A Novel Flocking Inspired Algorithm forSelf-Organization and Control in Heterogeneous

Wireless NetworksHaijun Zhang1, Jaime Llorca2, Christopher C. Davis3, and Stuart D. Milner4

1Department of Electronic EngineeringCity University of Hong Kong

2,3Department of Electrical and Computer Engineering4Department of Civil and Environmental Engineering

University of MarylandCollege Park, MD 20742, USA

Abstract—This paper presents a new model and algorithmfor slef-organization and control of a class of next generationcommunication networks: hierarchical heterogeneous wirelessnetworks (HHWNs), under real world physical constraints. Anature inspired flocking algorithm (FA) is investigated in thiscontext. Our model is based on the control framework atthe physical layer presented previously by the authors, wherenetwork robustness is characterized in terms of the system’s po-tential energy, and control mechanisms are designed to minimizepotential energy for optimized network performance. We firstfocus on the modeling of HHWNs under real world physicalconstraints. Second, we propose a new FA for self-organizationand control of the backbone nodes in an HHWN by collectinglocal information from end users. Our algorithm is examinedin our built simulation platform that supports various dynamicscenarios. Experimental results demonstrate that FA outperformscurrent algorithms for the self-organization and optimization ofHHWN under real world physical constraints.Index Terms—Heterogeneous wireless networks, directional

wireless communication, self-organization, flocking algorithm.

I. INTRODUCTIONRecent advances in directional wireless communications for

providing broadband wireless solutions are making next gen-eration communication networks increasingly complex. Thesenetworks are characterized by hierarchical architectures, withheterogeneous properties and dynamic behavior. The need forubiquitous broadband connectivity and the capacity limitationof homogeneous wireless networks is driving communicationnetworks to adopt hierarchical architectures with diverse com-munication technologies and node capabilities at different lay-ers that provide end-to-end broadband connectivity in a widerange of scenarios [1-3]. In particular, HHWNs use a wirelessbackbone network consisting of a set of base station orbackbone nodes that use directional wireless communicationsto provide end-to-end broadband connectivity to capacity-limited ad hoc networks and/or end hosts. As an example,backbone-based wireless networks use a two-tiered networkinfrastructure, which consists of a set of flat ad-hoc wirelessnetworks and a broadband wireless mesh backbone network of

higher capability nodes. In this architecture, backbone nodesuse directional wireless communications, either free spaceoptical (FSO) or directional radio frequency (RF), to aggregateand transport traffic from hosts at lower layers. The advantagesof directional wireless communications can be well exploitedat the upper layer, where line of sight constraints are lessrestrictive and interference-free, point-to-point communicationlinks can provide extremely high data rates [1-3].The most important concern in HHWNs is to assure net-

work coverage and backbone connectivity in dynamic wirelessenvironments. Llorca et al. [4] first proposed a quadraticoptimization method to jointly control network coverage andbackbone connectivity. They defined a quadratic energy func-tion to characterize the robustness of HHWNs and designeda force-driven algorithm that dynamically drives the networktopology to minimum energy configurations based on localforces exerted on network nodes. A quadratic model of theenergy function was then extended to an exponential modelthat takes into account the effects of atmospheric attenuationon the propagation of electromagnetic energy in directionalwireless links [5]. The convex energy model was used bythe authors to develop an Attraction Force Driven (AFD)algorithm, where the net force used to relocate the backbonenodes is computed as the negative gradient of the energyfunction at the backbone nodes locations. By consideringpractical power limitation constraints at the network nodes,recently Llorca et al. [1] further extended the energy modelusing the Morse potential [6], i.e. Morse Force Driven (MFD)algorithm, such that the convex energy function [5] wastransformed into a non-convex function where communicationenergy saturates with distance emulating the effects of linkbreaking due to power limitation constraints. Based on thisnon convex energy model, the authors developed a hybridcontrol model where communication links are retained orreleased autonomously based on their cost within the networkarchitecture [1]. Although these models take into account someconstraints on communication links such as transmitted power

978-1-4244-7177-5/10/$26.00 © 2010 IEEE ISSNIP 2010239

limitations, a comprehensive model with real world physicalconstraints such as taboo areas has not yet been developed.In this work, we show that when adding real world con-

straints into the problem, such as power limitations, capacityof the base stations and blockage from terrain, the problem canno longer be formulated as a convex optimization problem.This research thus focuses on the modeling of HHWNs underreal world physical constraints at the physical layer, andthe development of effective biology-inspired algorithms fortopology control in dynamic scenarios.

