows in the network. In other words,each link in E(G) of the original graph G is converted into avertex in Vc, i.e., ~ == E . There is an edge e E E; between twovertices (a,b) and (iJ) in the contention graph if link (a,b) andlink (iJ) cannot transmit simultaneously in the original graphG. In the protocol model [2], the transmission over link (u, v)is successful if (1) the distance between these two nodes iswithin the transmission range of node u, i.e., duv ::::; dtx ; (2) anyother transmitting node (k 7:- u ) should be out of theinterference range of the receiving node v, i.e., dkv > dint'

With the contention graph Gc, we can derive anotherimportant concept called maximal clique. In a graph, a cliqueis defined as a subgraph whose vertices are adjacent to eachother. A maximal clique is referred to as a clique such that noother clique is its superset. We denote the set of maximalcliques of a contention graph as Q. Each maximal cliqueQn (n == 1,2, ... ,N) in the contention graph may consist ofseveral links in the connectivity graph and each link in theconnectivity graph may belong to several maximal cliques. Inour scheme, a maximal clique can also be considered as alimited resource allocation unit contended by various flows.Within the maximal clique, only one of the contendingsubflows may transmit at any given time.

Based on the relationship between link flows and maximalcliques, we define a clique-link incidence matrix Q == {Qqz} as

{I, if clique q contains link I

Q z == (1)q 0, otherwise

B. Energy Consumption ModelConsider an ad hoc network with N nodes and L links,

where source node i communicates to destination node j on asingle hop. It is assumed that all the nodes can detecttransmissions from each other. The channel condition of eachlink is time-varying since it depends on the transmission

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power and the thermal noise from adjacent nodes. Normally,the link (i, j) is affected by path loss, shadowing andmulti-path fading [11]. Further, we consider P as a set ofpower levels P == {Pmin,. .. ,Pmax} where Pm in and Pm ax are theminimum and maximum transmit power allowed to sender i.Also, we define data rate R as a set of definite valuesR == {Rmin," ' ,Rmax } constrained by the minimum and themaximum data rates. It is assumed that all users in the wirelessnetwork have the same rate and power set. Let hij be the directchannel gain between sender i and receiver j. We can deduce

~ == hij~ (2)

where ~ is the transmit power of node i and ~ is thereceived power at node j.

Let 1]0 be the thermal noise. Then, thesignal-to-interference-plus-noise ratio (SINR) [11] on linkI == (i, j) is given by

h.. PSINR - lJ 1

Z - L hkj~ +1]0kt:-i,j

where L hkj~ represents the sum of interference power I ij

at node j due to the transmission of other users in the networkand

Pzmin < Pz < PzIrulX , VI E L (4)We assume that each link has a unique bandwidthB. From

Shannon theory of communication [12], the link capacity czfor link I is defined as

Cz == Blog(SINRz ) (5)

where Cz reflects a theoretical upper bound on the achieveddata rate for link I.

III. ENERGY-AWARE RESOURCE ALLOCATION ALGORITHM

We now present the energy-aware resource allocationalgorithm with utility constraints. Our derivation will be basedon the network utility maximization framework, which is aconvex optimization method developed for optimal ratecontrol over communication networks. We aim to calculatethe power allocation and rate allocation vector such that thefairness among flows is maintained and the total energyefficiency is maximized.

In this section, we focus on the energy-aware resourceallocation problem. Particularly, we integrate the power costinto the objective function, rather than as a constraint.

A. Problem FormulationSince the main goal of this paper is to improve the energy

efficiency of the network, it is common to define the user'scost function of the transmit power Pz related with the user'ssignal-to-interference-plus-noise ratio, i.e.

Cost, (Pz) == fJzPz (6)where fJz are non negative constants and the cost function canimply a weighted value of the transmit power.

For each flow f E F , we associate with the rate x a utilityfunction Uf (xf ) , which measures the degree of satisfaction

of its corresponding end user given rate xf . Following typical

definitions of utility, we assume that the function Uf (xf) isstrictly increasing, concave, and twice continuouslydifferentiable [2]. Moreover, by choosing appropriate utilityfunctions, different fairness models such as max-min andweighted proportional fairness can be achieved.

Based on the previous discussions, we can formulate theresource allocation problem as follows:

P :maximize ~Uf(xf)-~Costz(Pz)fEF ZEL

(14)

(11)

~(t+l)=[~(t)-rdD~~(t))r (15)

where y>O is a constant step size and [z]+= max {z, O}.By substituting (14) into (15), equation (15) becomes

Az(t+1)==[~(t)-lcz(p)- ~ Xf(A)]]+ (16)l fEF(Z)Given A, both (12) and (13) are strictly convex

programming. Hence, the two equations have the uniquesolution x; (A) and Pz* (A) respectively.

