using centrality-based power control for hot-spot mitigation in wireless networks.pdf

8/13/2019 Using Centrality-based Power Control for Hot-spot Mitigation in Wireless Networks.pdf

1/6

Using Centrality-based Power Control for Hot-spot Mitigation in Wireless Networks

Parth H. Pathak, Rudra DuttaDepartment of Computer Science, North Carolina State University, USA. Email: [email protected], [email protected]

AbstractWhen shortest path routing is employed in largescale multi-hop wireless networks, nodes located near the centerof the network have to perform disproportionate amount ofrelaying for others. To solve the problem, various divergentrouting schemes are used which route the data on center-

avoiding divergent routing paths. Though they achieve betterload balancing, overall relaying is increased significantly dueto their longer routing paths. In this paper, we propose powercontrol as a way for balancing relay load and mitigating hot-spotsin wireless networks. Using a heuristic based on the concept ofcentrality, we show that if we increase the power levels of only thenodes which are expected to relay more packets, significant relayload balancing can be achieved even with shortest path routing.Different from divergent routing schemes, such load balancingstrategy is applicable to any arbitrary topology. Also, it is shownthat centrality based power control results into better throughputcapacity in many different topologies.

I. INTRODUCTION

Many of the routing protocols proposed for multi-hop wire-

less networks depend on shortest path routing (SPR) due to itscharacteristics of simplicity, robustness and scalability. It hasbeen observed that when hop count based shortest path routing(SPR) is used for uniform node-to-node communications in amulti-hop network, certain nodes have to perform dispropor-tionate relaying of data for others. Such hot-spots are oftencreated near the center in uniform topologies and also at clusterperipheries in clustered topologies. Such increased congestionat certain nodes affects network capacity and reduces energyefficiency of energy-constrained networks.

The problem of disproportionate relaying has been ad-dressed mainly by devising routing strategies in which routingpaths intentionally try to avoid passing via center. Curvedpaths in curve-ball routing [1], [2], one-turn rectilinear paths in

Manhattan routing [3] and edge reflection paths of outer spacerouting [4] are some examples of such strategies. We refer tosuch center-avoidance routing strategies generally as divergentrouting. Any such divergent routing scheme increases relayingload of the nodes near the periphery of the network whiletaking away some relaying burden from the nodes aroundthe center. This results into better overall load balancing.This advantage comes at a cost of various other sacrifices.Most of the divergent routing schemes depend on geometricalproperties of the network (for mapping over symmetric spacelike torus or sphere) which limits their applicability to uniformtopologies only. Routing paths in any such scheme are alsolonger (higher stretch factor) when compared to shortest rout-

ing paths. Moreover, divergent routing schemes sacrifice thefundamental advantages of SPR such as robustness, scalabilityand simplicity. In many cases, divergent routing schemes donot eliminate the hot-spots in the network because the relayload of the nodes near the center decreases moderately whilethe load on nodes around the periphery increases significantly.This raises an interesting question is it possible to preserve

This work is supported by the U.S. Army Research Office (ARO) undergrant W911NF-08-1-0105 managed by NCSU Secure Open Systems Initiative(SOSI). The contents of this paper do not necessarily reflect the position orthe policies of the U.S. Government.

SPR (and all its advantages) while achieving better relay loadbalancing?

One of the assumptions in divergent routing schemes is thatall nodes operate at Compow [5] power level and routing isperformed on the resultant topology. In Compow, all nodes usea uniform power level which is minimum required to maintainnetwork connectivity. Compow achieves better concurrency inlink scheduling due to lesser interference but requires morerelaying at nodes because of longer routing paths. This moti-vates the question is disproportional relay load distributionin multi-hop communications also a consequence of Compowpower range together with SPR? And can it be dealt with usingpower control instead of modifying routing?

In this paper, we propose power control as a way to balancerelay load in static wireless networks. We show that if thecommunication range of nodes are properly increased byincreasing their power levels, better relay load balancing canbe achieved even when routing on the shortest paths. In all

cases, choosing only a small subset of nodes and increasingtheir power levels is sufficient to achieve load balancing thatis significantly better than divergent routing schemes. Thefundamental advantage of such power control based loadbalancing is that it preserves all the benefits of shortest pathrouting and still achieves significant relay load balancing.Because all the characteristics of shortest path routing isretained, such load balancing can be applied to any kind ofarbitrary topologies (e.g. clustered) and traffic patterns (e.g.node-to-gateway) where divergent routing can not be applied.

