Capacity Enhancement of RF WirelessMesh Networks Through FSO Links

Farshad Ahdi and Suresh Subramaniam

Abstract—RF-based technologies are often used to ad-dress the last-mile problem. However, RF technologiesgenerally create a bottleneck for the ever-increasing de-mand for bandwidth, causing the under-utilization of corenetwork resources. Enhancing the capacity of wirelessmesh networks can be done efficiently and cost effectivelythrough boosting the capacity of some strategically locatedlinks. In this paper, we propose link augmentation via free-space optics (FSO) links. The high capacity of optical linksis the key in link capacity enhancement in the resultinghybrid network. Adopting a TDMA-based framework, weformulate the problem of transceiver placement and thescheduling of RF links to maximize network capacity. Toavoid the complexity of the ILP, we also propose a random-ized greedy heuristic algorithm. In addition, simulatedannealing is used to provide a baseline for comparisonand to show the efficiency of our heuristic. We show bysimulations that our heuristic, which can be implementedefficiently, achieves a high fraction of the optimal networkcapacity.

Index Terms—Capacity augmentation; Free space optics;ILP; Wireless mesh.

I. INTRODUCTION

T here is an ever-increasing demand for bandwidthdue to emerging media-rich applications. Fiber-based

networks address such demands; however, the cost of theinfrastructure as well as infeasibility of deployment insome areas are the major barriers. Using wireless technol-ogies to form wireless mesh networks (WMNs) addressesthe last-mile problem. These networks are easy to deployand incur little deployment cost, but at the price of lowerdata rates. Despite their popularity, RF-based WMNs de-grade the overall network performance in terms of delayand throughput. In addition, the asymmetrical growth ofbandwidth demands in the uplink and downlink directionsleads to the under-utilization of the network. For example,the emergence of media-rich applications such as on-demand streaming of HD videos over the Internet hassignificantly tilted the growth rate in the downlinkdirection. Appropriate scheduling along with partialcapacity enhancement of WMNs can greatly improve suchinefficiencies.

Boosting the network capacity using RF-based solutionssuch as the deployment of multiple radios or MIMO anten-nas at some nodes is the standard practice. Besides requir-ing significant upgrades in the physical layer, theseapproaches are not scalable mainly due to the interferencethey introduce to the network. A wireless hybrid non-RFapproach is pursued in this paper, as it can potentially en-hance the network capacity significantly. In particular,free-space optics (FSO) as the link upgrade technology isinvestigated due to its high bandwidth, low interference,and quick setup time. Unlike their RF counterparts,FSO links are strongly dependent on weather conditions(e.g., fog, rain), so a network solely based on FSO technol-ogy may not be a reliable solution. Combining RF and FSOtechnologies, however, appears to be a promising approach.

Figure 1 shows a possible architecture that addressesthe last-mile problem by using a WMN in the front endwith a wired (fiber) network in the back end. In this archi-tecture, adopted in our paper, the wireless gateways are thehighest aggregation point in the WMN; they collect endusers’ traffic in a multihop manner. The aggregated trafficis routed from (to) the gateways to (from) the Internet.Due to ever-increasing need for bandwidth and long-termchanges in traffic patterns, congestion in some links couldlead to network bottlenecks. FSO transceivers can be usedeffectively to upgrade (create) a few links between nodesthat are within line of sight of each other, as shownin Fig. 1.

Sarkar et al. proposed a similar tree-like fiber-based ar-chitecture and addressed the gateway placement problemas a cost minimization problem [1]. Among the existingtechnologies, a passive optical network (PON) may be usedfor the high-speed optical backbone, and LTE, WiMAX, orWi-Fi can be used as aWMN in the front end. Narlikar et al.studied a general framework for link activation, routing,and scheduling of packets in wireless networks [2]. Theyshowed that well-known scheduling techniques such asweighted fair queuing can be applied to the wireless multi-hop network under their so-called even–odd framework toguarantee an end-to-end delay. A delay-aware routingalgorithm was proposed by Sarkar et al. [3]. Raez et al.propose a capacity and delay-aware routing scheme for asingle-radio WMN [4].

Using multiple radios at bottleneck nodes is suggestedfor capacity enhancement of WMN in Ref. [5]. However,this may require a new channel assignment for a large partof the network and could incur a high cost. We proposed ahttp://dx.doi.org/10.1364/JOCN.8.000495

Manuscript received July 30, 2015; revised April 14, 2016; accepted May14, 2016; published June 22, 2016 (Doc. ID 246910).

The authors are with the Department of Electrical and ComputerEngineering, George Washington University, Washington, DC 20052,USA (e-mail: farshad.ahdi@gmail.com).

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1943-0620/16/070495-12 Journal © 2016 Optical Society of America

MIMO-based solution in Ref. [6] to benefit spatial multi-plexing through multiple antennas and to avoid new chan-nel assignments to neighboring nodes imposed by usingmultiple radios. Mumey et al. suggested a joint-stream con-trol and scheduling problem for MIMO-based wireless net-works [7]. Such a solution requires every node to beupgraded with a MIMO antenna; this is not a cost-effectiveapproach and is probably unnecessary, because the trafficdistribution is typically non-uniform in hybrid wireless op-tical access networks. This is because there is more trafficto and from the gateways than from the wireless routers.

Krishnamurthy et al. investigated an FSO-based meshnetwork and proposed a routing and load-balancing algo-rithm to reduce the blocking probability [8]. Kashyap et al.proposed an integrated topology control and routing inFSO mesh backbone networks [9]. They emphasized thecost of FSO transceivers as the major constraint andshowed that the corresponding problem is NP-hard.Smadi et al. proposed an algorithm for placing FSO gate-ways in WMNs [10].

Tang et al. consider the enhancement of RF WMN net-work throughput using FSO links in Ref. [11]. Theyconsider both fading and non-fading communication chan-nels for the RF portion of the network. There are some simi-larities between their work and our problem in Ref. [12] inthat they propose a heuristic for the placement of FSOlinks. However, their physical layer model and formulationare different compared to ours in this paper. In their formu-lation, they maximize the total throughput of the networkwithout considering fairness in network capacity alloca-tion. In this paper, we define the network capacity suchthat the per-node traffic demand rates are maximized toguarantee fairness. We use a similar fading model for theFSO links as theirs in our formulation.

Rak et al. consider a hybrid FSO/RFapproach with a spe-cial focus on the resistance of FSO paths against link out-ages due to adverse weather conditions [13]. They proposeda link-disjoint FSO paths algorithm to increase reliability.

Their objective is different from this research in that theirfocus is mostly on reliable routing in an FSO-based net-work, while ours is about an existing RF-based networkwith some upgrades on the bottleneck links for increasingthe capacity. In the context of FSO network reliability, weproposed an algorithm for improving hybrid FSO/RF net-work reliability through transceiver reconfiguration inRef. [14]. We suggested using FSO relays for network dis-aster recovery in Ref. [15].