II. NETWORK CONTROL MODEL

The topology control problem in HHWNs can be effectivelyformulated as a potential energy minimization problem [4, 5].Llorca et al. defined the potential energy of a communicationsnetwork as the total communications energy stored in thewireless links forming the network, as follows:

U(bij , hik, B1, B2, ..., BN ) =α · ∑N

i=1

∑Nj=1 biju(Bi, Bj) +

∑Ni=1

∑Mk=1 hiku(Bi, Tk)

,

(1)where Bi is the location of backbone node i, Tk is the locationof terminal node k, N is the number of backbone nodes, Mis the number of terminal nodes, α (α ≥ 0) is a weightingparameter to balance the energy used for forming the meshbackbone network and covering end hosts, bij and hik are thebinary variables, which are given by

bij ={

1 if(i, j) ∈ ΛB is connected0 otherwise

, (2)

where ΛB refers to the backbone topology, and

hik ={

1 if(i, k) ∈ ΛT is connected0 otherwise

, (3)

where ΛT refers to the coverage topology, i.e. hik = 1indicates that backbone node i covers terminal node k. Themeasurement of communication cost u(Bi, Bj) is usuallyassociated with the Euclidean distance between link ends (i, j)and is precisely defined as the communications energy per unittime required to send information from node i and node j atthe specified BER (bit error rate) [2, 5]

uij = P jR0

4πDi

T AjR

(exp(γ||Bi − Bj ||))(||Bi − Bj ||2), (4)

where P jR0 is the minimum received power, Di

T is the direc-tivity of the transmitter antenna, Aj

R represents the effectivereceiver area and γ is the scattering coefficient [7].Note that the first term in the cost function in Eq. (1),

denoted by UBB , represents the total energy stored in thedirectional wireless links forming the mesh backbone network,and the second term in Eq. (1), denoted by UBT , represents thetotal energy stored in the wireless links covering the end hosts.Thus, UBB measures the cost for the backbone connectivity,and UBT measures the cost for network coverage [4].

The topology control problem in HHWNs is then formulatedas an energy minimization problem of the following form:

min{U(bij , hik, B1, B2, ..., BN )}(Bi = (xbi , y

bi , z

bi ), Bi ∈ 3),

(5)which is subject to Eqs. (2) and (3). Note that the optimizationproblem formulated in Eq. (5) is performed over: bij , theassignment of directional wireless links between backbonenodes; hik, the assignment of wireless links between backbonenodes and covered end users; (B1, B2, ..., BN ), the location ofthe N backbone nodes. But the link assignments bij and hik,and the location of backbone nodes (B1, B2, ..., BN ) must besubject to real world physical constraints, which include:

• Power limitation: refers to the maximum power at atransmitter. In practice, the increase in transmitted powerneeded to maintain a given link BER is limited by themaximum power at the transmitter. Both backbone nodesand terminal nodes have power limitations because eitherof them might be a transmitter or a receiver.

• Traffic capacity: refers to the maximum traffic that abackbone node can receive and transfer. In this paper, thecapacity of a backbone node is defined as the maximumnumber of terminal nodes a base station can handle.

• Distance threshold: is defined as the minimum distancefor a backbone node to avoid collisions with anotherbackbone node or a terminal node.

• Taboo areas: refers to constraints imposed by the phys-ical world such as geographic obstacles (e.g. mountainsand high-rise buildings), undesired weather events (e.g.heavy clouds or regions of precipitation), and securityareas (e.g. signals are fully blocked due to securityrequirements). It is worth noting that these taboo areasare dynamic. Note that the taboo area, for a particularbackbone node changes dynamically with the movementof the end user (here, we assume total blockage if thereis no direct line of sight between end user and backbonenode; in fact, the signal attenuation due to blockage canbe incorporated into the link energy function in Eq. (4)).