The proposed load balancing scheme does not route the dataon divergent routes to avoid passing through the nodes near thecenter. Instead, the data is routed on the shortest paths only andthe nodes which are expected to relay more packets for others

are skipped or jumped over. In the case of uniform topologies,this results into longer hops being taken near the center whichreduces the relay load burden of congested nodes withoutincreasing the relay load of the nodes on the periphery. Longerhops in routing paths can only be achieved by controlling thecommunication range of nodes using power control. Powercontrol based load balancing presented here assigns higherpower levels to nodes which are expected to relay morepackets. This has an underlying requirement of estimating therelay load of nodes in advance so that communication rangecan be assigned to them accordingly. We calculatebetweennesscentrality of nodes which assigns every node a score based ontheir expected relay load. The centrality value is then used

to assign every node a power level which is proportional toits expected relay load. This increases the connectivity of thenodes who were expected to relay more packets previously.When shortest paths between nodes are found in this new moreconnected network, they pass over congested nodes, producingbetter load balancing.

One of the disadvantages of the divergent routing schemes isthat there is a trade-off [6], [7] between length of the routingpaths (path-stretch) and amount of load balancing achieved.We show that power control based load balancing does notshow such a trade-off with path stretch. Instead, it is observed

978-1-4244-5638-3/10/$26.00 2010 IEEE

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings


2/6

(a) Shortest path routing

0

1000

2000

3000

4000

5000

6000

7000

8000

(b) Hot-spot generation (c) A divergent routing

1000

2000

3000

4000

5000

6000

7000

8000

(d) Load redistribution(e) Centrality power control

0

500

1000

1500

2000

2500

(f) Load balancing

Fig. 1: General nature of path and relay load characteristics

that load balancing and capacity sometimes show a trade-off when power control based load balancing is applied insome of the topologies. We characterize that such a trade-off is limited to the case of uniform node placement andas the node placement becomes more random and clustered,increased capacity can be achieved together with better relayload balancing. Also, in our contiguous work (currently undersubmission), we have shown that intelligently increasing ofpower levels of some nodes does not adversely affect theenergy expenditure and network lifetime in stationary energy-constrained networks. Due to increased relay load balancingand reduced overall relaying, in fact such a strategy increasesthe network lifetime by upto 30% when compared to divergentrouting schemes in wireless sensor networks. We also briefly

present these results for completeness.The rest of the paper is organized as follows - we start by

explaining network model and related assumptions in SectionII. Section III presents centrality based power control strategyand shows how betweenness centrality can be used for powerallocation. Instead of devoting a separate section for relatedwork, we discuss them in each individual section as andwhen necessary. We present several numerical results on loadbalancing and capacity in Section IV and conclude in Sec. V.

I I . NETWORKM ODEL ANDP RELIMINARIES

We model the network using a directed graph G= (V,E,r),where V is a set of n stationary nodes and r is a set ofcommunication range values assigned to each node in V.There exists an edge from nodeu to nodev if their Euclideandistanceduv ru. This allows the modeling of variable powercontrol where each node might have a different communicationrange. Note that when the value ofrv is same for all v V,the resultant network graph can be considered as an undirectedgraph (unit disk graph) since all the edges are bidirectional.In one such case, when there is no explicit power control, allnodes are assumed to be operating at Compow power level.Compow range (rmin) whererv = rmin,v Vis defined asminimum value of common range such that G is connected.We refer to the Compow graph as GC.

Centrality values of all nodes are determined from theCompow graph and used to assigned different power levels

to different nodes. Here, increase in power levels can actuallybe interpreted as bounding the maximum power level of nodes.That is, if a node increases its power level, this does notmean that it will always transmit at new increased powerlevel. If a neighbor is reachable at a lower power level, itwill utilize that to communicate with it. We use path lossmodel of signal propagation. If transmitted signal power is Ptand distance between the transmitter and the receiver is d thenreceived signal power (Pr) attenuates asPr Pt(d

), where is the path loss exponent which depends on environment(2 5). Let be the receiver sensitivity threshold such

that signal is properly decoded at the receiver ifPr . Fora node transmitting at power Pt, the communication rangeis the distance at which Pr = in absence of any otherinterference. Now, power level of nodes can be presented interms of their communication range. As an example, in GCallnodes are operating at power level P(rmin)which is necessaryand sufficient to achieve communication range ofrmin at allnodes. Now, if a node wants to increase its communicationrange by a factor off, it tunes its power level to P(f rmin).