In this paper, we propose a novel solution for incorpo-rating FSO technology into existing RF-based WMNs togreatly improve network capacity (throughput) at a frac-tion of the entire network upgrade cost. The contributionof this paper is two-fold. First, using a unified RF linkscheduling framework and FSO link placements scheme,we find the optimal locations for a given number of FSOtransceivers as well as the matching RF link schedulesthat maximize the network capacity. In other words, giventhe expected long-term uplink and downlink traffic de-mands at each node, we formulate an integer linear pro-gram (ILP) for the joint assignment of FSO transceiversand RF link scheduling to find the strategically locatednodes which increase the overall network capacity themost if they get upgraded. Second, to avoid the complexityof the original ILP, we relax it and propose a simple prob-abilistic greedy algorithm, which is shown by simulationto compute a comparable solution at a significantly lowercomputational cost. In both schemes, the computed sched-ules provide all nodes with appropriate routes to and fromthe gateway(s).

This approach is different from the existing work in thatit takes RF link-scheduling into account in determining theoptimal placement of the FSO links. The scheduling of RFlinks, which affects the traffic routing indirectly, influencesthe capacity of the network. Therefore, the optimal place-ment of FSO links cannot be addressed without consideringthe RF links schedule. To the best of our knowledge, thisproblem has not been investigated. We note that, typically,only a small set of links needs to be upgraded with FSO,and therefore, our approach requires minimal changes tothe network infrastructure.

The rest of this paper is organized as follows. InSection II, we present the network model used to formu-late the problem. The problem is stated and formulated asan ILP in Section III. We present a novel heuristic algo-rithm based on ILP relaxation and probabilistic schedul-ing in Section IV. In Section V, extensive simulationresults are presented to show the performance of the op-timal algorithm and the proposed heuristic on some rep-resentative network topologies. Results using a simulatedannealing approach are also provided for comparison.Section VI concludes the paper.

II. NETWORK MODEL

The multihop WMN is denoted by a directed graphG � �V;E�, where V and E represent the sets of wirelessrouters and the directed links between them, respectively.It is assumed that the set of gateways (nodes connected to

Fig. 1. Network architecture for hybrid wireless optical network.

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the Internet), which is denoted byG, is a subset of V. A goalof ours is to find a subset of V to be equipped with FSOtransceivers. It should be noted that while FSO technologyneeds line of sight, for RF transceivers, it is not a necessity.Therefore, not all links in E are eligible to be upgraded byFSO technology.

We consider only the WMN and the FSO network in ournetwork model and ignore the user nodes. The end usersare assumed to be connected to their respective accesspoints (i.e., wireless routers) using separate frequencybands that do not interfere with the wireless mesh net-work. We assume that the destination of the aggregateduplink traffic to be one or more gateways and that ofthe downlink traffic to be the respective wireless router.Thus, a wireless router, v, has an aggregated uplinkand downlink traffic demand denoted by ru�v� and rd�v�,respectively.

A. Physical Layer and Interference Model

We assume that the RF antennas in the WMN are omni-directional; however, our approach can be easily general-ized for sectorized antennas. The nodes communicate ina half-duplex manner, i.e., simultaneous transmissionand reception are not possible. It is assumed that the nomi-nal capacity of each link is given and that fading is insig-nificant due to the wireless routers being static. However,the shadowing effect is considered, and this might causetwo nodes that are physically proximate to not have a linkbetween them, while two nodes that are separated by alonger distance will have a link between them. Such amodel is used, for example, in Ref. [2]. Interference mayoccur at an RF node because of its neighboring nodes trans-mitting at the same time. All directed links that interferewith each link can be pre-calculated, and we assume thatthe set of interfering links for link e ∈ E is given and isdenoted by Ie ⊆ E. We assume the protocol model of inter-ference in this paper [2].

FSO links are assumed to provide interference-freechannels for communication. The average capacity of anFSO link can be calculated using the model inRef. [16]. In this paper, we assume that FSO transceiversuse narrow laser beams that are able to provide a capac-ity of up to CF � 2.5 Gbps up to a distance of 4 km inclear weather conditions [9]. In our simulation, we con-servatively consider a lower rate of about 1.2 Gbps[17]. We assume that FSO links may experience fadingthat may result in temporary link outages. To character-ize the effective capacity of a link, we take the link avail-ability into account. This parameter, which is denoted byπ, is the probability that an FSO link successfully oper-ates at the data rate of CF, resulting in an effective capac-ity of CFπ [11]. In fact, in order to obtain this effectivecapacity, the relay node must have enough memory tobuffer the data during the fade and transmit it oncethe link becomes available again. The details of such ascheme are out of the scope of this paper. Finally, we as-sume that such possible link outages due to fading arestatistically independent.

B. Link Scheduling Framework

We assume that all RF transmissions are done on a sin-gle common channel that is accessed according to a TDMA-basedMAC layer protocol.1 For this purpose, time is framedinto non-overlapping intervals within which a set of linkschedules is applied. These frames are periodically repeated,resulting in the periodic activation of the links according totheir schedules. Our goal is to determine the set of scheduleswithin a frame such that the overall network capacity ismaximized. The schedules for link e ∈ E are characterizedby a schedule vector S�e�. We assume that time within aframe is slotted in T equal-sized intervals. Therefore, theschedule vector S�e� consists of T binary elements that de-termine the status of link e at any time slot within a frame:S�e; t� � 1 implies that link e is active in time slot t.

III. PROBLEM DEFINITION AND FORMULATION

In this section, we formulate the problem of capacity en-hancement of an existing RF-based wireless mesh networkby upgrading some of the transceivers using FSO technol-ogy. Network capacity is defined as the total per-node traf-fic demand rates (both uplink and downlink) that areadmissible within our proposed scheduling framework.More precisely, the network capacity, R, is defined as thelargest factor by which all traffic demands can be scaledwith a feasible routing. In other words, if ru�v� and rd�v�are the uplink and downlink demands at node v ∈ V, thenetwork capacity is defined as the largest R for which de-mands R × ru�v� and R × rd�v� can be successfully routedusing our proposed framework.

In what follows, a matrix notation is adopted to simplifythe equations. For example, dot operator (·) implies matrixmultiplication and/stands for element-by-element matrix(vector) division. When no sign is used between two sym-bols, it represents the element-by-element product of ma-trices (vectors). We use 1 to show a matrix (vector) whoseelements are all ones. As an example, the summation of allelements of a vector denoted by q can be simply shown byq · 1. In addition, when comparative operators such as� or≤ are used, the operators apply to every pair of correspond-ing elements in both matrices.