Let Θ represent the set of physical constraints, which includespower limitation Cp, traffic capacity of backbone nodes Cc,minimum physical distance Cd, and taboo areas Ct, i.e. Θ ={Cp, Cc, Cd, Ct}, then the optimization problem described inEq. (5) is transformed into

min{U(bij , hik, B1, B2, ..., BN )}s.t. Θ = {Cp, Cc, Cd, Ct} . (6)

The energy based models such as AFD model [4] and MFDmodel [1], while leading to efficient, scalable and physicallyaccurate control methods for self-organization in HHWNs, areparameter-sensitive and require knowledge of the dynamics ofthe channel as well as explicit formulations, which can bedifficult to obtain when considering dynamic taboo areas suchas atmospheric agents and terrain. Furthermore, the presenceof taboo areas makes gradient-based methods not able toguarantee convergence to global optimal solutions. Therefore,in this research, we propose to use a novel approach for

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the self-organization and optimization of HHWNS, which donot require explicit knowledge of the channel nor rely ongradient methods: FA, which uses heuristic forces based onlocal information for the system’s self-organization.

III. FLOCKING ALGORITHM

The earliest works on flocking are derived from the an-imation of flocking dynamics of birds. Reynolds et al. [8]developed a basic flocking model using three simple steeringrules to control individual agents in the flock. These steeringrules [8] include

• Alignment: steer to move toward the average heading ofneighboring flock mates,

• Separation: steer to avoid collision with other local flockmates,

• Cohesion: steer to move toward the average position ofneighboring flock mates.

The size of a neighborhood is determined by the sensor rangeof a flocking agent. Since the movement of an agent is onlybased on local information, the computational time complexityis significantly reduced. These three rules in Reynolds’s model[8] are sufficient to emulate the group behavior in nature.Recall that the objective in HHWNs is to optimize the

total energy cost of the system while guaranteeing end-to-end communications with physical constraints. We indicatethat the use of energy functions makes it challenging toobtain the objective when considering physical constraints thatwe include in this research. In this section, we develop anew flocking algorithm that uses heuristic forces to straight-forwardly model the effects of various constraints on thenetwork, while preserving the distributed nature and low timecomplexity of the entire system.

A. Flocking Rules

In this paper, each backbone node represents an agent ina flock. A terminal node Tk(s) is assumed to be stationaryduring the movement of backbone nodes due to the timedelay, which is consistent with practical situations. Here srepresents the time series of terminal node dynamics. Thustime t ∈ [0, tmax] (tmax is the stopping time point) withrespect to backbone nodes is a sub-interval of [s − 1, s] withrespect to terminal nodes. A backbone node i at time t ischaracterized by its location Bi(t) associated with the realcoordinates (xb

i (t), ybi (t), z

bi (t)) and its force vector (or veloc-

ity vector) υi(t). Let bij(t) and hik(t) be the link assignmentvariables for backbone-to-backbone links and backbone-to-terminal links at time t, respectively. The forces acting onbackbone node i include

• Survival force: makes a backbone node to try to maintainconnection to those terminal nodes it had covered at thelast time period s − 1. This force enables the effectivereduction in the loss of the closest terminal nodes tobackbone node i due to the existence of taboo areas such

as geographic constraints. The force is given by

υiagn =

∑Mk δ(hik(s − 1) = 1)(Tk(s − 1)− Bi(t))∑M

k δ(hik(s − 1) = 1),

(7)where δ(·) is an indicator function (its value is 1 if thestatement within its argument is true, and 0 otherwise).

• Repulsion force: is produced by three sources: terminalnodes covered by the backbone node i at the bottomlayer in HHWNs, neighbor backbone nodes connectedto backbone node i at the upper layer, and the terrain.The whole repulsion force is determined by

υipul = υi,BT

pul + υi,BBpul + υi,ter

pul , (8)

υi,BTpul = −

∑Mk δ(Hsta)δ(D

pul,BTsta )(Tk(s)− Bi(t))∑M

k δ(Hsta)δ(Dpul,BTsta )

,

(9)

υi,BBpul = −

∑Nj δ(bsta)δ(D

pul,BBsta )(Bj(t)− Bi(t))∑N

j δ(bsta)δ(Dpul,BBsta )