We use uniform node-to-node traffic pattern for simulationand analysis. In uniform node-to-node traffic, every pair ofsource and destination communicate with amount of trafficwhich is uniform across all such pairs. With the considerationof dense node distribution, greedy geographical routing (where

packet is forwarded to the neighbor which is nearest to thedestination) also becomes shortest path routing and we useboth names interchangeably. We assume that the nodes arestationary and there is no consideration of mobility in thiswork.

III. CENTRALITY-BASEDP OWER C ONTROL

Conceptual difference between load balancing using di-vergent routing and power control is depicted in Fig 1. Itcan be observed that divergent routing schemes (Fig. 1c, 1d)transfers much of the relay burden onto the nodes aroundthe periphery. In power control based load balancing (Fig.1e, 1f), data is forwarded on shortest path only but nodesin hot-spot regions are skipped or jumped over. This resultsinto longer hops taken near the center hot-spot in uniformtopologies. To achieve such longer hops, nodes which areexpected to relay more packets should be assigned highpower levels and larger communication range. If the relayload at every node can be estimated, then a node can beassigned power levels proportional to its estimated load. Thisincreases the connectivity of the nodes which were likely torelay more packets previously. When shortest paths betweennodes are found in this new more connected network, theypass over congested nodes, producing better load balancing.The mentioned heuristic has an underlying requirement foraccurately estimating the relay probability of nodes for anygiven topology which we discuss next.

A. Modeling Relay Load

Techniques for modeling and estimating relay load havebeen limited to uniform topologies with assumptions like con-tinuous density of nodes. One of the first few such approacheswas presented in [1] where relay load probability of a nodewas derived as a function of its (Euclidean) distance from thecenter of the network, when routing over the shortest pathsbetween the nodes. It is possible to show that nodes at samedistance from the center can have different relay load if thetopology is even slightly non-uniform. Similarly, [8] presented

978-1-4244-5638-3/10/$26.00 2010 IEEE



3/6

0

0.5

1Simulated relay load

0

0.5

1

0 100 200 300 400Node ID (sorted based on simulated relay load)

Betweenness centralityin Compow graph

Fig. 2: Comparison of simulated relay load of nodes andtheir centrality values in Compow graph (all normalized withmaximum value, n=400 randomly distributed in unit square)

Voronoi cell based technique in which it was shown that relayload of a node is a function of perimeter of its Voronoi cell, itslocation in the network and the traffic pattern in consideration.Even with assumptions of uniform node-to-node traffic patternand node distribution, Voronoi tessellation based model mightnot always be sufficient because nodes adjacent to each otherin network graph might not always have neighboring Voronoicells. Such techniques do not always accurately estimate therelay load because they rely on geometrical properties of thenetwork and not the underlying network connectivity.

1) Betweenness Centrality: We are interested in devisinga relay load estimation technique which relies on propertiesof network graph. Centrality indices [9] proposed for analysisof large network assign relative importance or status to everynode in the network based on certain characteristic of interest.One such centrality named betweenness [10] of a node de-pends on how many end-to-end shortest paths between othernodes of network actually pass through it. In node-to-nodeuniform traffic, a node is likely relay more data for others if itfalls on relatively more number of shortest paths between othernodes. For a network graph G, ifSxy is number of shortestpaths between vertices x and y and Sxy(v) denotes number

of shortest paths between x andy which pass through vertexv, then betweenness centrality ofv (denoted by (b(v))) is

b(v) =

x=y=vV

Sxy(v)

Sxy(1)

The fraction in (1) (also known as pair-dependency) can beinterpreted as the probability that vertex v will be relayingdata between vertices x and y. Betweenness centrality of anode can be regarded as measure of how important a node isin carrying out relaying of data for other nodes.