= maxL1(x,A)+maxL2(P,A)XEX PEYThen, the dual function D(A) can be decomposed into the

following two sub-problems:D1(A) == max Z, (X,A)XEX

[ ](12)

=max ~Uf(xf)-~(Az log ~ xf)XEX f Z fEF(Z)

D2 (A) == max L2 (P, A)PEY

( J(13)

=max ~~ 10g(cz(P))- ~Costz(Pz)PEY Z Z

For each flow f, Af may be interpreted as the shadow price

of flow f Also, Az can be viewed as the link price one has topay for the link I. Thus, by solving the two sub-problems, wecan obtain the joint power and rate allocation that maximizesthe network performance under the constraints of powerconsumption and wireless link capacity. Obviously, equation(13) is related to energy efficiency and provides a useful toolfor power control.

Note that Lagrangian function L(X,P,A) is strictly

concave with respect to variable (x, P) . Hence, the dualfunction D(A) is continuously differentiable. We can solvethe dual problem using the sub-gradient method. According toequation (11), the sub-gradient of D(A) is given by

dD(A) = cz(P)- ~ Xf(A)aAz fEF(Z)

The Lagrange multiplier Az is adjusted in the oppositedirection to the gradient VD(A) as follows:

B. Flow Rate AllocationThe sub-problem D1(A) represents an optimal rate control

sub-problem for each variable xf. The gradient of L1(x,A)with respective to x is then given by

dLj(X,A) =U~(xf)- ~ A (17)aXf fEF(Z)

Consequently, we can derive the following algorithm ofsource rate adaptation for flow I

where the corresponding dual function is given byD(A) == max L(X,P,A)XEX,PEY

(8)

(9)

(7)

(10)

subjectto O~xf ~Mf' VIE F

subjectto O~xf ~Mf' VIE F

Pzmin <Pz <Pzmax, VI E L

loge ~ xf)~log(cz(P)), V/ELfEF(l)

Noticing that Cz(P) is concave and positive, log(cz(P)) isalso concave. It is easy to prove that problem (8) is a convexoptimization problem. Then the Lagrangian form of theproblem P is defined as follows:

L(X,P,A) == ~Uf (x f) - ~Cost, (Pz)f z

- ~AJIog( ~ xf )-lOg(Cz(P))]z l fEF(Z)

where A is the vector of Lagrange multipliers associated withthe capacity constraints.

The dual problem of Pcan be defined as:D: minD(A)

2~O

Pzmin <r, < Pzmax, V I E L

~ Xf ~Cz(P), VIE LfEF(Z)

where Pzmin and Pzmax are minimum and maximum transmit

power for link I respectively, and M f is the maximalbandwidth needed by flow f On the above formulation,Uf (x f) is the utility function of flow rate xf Since the costfunction of the transmit power can be defined asCost, (Pz) == fJzPz according to equation (6), fJz ~ 0 can beinterpreted as a tradeoff factor to balance the cost of transmitpowers and the network utility of flow rates. The lastconstraint indicates that the sum of flow rates traversing awireless link I should not exceed the capacity of the link.

In (7), the goal is to maximize the network utility of flowrates at the transport layer while minimizing power allocationfor all links at the physical layer. In order to solve the jointoptimization problem P, we tum our attention to the dualproblem D ofP.

Problem P appears to be a non-convex optimizationproblem which is difficult to solve, since the last constraint in(7) is non-convex. However, we can make a logarithmicprocessing and transform the problem into a convexoptimization problem as follows:

p :maximize ~Uf(xf)-~Costz(Pz)fEF ZEL

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=L(/LzBlog(SINRz))- LfJ~ (19)z z

Algorithm EARA:Rate Allocation1. Receives rates xI (t) from all flows / where

/ E F(/)2. Update link price as follows

/Lz(t+1):=[Az(t)-lcz(p)- L Xf(A,)J]+l IEF(l)

3. Send /Lz (t +1) to all flows/such that / E F(/)

4. Adjust the flow rate at times t:= 1,2, ...

xf (t +1)= [Xf (t) + f.1 a\~f(t))r5. Send xI (t +1) to all links on its path

IV. SIMULATION RESULTS

In order to evaluate the performance of EARA, we havedeveloped a simulator based on ns-2 simulator. A wireless adhoc network of size 1200 m x 1000 m is simulated, on which70 nodes are randomly generated. Each node n has minimumtransmission power limit ~min:= 10 and maximum

transmission power limit ~max := 100 . In all our experiments,the utility function of every flow / is U I (xI ) := logexI) forimposing proportional fairness among the flows, and theenergy-cost function is Cost, (Pz) := 3Pz . The constantstep-sizes in (16), (18) and (21) are set to y=O.l, f.l =0.05 andv=0.05 respectively.