,

(10)υi,ter

pul = δ(Zsta)((0, 0, zb,proi (t))− Bi(t)), (11)

where, Hsta denotes the statement (hik(t) = 1), Dpul,BTsta

denotes the statement (dBT (Tk(s), Bi(t)) ≤ dBTth,pul),

bsta denotes the statement (bij(t) = 1), Dpul,BBsta denotes

the statement (dBB(Bj(t), Bi(t)) ≤ dBBth ), Zsta denotes

the statement (zbi (t) − zb,pro

i (t) ≤ dterth ), dB·(·) = || · ||

is a distance function, dBTth,pul is the distance threshold

between backbone nodes and terminal nodes, dBBth is

the distance threshold between backbone nodes, dterth is

the minimum distance between a backbone node and theground, which is measured by the height difference in thez coordinate, i.e. zb

i (t)− zb,proi (t). Note that the exerted

repulsion force υi,terpul avoids collision with mountains or

other obstacles on the ground. The repulsion force alsocontributes to the balance between network coverage andbackbone connectivity and reduces the risk of solutionsgetting stuck in local minima, which it can be observedfrom the experiments presented in section 4.3.

• Retention force: is produced by two sources and it iscalculated according to

υiten = υi,BT

ten + υi,BBten , (12)

υi,BTten =

∑Mk δ(Hsta)δ(D

ten,BTsta )(Tk(s)− Bi(t))∑M

k δ(Hsta)δ(Dten,BTsta )

,

(13)

υi,BBten =

∑Nj κijδ(bsta)δ(D

ten,BBsta )(Bj(t)− Bi(t))∑N

j δ(bsta)δ(Dten,BBsta )

,

(14)where, Dten,BT

sta denotes the statement (dBTth,pul ≤

dBT (Tk(s), Bi(t)) ≤ dBTth,lea),D

ten,BBsta denotes the state-

ment (dBBth ≤ dBB(Bj(t), Bi(t))), dBT

th,lea is anotherdistance threshold between backbone nodes and terminalnodes (we explain it in the following section), and κij is

241

a coefficient that considers the effect of sharing the loadbetween backbone nodes, which is defined by

κij = exp

(Rj −

∑Mk δ(Hsta) +

∑Mk δ(Hsta)

Rj

),

(15)where Rj is the capacity of the backbone node j.

• Release force: is used to consider the effect of powerlimitation, which is controlled by a distance thresholddBT

th,lea. Here, we only consider the release force betweenbackbone nodes and terminal nodes because a large powerbetween backbone nodes is usually available in practiceto assure the connectivity at the upper layer. The releaseforce is given by

υilea =

∑Mk=1 γikδ(Hsta)δ(D

lea,BTsta )(Tk(s)− Bi(t))

δ(Hsta)δ(Dlea,BTsta )

,

(16)where, Dlea,BT

sta denotes the statement (dBTth,lea ≤

dBT (Tk(s), Bi(t))), and γik is a release coefficient de-termined by

γik = exp(−ε

(dBT (Tk(s), Bi (t))− dBT

th,lea

)), (17)

in which ε is a positive constant with small value, in thispaper we set ε = 0.001.

In order to achieve comprehensive flocking behavior, wesum up all the forces described above to obtain a net velocityfor the backbone node i as follows

υi(t) =υiten(t)+wpυ

ipul(t)+wlυ

ilea(t)+waυi

agn(t), (18)

where wp, wl, wa are positive weighting parameters to bal-ance the effects of the different forces. Then the location ofbackbone node i is updated according to the following

Bi(t+ 1) = Bi(t) + ρ · υi(t). (19)

Based on this flocking model, we are capable of straightfor-wardly addressing constraints such as power limitation withthe use of the release force υi

lea, capacity with the use ofthe sharing function κij , distance threshold with the use ofthe repulsion force υi

pul, and taboo areas with the use of thesurvival force.

B. Algorithm and ImplementationOur FA algorithm is developed using the above flocking

rules and based on discrete time. Suppose all the terminalnodes update their positions synchronously at every timeinterval [s, s + 1] (e.g. every minute), and all the backbonenodes move synchronously to update their positions andvelocities at every time step t until the movement of eachbackbone node is smaller than a pre-defined resolution μ,i.e. ||Bi(t) − Bi(t − 1)|| ≤ μ, or the maximum number ofiterations tmax is satisfied. Given a new input of coordinatesof all the terminal nodes {Tk(s)} (k = 1, 2, ..., M ), theinitial locations (i.e. the old locations at last time interval)of the backbone nodes {Bi(0)} (i, j = 1, 2, ..., N ), wefirst calculate the coverage topology hik(0) (i = 1, 2, ..., N ;