A. Problem Definition

Given:

• potential RF network topology, G � �V;E�,• subset of E for potential FSO upgrades,• availability of the FSO links, π,• number of FSO upgrades/transceivers, M,• set of interfering links, Ie, for each link e,

1This assumption can be generalized by enabling subchannelization inneighboring nodes and thus allowing simultaneous transmission in non-overlapping frequency bands.

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• number of time slots in a frame, T,• uplink and downlink demand vectors, ru and rd, and• nominal capacity of RF and FSO links, CR and CF

Find:

• schedule vectors of the RF links for each link e, SR�e�,• placement of FSO links, SF ,• uplink and downlink traffic, Λu and Λd such that the net-work capacity R is maximized.

In the following, we formulate the problem as an ILP,where the objective is to maximize R.

B. ILP Formulation

Please refer to Table I for notations.

Objective: max R

Flow constraints: A gateway as the interconnection nodebetween the wireless and the wireline network (Internet)sinks the uplink traffic from the wireless routers andsources from the downlink traffic in the reverse direction.Therefore, at the downlink traffic origin and uplink trafficdestination, we have

∀ e ∈ Eo�v� Λu�e� � 0; ∀ e ∈ Ei�v� Λd�e� � 0; (1)

where Λ�e� denotes the traffic flow along link e. For theuplink traffic flow of any non-gateway node, we have

Xe∈Eo�v�

Λu�e� −X

e∈Ei�v�Λu�e� � R × ru�v�; (2)

where v ∈ VnG. The downlink traffic flow constraints canbe obtained similarly. For the sake of simplification, we de-fine two jVj × jEj matrices as follows:

Vi�v; e� ��1 e ∈ Ei�v�0 o:w:

Vo�v; e� ��1 e ∈ Eo�v�0 o:w:

: (3)

In addition, we define Voi � Vo − Vi. Using this notation,Eq. (2) can be simply written as Voi · Λu � ruR, where Λu

and ru are the vectors of the uplink flow and demandson all links and nodes, respectively.

Link capacity constraints: Since for every link, the totaluplink and downlink flows can be at most equal to theeffective capacity of each link, we must have

Λu � Λd ≤ cF � cR: (4)

Here, elements of vector cF are either the nominal capacityof an FSO link if an upgrade happens or 0 otherwise. Also,cR denotes a vector whose elements are the effective,time-averaged capacity for each RF link.2

Half-duplexing constraints: An RF transceiver maynot transmit and receive simultaneously. Let the binaryvariables X�v; t� and Y�v; t� denote the transmitting andreceiving statuses of the RF interface at node v in timeslot t, respectively. Being in either mode makes the corre-sponding variable 1; otherwise, it is 0, and we must haveX�v; t� � Y�v; t� ≤ 1 or in general matrix form X� Y ≤ 1.

Link activity constraints: No outgoing link is activeunless the corresponding transmitter is in transmissionmode. Therefore, we have

Xv�t� �X

e∈Eo�v�SR�e; t�: (5)

The above constraint can be summarized by Vo · SR � X.With minor modifications, a similar constraint can bederived for incoming links.

Interference constraints: Once link e is active in time slott, i.e., SR�e; t� � 1, all its interfering links e0 ∈ Ie must beinactive in t. In other words, we must have

Xe0∈Ie

SR�e0; t� ≤ jEj × �1 − SR�e; t��: (6)

We summarize these constraints by �I� jEj� · SR ≤ jEj,where I denotes the interference matrix, which is anjEj × jEj binary matrix whose eth row is zero except forall elements of Ie.

TABLE ISYMBOL DESCRIPTION

Symbol Description

G, G, V , E Graph, gateways, transceivers, linksru, rd Traffic demand: uplink, downlinket, er Transmitter, receiver node of link eS, S�e� Schedule: matrix, vector for link eπ�e� Avaiabilty of FSO link eT, M Number of: time slots in a frame, FSO linksR, Λu, Λd Network capacity, traffic flow: uplink, downlinkEo�v�, Ei�v� Links from and to node v: outgoing, incomingVo, Vi, Voi Link matrix: outgoing, incoming, outgoing–

incomingcF, cR Link capacity: FSO, RF (effective time

averaged)X�v; t�, Y�v; t� Node v status at time slot t: transmitting,

receivingIe, I Interfering links set of e, interference matrixCR, CF Nominal link capacity: RF, FSOpt�v�, pr�v� Node v status probability: transmitting,

receivingσ, σ Time-averaged schedule vector: relaxed ILP,

PGSα, η Projection of σ on σ, link probability update

factorcR, ¯cR Time-averaged RF capacity: relaxed ILP, PGSρ�t� Link activation probability at time slot tθ0, θf in, θ, β Initial, final, current temp., decay factor (SA)A, L The set of active links, remaining linksOPT, PGS, SA Optimal Alg., rand greedy Alg., simulated

annealing2This capacity cR is defined a bit later in the subsection “Average link capac-ity.”

498 J. OPT. COMMUN. NETW./VOL. 8, NO. 7/JULY 2016 Farshad Ahdi and Suresh Subramaniam

Average link capacity: Depending on the link activityin each time slot, the overall capacity of the link can be de-termined in a time frame. The time-averaged activity oflink e in a time frame can be calculated by 1

T

PtSR�e; t�.

Therefore, we have

cR � CR

�1TSR · 1�; (7)

where CR is the nominal capacity of an RF link.

Link capacity: The binary variable SF�e� indicateswhether a link is upgraded with an FSO or not. The capac-ity of such a link can be calculated as follows:

cF�e� � CFSF�e�πF�e�; (8)

where CF is the nominal capacity of an FSO link and πF�e�denotes the availability of link e.

Number of upgrades constraint: Considering the totalnumber of upgrades, M, we have

Xe

SF�e� ≤ M: (9)

The resulting ILP is shown in Table II.

In the presented formulation, T plays a key role in termsof performance and complexity. For the same frame length,clearly, the achievable capacity monotonically increases forinteger multiples of T. However, the complexity of the prob-lem significantly increases with T. We will explore thistrade-off later in the paper. Apart from the effect of T onthe complexity and on the capacity, there is a practical con-sideration in the choice of T. A too-small value for T couldpossibly leave too few slot options for activating the linksand may possibly make the resulting topology discon-nected. On the other hand, when T is too large (withoutchanging the duration of the frame), too-frequent switchingof the transceivers is required, possibly increasing packetdelays.3

IV. ILP RELAXATION AND HEURISTIC ALGORITHMS

The network capacity maximization ILP is computation-ally expensive. Some relaxation can be applied in order toreduce its complexity and obtain an upper bound on thenetwork capacity. While relaxation is meant to reduce

the complexity of the ILP in order to obtain a meaningfulupper bound, deliberate relaxations are necessary to avoidending up with a loose upper bound. Investigating theconstraints of the ILP reveals that there are three maincategories of constraints (as shown in Table II), all of whichhave different levels of complexity.