Betweenness centrality is a structural index of the graph,that is ifH is isomorphic to G (G H), then betweennesscentrality satisfies the condition: v V :G H bG(v) =

bH((v)). Also, betweenness of nodes change considerablywith changes in edge set of network graph which may requirefrequent recalculations. This is not a concern here since wedo not consider any mobility of nodes. As described in [9],straightforward usage of Dijkstras algorithm for computingbetweeneness of nodes can have running time ofO(n3). Bran-dess algorithm [11] can compute betweenness of all nodes inO(nm) time for unweighted graphs and O(nm+n2 logn)forweighted graphs, wherem is number of edges in the graph. Interms ofn, this does not impose significant computational costfor moderate to large sized networks (400-1000 nodes). While

in terms ofm, as it is described below, betweenness centralityis required to be determined in the Compow graph which isa relatively sparser graph (m n(n 1)). Fig. 2 showsbetweenness centrality of nodes and compares it with theiractual simulated relay load in Compow graph when employinguniform node-to-node traffic pattern and SPR.

B. Centrality-based Power Control

Following steps describe how betweenness indices are usedto assign power levels to nodes.

1) For a givenV, first Compow range(rmin)is determinedand GC= (V, EC, rmin) is created.

2) Betweenness centrality of all nodes inGCare calculatedusing Brandess algorithm and are normalized using

max{b(v) | v V}.3) Every node v V is assigned a power level (Pv) as:

Pv = Pmin+ (b(v) (Pmax Pmin)), where Pmin P(rmin) to guarantee connectivity and Pmax Pmin.Even ifPmax = Pmin= P(rmin), resultant graph is atleastGC.

Any such assignment is uniquely referred as (Pmin, Pmax)

and resultant more connected graph of betweenness centralitybased power assignment is called GB. We often set Pmin =P(rmin) and vary Pmax = P(f rmin) using a factor f 1.In such case,Pmin andPmax are dependent onrmin which isa property ofV, only control parameter is f which we referas growth factor. For any reasonable value of f, resultsinto increased power levels and communication range of nodeswhich were expected to relay more packets. Nodes near thecenter in uniform topologies have higher betweenness and areassigned higher power levels. As shown in Fig. 1f, this allowsthem to jump over other nearby congested neighbors. If asource and a destination are on opposite side of each otherover the periphery, packet from source first starts progressingalong shorter hops. As it reaches near the center, long-distance

transmissions occur which results into longer hops, followedby fewer shorter hops at the end. This results into subsequentreduction of relay load of nodes near the center withoutincreasing relay burden on nodes on periphery.

Foremost advantage of such load balancing using powerassignment is that it can be applied to any kind of arbitrarytopology like clustered where divergent routing mechanismscan not be applied. Also, centrality measure of nodes canbe calculated for any specific set of shortest paths pertainingto traffic pattern of interest, which makes the mechanismapplicable for load balancing in any other traffic patterns (e.g.node-to-sink uniform). The complexity of the scheme is domi-nated by the complexity of centrality algorithm, and Brandess

algorithm performs well even with moderately large networksas we saw above. The presented scheme is static and cen-trality calculation is necessary only once. The only necessaryrequirement of the scheme is that the nodes should be able tovary their power levels as per the centrality based calculations.Note that the proposed power control is centralized and itsdistributed extensions are discussed in future work. Fig. 3shows the impact of growth factor on load balancing in a 20 x20 grid network. As discussed before,Pmin is set to P(rmin)andPmax = P(frmin). Initially, whenf= 1,Pmax = Pminand resultant topology is a Compow graph of V. In such

978-1-4244-5638-3/10/$26.00 2010 IEEE



4/6

0

150

300

450

600 f = 1

0

2000

4000

6000

8000

0

150

300

450

600 f = 2

0

2000

4000

6000

8000

0

150

300

450600 f = 3

0

2000

4000

60008000

0

150

300

450

600

Communication range

f = 4

Communication range

0

2000

4000

6000

8000

Relay load distributionRelay load distribution

Fig. 3: Effect of growth factor on load balancing in 20x20 grid

case, there is no explicit effect of centrality values becausegrowth factor is set to 1 and relay load distribution displays

hot-spots near the center. When growth factor increases, theactual difference between maximum and minimum power levelassigned in the network also increases. This results into higherpower levels and communication ranges for nodes which havehigher betweenness centrality and are expected to relay morepackets. As can be observed in Fig. 3, central nodes are nowassigned higher power levels which results into better loadbalancing. The growth factor f is a tunable parameter hereand its value can be decided based on several factor which wediscuss later.