k = 1, 2, ..., M ) while satisfying physical constraints. Inthe current implementation, the constraints with respect totaboo areas only include mountains in a 3-D space withfull terrain information. A large number of mountains withdifferent heights are randomly generated. In the simulationenvironment, we partition the x-y plane with a fixed gridsize, which is fine enough to produce satisfactory resolution,corresponding to a terrain matrix Aterrain = [apq]m×m, whereeach component represents the altitude of a point in the x-yplane. Given a terminal node with location Tk = (xt

k, ytk, zt

k)and a backbone node located at Bi = (xb

i , ybi , z

bi ), we have

developed an effective approximation algorithm to evaluateif there is direct line of sight between the terminal node Tk

and the backbone node Bi bearing in mind the location ofmountains. In this research we only consider blockage betweenterminal nodes and backbone nodes, as the backbone nodesare usually located at fixed high altitudes. It is easy to extendour approach to include blockage between backbone nodes inmilitary applications. The terrain checking algorithm is aidedby the interpolation function ’interp1’ from the MATLABtoolbox (we used MATLAB as our simulation environment).Forming the coverage topology, we first check the con-

straints from the terrain. The basic idea is that each terminalnode will first connect to its closest backbone node. If thereis no line of sight between them, we put the backbone nodeinto a taboo archive and connect to the second closest back-bone node. The process stops when a connection is achievedthat satisfies the geographic constraints. If there is no lineof sight for all the backbone nodes, the terminal node isconsidered isolated. We then consider the capacity constraintRi (i = (1, 2, ..., N)), i.e. the maximum number of terminalsthat can be connected to each backbone node. In other words,if the number of terminals ni connecting to backbone node iexceeds the capacity Ri, we reconnect (ni −Ri) terminals toother backbone nodes. The selection of terminal nodes thatneed to be reconnected is based on the minimum-energy-cost-first principle. The capacity checking process is similarto the geography checking algorithm, but the reconnection toother backbone nodes is required to first satisfy the geographicalgorithm, i.e. the geography checking algorithm is embeddedin this process. Finally, the overall implementation for theflocking algorithm is summarized as follows

1) Given the initial positions of terminal nodes {Tk(0)},the physical constraints Θ = {Cp, Cc, Cd, Ct}, set times = 0 for the dynamics of terminal nodes.

2) Given the initial positions of backbone nodes {Bi(0)},set time t = 0 for the dynamics of backbone nodes.

3) Set time t ← t + 1, use the topology configurationalgorithm [9] to determine {bij}, then check the geo-graphic constraints and the capacity constraints for allthe terminal nodes to determine the coverage topology{hik}.

4) Calculate the force or velocity υi(t) for the backbonenode i according to Eq. (18).

5) Update the positions of backbone nodes {Bi(t)} ac-

242

cording to Eq. (19).6) Evaluate ||Bi(t)−Bi(t−1)|| for each backbone node, if

||Bi(t)−Bi(t−1)|| ≤ μ, then fix the current position ofbackbone node i. If the maximum number of iterationstmax is satisfied, go to Step 7); otherwise, go to step3).

7) Set time s ← s + 1, terminal nodes move to newpositions {Tk(s)}, i.e. the new dynamics from terminalnodes. Set Bi(0)← Bi(t) for each backbone node, andgo to step 2) until simulation is over.

Note that the FA can be executed in a distributed mannerbecause each backbone node only uses local informationfrom neighbor backbone nodes and the terminal nodes inits coverage range. It is difficult to provide an explicit formwith respect to the computational time complexity of thewhole system due to the heterogeneous dynamics of the endusers. In each time step t, the computational time complexityapproximates to O(NM), where we do not take into accountthe computation time required for the geography and capacitychecking algorithms. In practice, geographic information canbe directly obtained by the system almost in real time. Thecomputational time with respect to the capacity checking al-gorithm is closely related to the dynamics of the end users andbackbone nodes. Thus, FA is able to maintain the distributednature and low time complexity of the entire system, whilesignificantly improving the system’s performance over existingalgorithms (as will be shown in the next section).