The flow constraints are mostly real-valued. These con-straints specify the routing information by providing theamount of traffic flow on each link. The second batch of con-straints is related to the RF links’ schedules, which charac-terize the solution space for the schedule matrix. Thevariables involved in this part of the ILP are all integersand their numbers scale as O�T�. The third group of con-straints is about the FSO upgrade locations. These con-straints, although they involve integer variables, are farfewer and scale as O�jEj � jVj�. As a result, the relaxationof the latter constraints provides us with minimal improve-ment compared to the second group, namely, schedule con-straints. In this paper, we opt to only focus on relaxing thescheduling constraints. In other words, the relaxed versionof our ILP still provides the placements (locations) of theupgrades, but not the detailed RF link activation sched-ules. Later, we propose a randomized algorithm to approxi-mate the optimal schedule matrix, but at a significantlylower computational cost.

Assume the optimal schedule matrix, S, is found for agiven T by solving the ILP. This jEj × T binary matrixdetermines the status of all links at any time slot t.Regardless of the sequence of activation, if all schedule (col-umn) vectors are used to activate the links, the optimalcapacity can be achieved. Consider an approach to ran-domly select the sequence of schedule vectors for a framewithout replacement such that at the first round, the prob-ability of selection for each schedule vector is 1

T . Afterselecting the first schedule, the second one is selected fromthe remaining schedules with probability 1

T−1. This pro-cedure is continued until all schedules are used. At theend of this procedure, the expected number of times wherelink e is active, denoted by σe, can be calculated as1T

PtSR�e; t�. Obviously, the time-averaged vector σ whose

entries are real-valued is the centroid4 of the schedulematrix.

The time-averaged vector σ can be used to relax thescheduling constraints and still preserve meaningful infor-mation about the schedule matrix. Using this variable, theset of constraints that have the term SR�e; t� can be con-densed to convert the ILP to one that is much simpler, withfar fewer variables and constraints. For example, we cantake the summation over t on both sides of Eq. (5) to get

1T

Xt

�Xv�t�� �1T

Xt

" Xe∈Eo�v�

SR�e; t�#: (10)

By replacing the termP

tSR�e; t� with Tσe, the resultingconstraint becomes

TABLE IIILP FOR CAPACITY MAXIMIZATION

capacity � max R

Flow

Vi�v� · Λu � 0 Vo�v� · Λd � 0 v ∈ G

Voi ·Λuru� −Voi ·

Λdrd� R v ∈ VnG

Λu � Λd ≤ CFSFπF � CR�1T SR · 1�Schedule

Vi · SR � Y Vo · SR � XX� Y ≤ 1 �I� jEj� · SR ≤ jEj

Location SF · 1 ≤ M

3Consideration of delays is outside the scope of this paper.

4The centroid is considered as the average position of all points (vectors)represented by the matrix.

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pt�v� �X

e∈Eo�v�σe; (11)

where pt�v� is the probability of node v being in transmis-sion mode at time slot t. Using the above randomized ap-proach, we obtain the relaxed ILP shown in Table III,which is much easier to solve.

It should be noted that the solution of the relaxed ILPjust provides an upper bound on capacity, and it may notbe achievable. For example, the relaxed constraint result-ing from Eq. (6) does not guarantee interference preventionin each time slot, as Eq. (6) does. Moreover, the solution ofthe relaxed ILP does not provide detailed informationabout the schedules and activity of the links in each slot.In the next section, we propose a probabilistic algorithmthat uses the relaxed ILP solution to activate the links.In fact, any algorithm (if it exists) that is able to realizethe solution of the relaxed ILP is optimal.

A. Solution Space Characteristics

The optimal schedule matrix can be approximated by ap-propriate sampling of the schedule vector space. For thispurpose, T schedule vectors must be found to determinethe status of the links. From a geometrical perspective,each schedule vector represents a point in the solutionspace which is itself a subspace of an jEj-dimensionalspace. Each point in the solution space corresponds to amaximal set of non-interfering links that can be activein a half-duplex manner simultaneously.

Loosely speaking, the set of scheduling constraints inthe ILP characterizes a subset of points in the jEj-dimen-sional space. The flow constraints along with the maximi-zation objective select T points as schedule vectors to formthe schedule matrix. The vector σ can be used to approxi-mate the weights of different links’ involvement in thesuboptimal solution. Based on this, we propose a probabi-listic greedy scheduling algorithm to construct the sched-ule matrix. Once the matrix is calculated, it can beplugged back into the original ILP to find the actual trafficflow on each link. The resulting program is an LP withmuch less complexity, as the integer variables no longerexist and the only unknowns are the traffic flows, whichare real-valued.

In constructing the schedule matrix, all constraints thatshape the solution space are taken into account. Based onits definition, σ � 1

T SR · 1 is the centroid of the schedule

matrix. In other words, the relaxed ILP suggests a direc-tion that is a good approximation of the schedule matrixthrough σ. We define a constructed schedule matrix, S,to be an α-approximate schedule matrix if the resultingR � α ·R, where 0 < α ≤ 1 and R is the solution of therelaxed ILP. In order to find a good approximation of theoptimal solution, we may maximize the projection of σon σ, which can be performed by maximizing the minimumelement of σ∕σ according to the following Lemma.

Lemma 1: S is αm-approximate if αm � mine�αe�.Proof: For matrix S, we must have ¯cR�e� ≥ αmin · CR · σe,

as αmin is the minimum projection of σ on σ. In other words,we can have ¯cR�e� ≥ αmin · cR�e� for all links. Therefore, wehave Λu

e � Λde ≤ αmin · �cR�e� � cF�e��. As a result, the link

with the minimum effective capacity (i.e., projection) be-comes the bottleneck for the network flow that results inR � αmin ·R. ▪

B. Probabilistic Greedy Scheduling (PGS)Algorithm

Our PGS algorithm essentially reverse-engineers thetime-averaged schedule vector to approximate the schedulematrix. In other words, by knowing the constraints, wesample the vector space in a way that the centroid of thesampled points is in the direction of interest indicatedby σ. Ideally, a subset of points in the solution space mustbe selected such that their centroid is as close as possible tothe time-averaged schedule vector provided by the relaxedILP. The first step in PGS is to solve the relaxed ILP to cal-culate σ. Using the solution of the relaxed ILP, the place-ments of the FSO upgrades are found. Then, an iterativeprocedure finds the T schedule vectors (columns), as themain objective of PGS is to find a schedule matrix thatis α-approximate, and α is maximized.