IV. NUMERICAL R ESULTS

Three sets of simulation results are presented to confirm theclaims of load balancing using centrality-based power control.In the first set, load balancing strategy is applied to differentkinds of topologies. We also compare its load balancingperformance to existing divergent routing schemes. Next, weshow how the load balancing affects the attainable capacityin different topologies. At the end, we briefly present energy-efficiency and network lifetime results for sensor networks.

A. Load Balancing

Fig. 4a shows the nature of load balancing achieved by usingSPR in GCand centrality based more connected graph GB .We use 2020 grid and set the growth factor f= 6. That is,ifb(v) was the betweenness centrality of a node v , operatingat power level P(rmin) in GC, in GB , it is assigned power

level Pv =P(rmin) + (b(v) (P(6 rmin) P(rmin))). Asexpected, relay load distribution inGCclearly shows hot-spotsnear the center. In GB, even with shortest path routing, relayload is very well distributed among nodes.

Next, we analyze the effect of growth factor on load balanc-ing achieved by (Pmin, Pmax) power control. We considergrid (Fig. 4b), random (Fig. 4c) and clustered topologies(Fig. 4d). Random topologies (n 400) are modeled ashomogeneous Poisson point processes while clustered topolo-gies (n 300) are generated using Matern cluster process[12]. Shortest path routing is used with node-to-node uniform

traffic pattern. In all cases, maximum power level Pmax isvaried by growth factor f using Pmax = P(f rmin).We set minimum power level Pmin to P(rmin). Wheneverrandom topologies are considered, results are presented for 30instances of random topology with 95% confidence interval.Here relay load is defined as number of packets a node hasto relay for other nodes. It is observed that even for smallgrowth factor, relay load balancing improves significantly in

all topologies. Though initial decrease in maximum, averageand standard deviation of relay load is more significant, itconsistently decreases with higher values of f. In clusteredtopologies, nodes providing inter-cluster connectivity becometraffic bottlenecks and resultant relay load distribution can behighly disproportionate. Divergent routing based load balanc-ing schemes are not applicable in such clustered topologies.As can be observed, achieves significantly better relay loadbalancing in clustered topologies even for very small valuesoff.

Now, we compare the with other well-known divergentrouting schemes. Load balancing of greedy routing in cen-trality based power controlled topology is compared with the

load balancing of greedy routing in Compow topology (GC)and three well-known divergent routing schemes, namely outerspace routing [4], Manhattan routing [3] and curve-ball routing[1]. In outer space routing, packets are first forwarded towardsthe periphery of the network and is then reflected back fromsome intermediate node towards the actual destination. InManhattan one-turn routing, source forwards the packet to anintermediate node which is near the intersection of horizon-tal/vertical lines passing through the source and destination. Incurve-ball routing, network plane is first mapped on a sphereand shortest paths on sphere are then mapped back to theplane. This results into center-avoiding curved routing paths.All divergent routing schemes are also employed in GC.

Fig.4e shows the results of load balancing in a 400 nodes

network and uniform node-to-node traffic pattern. We usegrowth factor f = 6 in as described in Section III-B.Centrality based power control mechanism achieves signifi-cantly better load balancing compared to greedy and diver-gent routing schemes. Divergent routing schemes increasethe average relay load of nodes when compared to greedyrouting but decreases the overall deviation, which shows betterload balancing. On the other hand, decreases the standarddeviation of relay load substantially without even increasingthe average relay load. In most cases, achieves upto 50%better load balancing than divergent routing schemes which isa useful practical result.