IV. EXPERIMENTS

A. Experimental Setup

In order to verify the performance of our proposed self-organization and optimization algorithm for HHWNs, weconducted experimental studies and present the correspondingresults for the dynamic scenario in which the HHWN includes100 terminal nodes and 10 backbone nodes, i.e. M = 100,N = 10. In all simulations, M terminal nodes are distributedover a 50km × 50km plane and organized in clusters usingthe Minimum Spanning Tree algorithm [10]. Nm mountainsare randomly generated in this plane with a maximum heightof 1.6km (we set Nm = 80 in this research). The altitudesof terminal nodes are updated according to the terrain. Thebackbone network in the upper layer is constructed using Nbackbone nodes forming a ring topology. We use ring topolo-gies for the backbone network to assure resilience throughbi-connectivity. Terminal nodes move according to the RPGMmodel [11]. We place the backbone nodes at an altitude of 2km, which indicates the backbone nodes move in 2D space(i.e. x-y plane), and compare FA to the AFD model [4] andthe MFD model [1]. FA, AFD and MFD are used to makebackbone nodes adjust their locations until convergence to thebest possible backbone configuration.In our experiments, FSO links with 2 mrad half beam

divergence are used for the backbone-to-backbone links andRF links with π/4rad half beam divergence for the backbone-to-terminal links. The minimum required received power used

TABLE ICOMPARATIVE RESULTS OF ENERGY COST

Time 0 1 2 3 4 5 6 7 8 9 10FA Initial 3100.7 650.2 813.6 617.1 621.2 537.7 534.5 511.4 510.8 634.8 674.5

Optimized 654.5 798.5 565.6 564.3 511.8 507.1 466.2 442.5 555.3 598.4 631.2MFD Initial 3100.7 1623.1 1061.8 767.8 700.1 633.7 568.5 585.3 641.8 757.5 936.0

Optimized 1749.6 1545.1 799.7 747.7 671.8 584.4 537.3 541.4 606.9 815.2 837.1AFD Initial 3100.7 680.4 816.5 724.1 632.7 583.8 517.1 496.9 548.5 634.9 956.5

Optimized 663.3 815.7 692.2 644.3 573.7 501.2 458.7 492.6 560.5 916.6 727.5

TABLE IINUMBER OF LOSS OF CONNECTIONS

Time 0 1 2 3 4 5 6 7 8 9 10FA Initial 4 1 1 0 0 0 0 0 0 0 0

Optimized 1 1 1 0 0 0 0 0 0 0 0MFD Initial 4 2 1 0 0 0 0 0 0 0 0

Optimized 3 1 1 0 0 0 0 0 0 0 0AFD Initial 4 1 1 0 0 0 0 0 0 0 0

Optimized 1 1 1 0 0 0 0 0 0 0 0

was -45 dBm (31.6 nW) for all network nodes. The scatteringcoefficient γ is set to zero. We set the power limitation forboth backbone nodes and terminal nodes at PTmax = 5W.The configuration of parameter settings for FA is: the distancethreshold for the backbone-to-terminal links dBT

th,pul = 2km,the distance threshold for the backbone-to-backbone linksdBB

th = 10km, the threshold to control the release forcedBT

th,lea = 10km, all the weighting parameters used in Eq.(18) wp = 1, wl = 1 and wa = 1, the step size used inEq. (19) ρ = 0.01, the resolution μ = 0.1, capacity of eachbackbone node Ri = 40, and maximum number of iterationsfor FA tmax = 2000. The basic parameter settings for the AFDmodel [4] and MFD model [1] follow the FA setting. All thescenarios were run continuously for 10 minutes in simulatedclear atmosphere conditions.

B. Performance MetricsWe use three metrics, which are energy cost, loss of connec-

tions (LC), source-to-destination (SD) and standard deviationof communication load in backbone nodes, to evaluate theperformance of the different algorithms including FA, AFD[4] and MFD [1]. The metrics are specified as follows

• Energy cost U : the total communication energy storedin the wireless links as defined in Eq. (1) (here, α = 1),i.e.