Each schedule vector partitions the set of links into twosubsets of active and idle links at each iteration. In orderto maximize the projection ratio, namely, max�mine�αe��,the frequency of link activation must be done such thatthe selection probability is α · σe. This is similar to theconcept of weighted max–min fairness. We design a simpleiterative procedure to activate links e in each time slot t.Suppose that the calculated schedule matrix is α-approxi-mate; this means that the expected number of slots inwhich link e is active in one frame S is ασeT. Therefore,we have

E

"Xt≤T

S�e; t�#� ασeT

1T

Xt≤T

E�S�e; t�� � 1T

Xt≤T

ρe�t� � ασe; (12)

where ρe�t� is the probability of link e being active in timeslot t. Equation (11) suggests that the time average of theselection probabilities must be equal to ασe. In order totake fairness into account, we cannot simply assume thatρe�t� remains fixed during the selection procedure. This isbecause there is strong dependence among the links due to

TABLE IIIRELAXED ILP FOR CAPACITY ENHANCEMENT

UB � max R

Flow

Vi�v� · Λu � 0 Vo�v� · Λd � 0 v ∈ G

Voi ·Λuru� −Voi ·

Λdrd� R v ∈ VnG

Λu � Λd ≤ CFSFπF � CRσ

ScheduleVi · σ � pr Vo · σ � ptpr � pt ≤ 1 �I� jEj� · σ ≤ jEj

Location SF · 1 ≤ M

500 J. OPT. COMMUN. NETW./VOL. 8, NO. 7/JULY 2016 Farshad Ahdi and Suresh Subramaniam

interference. In other words, a link with a high probabilityof selection will dominate those with smaller probabilitiesby putting them in the back-off set more frequently thantheir fair share. The resulting solution would be far fromfair and would reduce the resulting network capacitysignificantly.

We consider a randomized round robin approach toapply fairness in the link selection procedure such thatthe selection weight is ρe�t�. In other words, for the linksto be selected, we take their prior selection record intoaccount. For example, suppose that we have alreadyselected t schedule vectors and we know that link e hasbeen active in ht time slots so far. In order to be fair toother links, we propose updating the selection probabilityas follows:

ρe

�t� 1jXτ≤t

S�e; τ� � ht

�� α max

�0; σe −

ηht

T

�; (13)

where ασeT is the expected number of times link e is ac-tive in the entire time frame, and η � 1

α and max�0;…� isused to ensure the weight cannot be a negative number.Since the probability of links’ selection is performed com-paratively, we can simply factor α out and derive a recur-sive approach, as follows:

ρe�t� ��ρe�t − 1� S�e; t − 1� � 0

max�0; ρe�t − 1� − η

T

�S�e; t − 1� ≠ 0

; (14)

where Eq. (14) is initialized by ρe�1� � σe. The iterativeprocedure selects the links to be active one by one ateach time slot t probabilistically. Let us denote the setof remaining links to be processed by L at each iteration.At each iteration, this procedure is initialized with L � E.Each link e is randomly selected with a probability pro-portional to ρe�t�. Once a link is selected, a set of varia-bles must be updated, as follows:

• The selected link in this stage, say e, is added to the activelinks’ set, denoted by A.

• All outgoing links from the receiver of e, namely er, andincoming links to its transmitter, namely et, are removedfrom L to comply with half-duplexing.

• Link e and its potential interfering links, namely, Ie, areremoved from L.

• All remaining links e0 in L where e is among their inter-fering links must be removed from L.

• Update schedule vector S�e; t� � 1.• The selection probability for e is reduced by η

T.

The procedure is repeated among the remaininglinks until L is empty. The first iteration determines theschedule vector S�e; 1�. In order to get the remainingschedule vectors, we repeat the algorithm T − 1 moretimes. The PGS algorithm is summarized in Algorithm 1.It should be noted that the above algorithm does notguarantee Eq. (12) and in practice, we often have

1T

Pt≤Tρe�t� ≤ σe

η . In other words, the effective α always sat-

isfies α ≤ 1η .

Algorithm 1 The PGS algorithmData: V , E, I, p, T, ηResult: Sbegin

τ ← 1S ← 0while τ ≤ T do

L ← EA ← Øfor e ∈ L do

if τ � 1 then ρe�τ� � σeelse

ρe�τ� � ρe�τ − 1�end

endwhile L ≠ Ø do

e � RandomPick�p; L�A ← A∪ fegρe�τ� � max�0; ρe�τ� − η

T�L ← Lnfe∪ Ie ∪Eo�er�∪Ei�et�gfor e0 ∈ L do

if e ∈ Ie0 then L ← Lne0endS�e; τ�← S�e; τ� � 1

endτ ← τ� 1

endend

The output of this algorithm finds α � min�1T SR · 1∕σ�for a given η. A good value needs to be found for η thatmaximizes the calculated α. Due to the ease of computa-tion, this heuristic can be run multiple times for random ηvalues that are uniformly selected in a given range. Welater show that the distribution of good choices for η is con-centrated around a certain value that can be found by trialand error. In our simulation, depending on the computa-tional budget we run the heuristic for a certain numberof times, say 1000, and keep the best result at the endof the procedure.

C. Geometrical Interpretation of PGS

The PGS algorithm may not realize the time-averagedschedule vector of the relaxed ILP, namely σ. However,we will show later that it performs quite well when com-pared with the optimal solution. Considering the geomet-rical notion of the schedule matrix, the centroid of theschedule vectors, which determines the performance ofPGS, must provide a balance between being along the σvector (fairness) and having a large projection on the coor-dinate axes (individual link throughput). This balance iscontrolled by parameter η, for which a good value needsto be found. A simple analytical bound on the performanceof the heuristic based on η can be derived due to its relation-ship with α, namely α ≤ 1

η.

Farshad Ahdi and Suresh Subramaniam VOL. 8, NO. 7/JULY 2016/J. OPT. COMMUN. NETW. 501

In order to clarify this bound, recall that the link selec-tion algorithm is a contention-based procedure because ofinterference. In other words, interference does not allowsome links to be active simultaneously. Hypothetically, as-sume that there is no interference and the time-averagedactivation for link e is σe. Without interference, this link isexpected to be active in σeT time slots, which translates toη � 1. In reality, due to interference, this link can only beactive in a fraction of this many time slots. Based on theprobability update formula Eq. (14), the total number oftime slots in which link e can be selected is ⌈ σ

η∕T ⌉ , provid-ing that the probability tends to zero after T time slots.Therefore, the link activation ratio is at most around σ

η ,decided by η.