In figure 1, we can see how the flow rates are adaptivelyallocated as time changes. In the wireless scenario, there arethree network flows. At the beginning, the data rate of flow1 isfastest, while flow2 and flow3 are very close to each other. Astime goes, the data rate of flow1 drops quickly from 300 to170, while flow2 and flow3 increase their data rates gradually.This also reflects the law of supply and demand. In the earlytime, flow1 chooses a higher data transmission rate since itsprice is lower than others. In the middle stage, flow2 thenchooses a lower transmission rate as its price increases. Later,they kept to adjust and eventually converge to the optimalvalue. So, the data transmission rate can be adaptivelyallocated with the price changes. In fact, based on theproposed algorithm EARA, the three flows can achieve theiroptimal rates within short times. The simulation results

Power Allocation1. The sender on link I calculates the interference level

and message mz(P) based on locally measuredinformation

2. The transmitter on link I broadcast the message to allthe neighborhoods

3 . Each link update its transmission power as follows

Pz (t +1) := [Pz (t) +v aLz(P(t)) ]Pzmax

dPz minPz

4 . Send new Pz (t +1) to all nodes along the link

(18)

(20)

Then, we can derivedL2 (P,/L)

d~

Xf (t +1)= [Xf (t) + f.1 a\~f(t))rwhere f.l is a positive step size.

C. Power AllocationThe power control and energy issues can be dealt with by

sub-problem D2 (/L) . Note that the objective functionL2 (P, /L) is differential with respect to variable P. Accordingto equation (5), (6) and (13), we have

L2 (P , /L ) := L~ 10g(cz(P))- LCostz(~)z z

where/LzSINRzmk := (21)

~hll 10g(SINRz)represents the message information passed from thetransmitter on the link k.

Thus, power allocation can be iterated as follows:

~ (t +1):= [Pz (t) + v aLz(P(t)) ]p,mu (22)d~ min

Pz

where v is a small step size and [z]{ denote the projectiononto the range [Pzmin, Pzmax ] .

Note that mk as defined in (21), represents the interferencelevel on link k. So it can be easily measured at the receiver oflink k.

D. Algorithm For Energy-aware Resource AllocationBelow, we will present our energy-aware resource

allocation algorithm (EARA).The EARA algorithm will proceed a two-stage iteration.

First, the link price and power price is updated based onlocally measured information. Then, the rate allocation andpower allocation process is executed after the price is updated.Note that the flow rate and power control messages areexchanged among the interfering nodes. The EARAalgorithm is expected to be implemented in a distributedmanner. Since the power control process and the rateallocation process belong to the gradient projection schemes,the EARA algorithm will converge to the optimal solutionwith an appropriate step size. EARA will repeat the two stepsuntil the flow rates and the transmit powers converge.

13

further verify the correctness and convergence of the EARAalgorithm.

Fig. 1. Rate allocation of different flows

As energy efficiency is our main performance metric, wewill compare our solution (EARA) with two other resourceallocation schemes. One is a simple resource allocationalgorithm (SRA). The basic idea of SRA is to maximize theutility of a single-user rather than all users. So, SRA can notachieve the global optimum. The other is similar to the"Jointly Optimal Congestion Control and Power Control"algorithm proposed by Mung Chiang [12]. We make somemodifications and call it PowerRA. This is a resourceallocation algorithm based on power control.

Fig. 2. Energyefficiency of various algorithms

Figure 2 shows how the energy efficiency of the threealgorithms behaves when subjected to scenarios with differentnumber of users. On the X-axis we have the number of users,and on the Y-axis the energy efficiency which refer to the totalutility of the users. We can see that EARA exhibits averagely51% higher energy efficiency than PowerRA and almost 2times more than SRA. When the user number is more than 13,the performance of PowerRA and SRA begins to decline,while EARA is still rising. When the user number reaches 19,EARA performs much better than PowerRA and SRA. In allexperiments, PowerRA performs slightly better than SRA,while EARA performs best among the three algorithms. Themain reason for the above results is that EARA has theenergy-aware feature and can allocate rate and power moreefficiently. Especially in scenarios with heavy traffic, EARAperforms much better than PowerRA and SRA because EARA

14

can achieve the global optimum with both consideration offlow rate and power control.

V. CONCLUSIONS

In this paper, we have presented a novel energy-awareresource allocation algorithm for mobile ad hoc networks.First, we adopt the network utility maximization frameworkfor joint power and rate optimization at both transport andphysical layer. Second, we present our resource allocationalgorithm by integrating the power cost into the objectivefunction. The new algorithm has been implemented in adistributed manner. Simulation results show that EARAalgorithm has good convergence and can improve the energyefficiency of the network significantly.

ACKNOWLEDGMENT

This research was supported by the Jiangsu ProvincialNatural Science Foundation ofChina(Grant No.BK2011692),and the Natural Science Foundation of Jiangsu HigherEducation Institutions 0 f China(Grant No.10KJB520008).

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