U =∑N

i=1

∑Nj=1 biju(Bi, Bj)

+∑N

i=1

∑Mk=1 hiku(Bi, Tk)

. (20)

• Loss of connections ULOS : the number of isolated endusers (terminal nodes) that are not able to connect to anybackbone node due to physical constraints. Its definitionis described as

ULOS = (M −∑N

i=1

∑M

k=1hik). (21)

• Source-to-destination USD: note that wireless links willnot always be available with respect to power constraints.Exceeding link distances and atmospheric obscuration

243

TABLE IIIPERFORMANCE OF AVERAGE ENERGY COST

Algorithm Initial Optimized Energy SaveFA 836.95 572.31 31.62%MFD 1034.20 857.84 17.05%AFD 881.10 640.57 27.30%

TABLE IVCOMPARATIVE RESULTS OF SOURCE-TO-DESTINATION

Time 0 1 2 3 4 5 6 7 8 9 10FA Initial 1122 3080 2352 3306 3422 4556 4032 4290 4032 3906 3782

Optimized 3442 3660 4160 4160 4556 4422 4556 5122 4692 4422 4556MFD Initial 1122 1560 3660 4160 4160 4830 5112 5852 5550 4556 4970

Optimized 2652 4032 4160 4422 4692 5256 5402 5550 5256 4970 5112AFD Initial 1122 3422 3422 3422 3306 3782 3906 4290 4160 3906 3906

Optimized 3660 3660 3540 3540 4160 4556 4692 4970 4422 4290 3906

will cause link breaks that will terminate SD connectionsin the network [1]. Here, SD refers to the number ofSD pairs for which a path exists between them, which isdefined as

USD =∑Ns

i=1nsi(nsi − 1), (22)

where Ns represents the number of clusters or connectedcomponents at the backbone network and nsi

representsthe number of terminal nodes connected to a backbonenode in cluster si.

C. Results and comparison

In this section, we compare the performance of our proposedalgorithm, i.e. FA, to AFD [4] and MFD [1] based on the abovedefined metrics. Table I lists the energy costs of the system atthe starting point and at the end of each time interval during10 minutes. For each interval, we list the results based onthe initial configuration of the HHWN and the results afterthe optimization by the algorithms. On the other hand, wesummarize the results associated with LC in Table II. Weclarify that a large value of LC brings low the energy cost, butresults in bad quality of service. Based on the similar resultsfor LC, it is observed that FA delivers better results comparedto AFD and MFD in overall simulation time. Table III showsthe average energy cost for the different algorithms accordingto Table I. FA saves 31.62% energy, which significantlyoutperforms AFD and MFD. Another observation is that thevalue of the energy cost produced by FA during minutes 4, 7, 9and 10 oscillates, which is caused by the pre-defined resolutionμ. In terms of the SD metric, we compare the results in TableIV for every time interval and also summarize the averageSD in Table V. From minute 3 to minute 7, MFD producesa larger number of SD connections than FA and AFD, butFA delivers a more significant improvement based on averageSD connections as shown in Table V. It is noted that althoughMFD achieves a large number of average SD connections, theimprovement it delivers is relatively small due to the largeinitial number of SD connections.

TABLE VPERFORMANCE OF AVERAGE SOURCE-TO-DESTINATION

Algorithm Initial Optimized Energy SaveFA 3443.6 4340.7 26.05%MFD 4139.3 4682.2 13.12%AFD 3513.1 4126.9 17.47%

V. CONCLUSIONS AND FUTURE WORK

This paper presents a new framework to model and optimizeHHWNs under real world physical constraints. First, we pro-pose a mathematical modeling method for the self-organizationand optimization of HHWNs by taking into account phys-ical constraints. Second, using only local information, wedevelop new flocking rules and a corresponding algorithmto autonomously assure and optimize network performancein a practical way. Experimental results confirm that FAoutperforms current algorithms. FA is capable of maintainingthe distributed nature and low complexity of the systemwhile achieving improved performance associated with thedynamic configuration of an HHWN under real world physicalconstraints. Furthermore, with the use of FA, the backbonenodes can move flexibly in 3D space by taking into accountthe repulsion force from physical constraints (e.g. mountains).In future work, we plan to investigate our algorithms in morecomplex dynamic environments. We also note that the stabilityanalysis of dynamic HHWNs is still an open problem. We planto conduct a theoretical analysis of the stability of an HHWNin the context of self-organization and control.

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self-organization in heterogeneous wireless networks. EURASIP Journalon Wireless Communication and Networking, accepted for publication.

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