Parameter η plays a key role in providing a fairness levelby limiting the total number of active time slots for linkswith higher activation probability and providing the lowprobability links a chance of activation. For example, in thecase that η is considerably large, the fairness level is high,as after a few times of being active, the probability of se-lection becomes zero even for highly probable links, therebyresulting in all links having the same fractional chance ofactivation. Geometrically, this corresponds to the casewhere several zero vectors (a vector with all elements equalto zero) are included as schedule vectors in the schedulematrix. These vectors correspond to points located at theorigin of the coordinate system, and make it easier forthe centroid to be along the σe vector. Such values, however,provide a higher fairness level to limit the performance ofthe heuristic by α ≤ 1

η. When η is zero or a small number,which is close to the case with no probability update, thelinks with the higher probability of selection will dominatethe other links, reducing the overall performance. This casegeometrically refers to the state where the centroid has avery small or no projection for some of the links (with lowprobabilities) and large projection for some others. As afinal note, good performance of the heuristic, which willbe shown later, is due to updating the probability of linkselection at each iteration (e.g., η > 0). As mentioned, themain reason for updating this probability is to providefairness in the contention process. Therefore, dependingon the network topology, a good value for ηmust be selectedto provide a balance between fairness and throughput.

D. Simulated Annealing

In order to provide a baseline to compare the perfor-mance of PGS, simulated annealing (SA) is employed.This probabilistic algorithm can provide a good approxima-tion of the globally optimal solution [18]. SA is analogous tothe thermodynamics process involved in the formation ofcrystals such that a temperature parameter, θ, is incorpo-rated into the optimization procedure, and it is decayedgeometrically according to θ · β for the next iteration, whereβ ≤ 1 is a decay factor. SA is initialized with a trial pointbased on current estimates, which might not even be closeto optimal, and it iteratively evaluates the objective func-tion in a new proposed location. The new value is acceptedif it improves the solution. Otherwise, it is accepted with a

certain probability which is calculated based on the currenttemperature and the difference between the cost functionat the new value and the last found solution. It is knownthat if the cooling procedure is sufficiently slow, the glob-ally optimal solution will be reached. The SA algorithm issummarized in Algorithm 2.

Algorithm 2 Simulated AnnealingData: V , E, I, p, θf in, βResult: Sbegin

θ � θ0 ← 1while θ ≥ θf in do

αmin ← mine�αe�emin ← Arg � mine�αe�τ ← ftjt ∈ S�t; emin� � 0gS0 ← SS0�E; τ�← 0L ← EA ← Øwhile L ≠ Ø do

if A � Ø then A ← emin

elsee � RandomPick�p; L�A ← A∪ feg

endL ← Lnfe∪ Ie ∪Eo�er�∪Ei�et�gfor e0 ∈ L do

if e ∈ Ie0 then L ← Lne0endS0e�τ; e� ← S0e�τ; e� � 1

endα0min ← mine�α0e�if αmin < α0min then S ← S0

else if rand < exp�− αmin−α0min

θ � thenS ← S0

endθ ← θ · β

endend

V. SIMULATION RESULTS

The RF physical layer in our experiment is WiMAX(802.16e), where with 20MHz of bandwidth, the link capac-ity can be as high as 75 Mbps [19]. We consider FSO linksusing narrow laser beams that provide a capacity of up to1.2 Gbps within a range of around 4 km [17]. For the firstpart of the simulation, we assume the FSO links are avail-able 100% of the time. In Subsection V.C, we considervarious availabilities of the FSO links and analyze theperformance of the algorithm. CPLEX 12.2 is used to solvethe integer linear programs. We assume that there is onlyone gateway in the wireless mesh network. In fact, by add-ingmore gateways or relocating them appropriately, highergains can be achieved, but we do not investigate that in thispaper. Such approaches can be found in Ref. [1]. We com-pare the performance of the proposed heuristics with thatof the optimal algorithm.

502 J. OPT. COMMUN. NETW./VOL. 8, NO. 7/JULY 2016 Farshad Ahdi and Suresh Subramaniam

For the simulation, we generate 20 random graphs con-sisting of 15 nodes each, one of which is a gateway. Thenodes are randomly placed in a square area of side10 km, and the maximum range of RF transmission is4 km. Figure 2 shows one such graph. We assume thatall nodes have equal uplink and downlink demands andthe capacities of all RF links are the same and equal to75 Mbps. It should be noted that actual capacities do notaffect the formulation and different link capacities canbe considered. We employ the standard interference model,i.e., interference is restricted to nodes within one hop fromeach other. For example, link e1 is in the interfering set ofe2, i.e., e1 ∈ Ie2 , if its transmitter has a link to the receiverof e2.

The solution of the ILP in Table II provides the optimalplacements of FSO links. Figure 2 shows an example of op-timal solution for M � 4, i.e., 4 links are upgraded. As canbe seen, the FSO links provide a high-capacity backbone forthe WMN through which the uplink and downlink trafficfor several nodes are routed to and from the gateway.This figure shows the general topology of the underlyingRF wireless mesh network. Among the RF links, someare active in at least one time slot within a frame, and theseare shown using dashed lines. The other RF links that arenever used in a frame are illustrated using dotted lines.

A. Performance Comparison of PGS and SA Withthe Optimal Performance

The optimal capacity of the network is calculated for allrepresentative graphs using FSO upgrades. For the sake ofsimplicity, we considerM ∈ f1;2;3;4g for T � 10 and 20, aslarger values result in very complex and computationallyexpensive solutions. We consider larger values for T inour heuristics. Figure 3 shows the average of optimal net-work capacities for the random graphs. As expected, thecapacities increase with the number of FSO links. It isnoteworthy that the performance increases more than lin-early as M increases.

The error bars show one standard deviation of the com-puted capacities in different cases. For T � 20, the achiev-able network capacity is slightly higher than that forT � 10, as expected. This is because the former providesa larger solution space due to more relaxed constraints.

As can be seen in this figure, the interpolating line forthe optimal solution has a slope of 3.2578, which impliesabout 76% of potential network capacity enhancementper each additional FSO link. However, the gain is lowerat smaller values of M and higher for larger values.

Figure 3 also shows results for PGS and SA for T � 20and 50. These approaches do not provide a competitive sol-ution for T � 10, as the corresponding solution space is lim-ited in size, resulting in low performance (not shown here).The general trend of capacity enhancement is similar to theoptimal solution, but with a lower efficiency for both ap-proaches. Based on the calculation, the interpolating linefor PGS has a slope of 2.0129, which is about 50% of net-work capacity improvement per each additional FSO link.In other words, the performance of these approaches isaround 62% of the optimal solutions. SA and PGS havea similar performance, with SA performing slightly betterfor M � 1, and PGS outperforming SA for larger values ofM. PGS, however, has lower complexity than SA.

Table IV shows runtimes of all approaches.5 According tothis table, the average runtimes for the optimal algorithmare about two orders of magnitude larger than those forPGS and SA; for larger network topologies, the ILP solu-tion is computationally prohibitive and was unable to ob-tain results in a reasonable amount of time. Further, theruntime of the algorithm scales almost linearly with Tfor the same algorithms. As can be seen, PGS runs gener-ally faster than SA.

B. Comparison of PGS and SA

The performances of the proposed PGS algorithm andthe simulated annealing approach are generally close toeach other. This is mainly because the core of both algo-rithms is based on the solution of the relaxed ILP shown

Fig. 2. Random wireless mesh network topology.

0 1 2 3 40

2

4

6

8

10

12

14

16

18

20

FSO Links (M)

R (

Mbp

s)

OPT (T = 20)OPT (T = 10)PGS (T=50)SA (T=50)

RPGS

= 2.0129 M + 1.7326R

OPT = 3.2578 M + 3.0754

Fig. 3. Performances of PGS and SA compared with the optimalperformance.

5Multiple machines equipped with Quad Core Intel Xenon processors (8Mcache, 2.13 GHz) and 8 GB RAM were used.

Farshad Ahdi and Suresh Subramaniam VOL. 8, NO. 7/JULY 2016/J. OPT. COMMUN. NETW. 503

in Table III. The relaxed ILP solution, which is character-ized by σ, governs the general direction of the schedulematrix regardless of the approach. That directionitself may not necessarily be optimal, but it suggests a sub-optimal solution. Therefore, the performance deficiencyincurred by the limitations of the relaxed solution is justi-fied through the trade-off with the extensive complexityof the original ILP.

The quality of the PGS solution compared with that ofSA depends on different factors. For example, it appearsthat when the size of the solution space is small (e.g.,T � 20), SA performs better, while for larger solutionspaces (e.g., T � 50), that is not necessarily true. The rea-son is that SA generally performs a randomized exhaus-tive search depending on the computational budgetassigned to it through the cooling temperature. For agiven computational budget, when the space size issmaller, the algorithm has a better chance to obtain aglobally optimal solution. However, when the space sizeis large, for the same computational budget, it is lesslikely to find a globally optimal solution. Even whenthe budget is higher, there is a chance that SA loses itsperformance due to the concavity of the huge solutionspace. On the other hand, PGS has a generally randombehavior as opposed to the exhaustive search behaviorof SA. In other words, depending on the input variableη, the solution space is sampled at random, especiallywhen η is in a range that can potentially provide a goodsolution.

Figure 4(a) shows α for both SA and PGS calculated forT � 50. Clearly, except for the case of M � 1, PGS has agenerally better performance. It must be mentioned that

PGS incurs much less computational complexity as op-posed to SA, as can be seen in Table IV.

C. Effect of FSO Link Availability on NetworkCapacity

In order to analyze the effect of FSO link availability onthe network capacity, we consider three low availabilitiesfor the FSO links, namely, π ∈ f0.1;0.2; 0.3g, which resultin an effective capacity of cF ∈ f160;320;480g Mbps,where the nominal capacity of an FSO link is 1.2 Gbps.We assume the availability to be the same for all FSOlinks and solve the problem using PGS for the cases whereM ∈ f1; 2; 3; 4; 5g FSO links can be added to the network.Figure 4(b) shows the solutions of the heuristic averagedover the generated random graphs.

As can be seen in Fig. 4(b), when the availability of theFSO links is very low, i.e., π � 0.1, addingmore than 2 linksdoes not provide a significant improvement. The reason isthat the effective capacity of FSO links is comparable tothat of RF links. In other words, adding more links doesnot solve the bottleneck issue that might exist due to somecongested RF links. Especially, no improvement is observedfor M > 3. When the FSO links are available with a higherprobability, namely π � 0.2, more improvement is observedand the network capacity curve is saturated at a highervalue. The same trend is observed for π � 0.3whereM > 5.

In the latter scenario, the achievable throughput isclose to the case where the FSO links are 100% availableand M ≤ 4, as shown in Fig. 3. In conclusion, in order toachieve the optimal network capacity for a certain numberof FSO link upgrades, these links do not need to have100% availability. This observation shows that upgradinga limited number of network links with FSO technology isworthwhile even if the links are not highly available. Inaddition, obtaining almost the same network capacityas π � 1 for π � 0.3 availability of the FSO link confirmsthat the PGS algorithm performs well at lower linkavailabilities.

TABLE IVALGORITHM RUNTIME IN SECONDS

Method OPT PGS SA

T � 10 3.536 × 104 NA NAT � 20 8.121 × 104 1.142 × 102 1.519 × 102

T � 50 NA 2.345 × 102 3.211 × 102

1 2 3 40.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

FSO Links (M)

α (

T=

50 )

SA (γ=0.9)PGS

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

2

4

6

8

10

12

FSO Links (M)

R (

Mbp

s)

π = 10%π = 20%π = 30%

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

η

P(η

| α

≥ kα

max

)

k=0.99k=0.9k=0.8k=0.7

(c)(b)(a)

Fig. 4. (a) Comparison between achieved α for PGS and SA for T � 50. (b) Effect of link availability on the network capacity for T � 50.(c) Estimated probability density function of α versus η.

504 J. OPT. COMMUN. NETW./VOL. 8, NO. 7/JULY 2016 Farshad Ahdi and Suresh Subramaniam

It must be noted that although in theory, the optimalnetwork capacity can be achieved at a fraction of the fullavailability of FSO links, in practice, more memory is re-quired in the relay nodes to be able to buffer data in thecase that a channel fade happens. This is likely to increasethe average end-to-end delay.

D. Analysis of PGS

As mentioned above, PGS is less complex than SA sinceparameter η splits the solution space into several subspa-ces and randomly samples the subspace with the highestlikelihood of providing a better solution. In this section,using a Monte Carlo approach, the density function of αversus η is calculated to analyze the key role played by ηfor one representative graph withM � 3. Figure 4(c) showsthe estimated probability density functions of α given thatits value is greater than k × αmax in 10,000 trials performed.As can be seen in this figure, for k ∈ f0.7;0.8; 0.9;0.99g, theconditional density functions are concentrated aroundsome value of η in the range of [1,2]. In other words, thebetter the performance, i.e., the larger the value of k, thesharper and narrower the density function becomes. Thisimplies that for a reasonable quality of the solution, onemay not need to search the entire space. Especially, itcan be seen that when k � 0.99, only the range ofRefs. [1,2] needs to be searched. It should be noted thatthe range depends on the network topology and the numberof upgrades. A simple binary search algorithm may beused along with the upper bound α ≤ 1

η to explore a goodrange for η.

VI. CONCLUSION

In this paper, we proposed a new method for networkcapacity enhancement using FSO transceivers in hybridwireless-optical networks. We formulated the problem ofjoint FSO placement and link scheduling in the form ofan integer linear program. It was shown that upgradinga few strategically located nodes with such transceiverscan greatly improve the capacity of the network. We alsoproposed a probabilistic heuristic and a simulatedannealing scheme that can perform competitively com-pared to the optimal approach at significantly lower com-putation costs. Considering switching delays imposed bylink scheduling and the reliability of the FSO links is partof our future work.

REFERENCES

[1] S. Sarkar, H.-H. Yen, S. Dixit, and B. Mukherjee, “Hybridwireless-optical broadband access network (WOBAN):Network planning using Lagrangean relaxation,” IEEE/ACM Trans. Netw., vol. 17, no. 4, pp. 1094–1105, 2009.

[2] G. J. Narlikar, G. T. Wilfong, and L. Zhang, “Designingmultihop wireless backhaul networks with delay guaran-tees,” in Proc. of IEEE INFOCOM, Barcelona, Spain,April 2006.

[3] S. Sarkar, H.-H. Yen, S. S. Dixit, and B. Mukherjee, “DARA:Delay-aware routing algorithm in a hybrid wireless-opticalbroadband access network (WOBAN),” in IEEE Int. Conf.on Communications (ICC), Glasgow, June 24–28, 2007,pp. 2480–2484.

[4] A. A. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, S. S. Dixit,and B.Mukherjee, “CaDAR: An efficient routing algorithm forwireless-optical broadband access network,” in IEEE Int.Conf. on Communications (ICC), Beijing, May 19–23, 2008,pp. 5191–5195.

[5] A. S. Reaz, V. Ramamurthi, S. Sarkar, D. Ghosal, and B.Mukherjee, “Hybrid wireless-optical broadband access net-work (WOBAN): Capacity enhancement for wireless access,”in Global Telecommunications Conf. (GLOBECOM), 2008,pp. 2812–2816.

[6] F. Ahdi and S. Subramaniam, “Capacity enhancement ofhybrid wireless optical networks using MIMO links,” inGlobal Telecommunications Conf. (GLOBECOM), 2011,pp. 1–6.

[7] B. Mumey, J. Tang, and T. Hahn, “Joint stream control andscheduling in multihop wireless networks with MIMO links,”in IEEE Int. Conf. on Communications (ICC), Beijing, May19–23, 2008.

[8] S. Krishnamurthy and A. Acampora, “Capacity of a multihopmesh arrangement of radio cells connected by free-spaceoptical links,” in 12th IEEE Int. Symp. on Personal, Indoorand Mobile Radio Communications, San Diego, CA, Sept.2001, vol. 2, pp. G-49–G-54.

[9] A. Kashyap, K. Lee, M. Kalantari, S. Khuller, and M.Shayman, “Integrated backup topology control and routingof obscured traffic in hybrid RF/FSO networks,” Comput.Netw., vol. 51, pp. 4237–4251, Oct. 2007.

[10] M. Smadi, S. Ghosh, A. Farid, T. Todd, and S. Hranilovic,“Free-space optical gateway placement in hybrid wirelessmesh networks,” J. Lightwave Technol., vol. 27, no. 14,pp. 2688–2697, July 2009.

[11] Y. Tang and M. Brandt-Pearce, “Link allocation, routing, andscheduling for hybrid FSO/RF wireless mesh networks,”J. Opt. Commun. Netw., vol. 6, no. 1, pp. 86–95, 2014.

[12] F. Ahdi and S. Subramaniam, “Optimal placement ofFSO links in hybrid wireless optical networks,” in GlobalTelecommunications Conf. (GLOBECOM), 2011, pp. 1–6.

[13] J. Rak and W. Molisz, “Reliable routing and resourceallocation scheme for hybrid RF/FSO networks,” in 16thInt. Conf. on Transparent Optical Networks (ICTON), 2014,pp. 1–4.

[14] F. Ahdi and S. Subramaniam, “Improving hybrid FSO/RF net-work reliability through transceiver reconfiguration,” inGlobal Telecommunications Conf. (GLOBECOM), 2012,pp. 2947–2952.

[15] F. Ahdi and S. Subramaniam, “Optimal placement of FSO re-lays for network disaster recovery,” in IEEE Int. Conf. onCommunications (ICC), 2013, pp. 3921–3926.

[16] H. E. Nistazakis, E. A. Karagianni, A. D. Tsigopoulos, M. E.Fafalios, and G. Tombras, “Average capacity of opticalwireless communication systems over atmospheric turbu-lence channels,” J. Lightwave Technol., vol. 27, no. 8,pp. 974–979, 2009.

[17] B. Epple and H. Henniger, “Discussion on design aspects forfree-space optical communication terminals,” IEEECommun.Mag., pp. 62–69, Oct. 2007.

[18] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimizationby simulated annealing,” Science, vol. 220, no. 4598,pp. 671–680, 1983.

Farshad Ahdi and Suresh Subramaniam VOL. 8, NO. 7/JULY 2016/J. OPT. COMMUN. NETW. 505

[19] J. G. Andrews, A. Ghosh, and R. Muhamed, Fundamentals ofWiMAX: Understanding Broadband Wireless Networking,Prentice Hall Communications Engineering and EmergingTechnologies Series. Upper Saddle River, NJ: PrenticeHall, 2007.

Farshad Ahdi (M’06) earned his B.Sc. andM.Sc. in electrical engineering from SharifUniversity of Technology in 2003 and2005, respectively. In 2010, he joined theUniversity of Maryland, College Park, as afaculty research assistant, where he de-signed and developed wireless sensors hard-ware and software for traffic engineeringapplications. He earned his Ph.D. in electri-cal engineering from George WashingtonUniversity in 2016, where he studied capac-

ity and reliability planning of hybrid optical and wireless net-works. He has published in several journals and conferencesbroadly in the area of optical, wireless, and sensor networks.

Suresh Subramaniam (S’95-M’97-SM’07-F’15) received his Ph.D. in electrical engi-neering from the University of Washington,Seattle, in 1997. He is a Professor in theDepartment of Electrical and ComputerEngineering at George Washington Uni-versity, Washington, DC. His research inter-ests are in the architectural, algorithmic,and performance aspects of communicationnetworks, with current emphasis on opticalnetworks, cloud computing, and data center

networks. He has published over 150 peer-reviewed papers inthese areas.

Dr. Subramaniam is a co-editor of three books on opticalnetworking. He is or has been on the editorial boards of sixjournals, including IEEE/ACM Transactions on Networkingand IEEE/OSA Journal of Optical Communications andNetworking, and has chaired several conferences, includingIEEE INFOCOM 2013. He is a co-recipient of the BestPaper Awards at ICC 2006 and at the 1997 SPIE Conferenceon All-Optical Communication Systems. He is a Fellow ofthe IEEE.

506 J. OPT. COMMUN. NETW./VOL. 8, NO. 7/JULY 2016 Farshad Ahdi and Suresh Subramaniam