Fig. 4f shows comparison of average routing path stretch

and distance stretch between the same set of schemes. Averagerouting path stretch can be defined as average ratio of hop-length of routing paths in any load balancing scheme to hop-length of the shortest routing path. Average distance stretchcan be defined as average ratio of Euclidean length of arouting path (summation of length of all of its hops) toactual Euclidean distance between source and destination. Thismeasures on an average how much routing paths of a schemedeviates from the straight line between the endpoints. All thedivergent routing schemes increase path and distance stretchcompared to greedy routing in Compow graph. Different

978-1-4244-5638-3/10/$26.00 2010 IEEE



5/6

00.5

1 0

0.5

1

0

2000

4000

6000

8000Relay loadRelay load

00.5

1 0

0.5

1

0

2000

4000

6000

8000

(a) Nature of load balancing using

0

1000

2000

3000

4000

5000

6000

7000

8000

0 2 4 6 8 10 12 14 16 18

Relayload

Growth factor (f)

MaximumAverageStandard deviation

(b) Load balancing using in grid (n=400)

0

5000

10000

15000

20000

25000

30000

0 2 4 6 8 10 12

Relayload

Growth factor (f)


(c) Load balancing, random topologies (n 400)

0

5000

10000

15000

20000

25000

0 1 2 3 4 5 6 7

Relayload

Growth factor


(d) Load balancing, clustered topologies (n 300)

0

2

4

6

8

10

12

Relayload[x10

3]

Maximum Average Standard deviation

GreedyOuter spaceManhattan outerCurve-ballCentrality-based

(e) Relay load compared to divergent routing

0

1

2

Averagestretch

Routing path stretch Distance stretch

GreedyOuter spaceManhattan outerCurve-ballCentrality-based

(f) Path characteristics compared to divergent routing

Fig. 4: Effects of centrality based power assignment

from this, actually reduces path stretch below one. This isbecause power control increases network connectivity whichreduces number of hops required to be taken to reach thedestination. Also, reduces distance stretch when comparedto Compow graph because increased connectivity makes end-to-end shortest paths deviate less from the straight line. It isgenerally believed that when divergent routing is used for loadbalancing, stretch factor and load balancing ratio are inverselyproportional to each other [7]. As shown in [6], divergentrouting strategy which has stretch factor of with comparedto shortest path routing, can achieve load balancing ratio of

O(n/). But when power control is used for load balancing,

it is in fact possible to reduce stretch factor together with loadbalancing ratio, using shortest paths only.

B. Throughput Capacity

Increasing power levels of nodes certainly results into betterload balancing, but it also affects achievable spatial reuse andthroughput. Increasing communication range and connectivityof nodes using power control results in longer links whichcauses interference in a larger area, reducing simultaneoustransmissions. In this section, we show that centrality basedpower control also increases throughput capacity in randomand clustered topologies under uniform node-to-node traffic.

In case of uniform topologies such as grid, centrality basedpower control shows a trade-off between load balancing andthroughput capacity.

We use spatial reuse TDMA-based greedy link scheduler[13] for generating time slotted, conflict-free and feasible linktransmission schedule. The end-to-end traffic demand betweennodes is represented using a traffic demand matrix (TR).Once the shortest path routing is performed, TR yields per-link transmission matrix (TX). We assume that there is acentral controller entity which performs link scheduling. Inthe operation of greedy scheduler, first all links of TX are

sorted based on their interference score. Interference scoreof a link is the number of other links with whom the givenlink interferes and hence can not be scheduled simultaneously.Then scheduler chooses the first link in order to be scheduledin the current slot and tries to add more and more non-interfering links greedily until no more links can be added tothe slot. The procedure repeats until all transmission requestsofTX are satisfied. [13] showed that such a scheduler has thetime complexity ofO(m n T), where T = ni=0

nj=0TXij .

If the total offered load G = ni=0nj=0TRij and greedy

scheduler requiresSslots to schedule all the links, the networkthroughput is G/S traffic units per unit time. The TDMAscheme used here is centralized and we assume that thereis tight synchronization between nodes, and resultant TDMAschedule is distributed to the nodes without any additionaldelay. Such an idealistic TDMA scheme is appropriate to studyperformance of centrality based power control which is thecentral focus of the work.

We assume that simultaneous transmissions on two linksuvandxy results into collision-free data reception at the receiversiff dux, duy, dvx, dvy > ( duv) and dux, duy, dvx, dvy >( dxy), where dxy is the distance between nodes x and yand interference ratio = 2. As an example, in coarse-grainedTDMA, if every slot is 1 second and channel goodput (B) isapproximately 6 Mbps (as in 802.11b without RTS/CTS) inabsence of interference, then resultant throughput with abovementioned TDMA scheduler is (G/S) B.

Fig. 5a shows the aggregate network throughput for threedifferent topologies. In case of grid, increasing the growthfactor results into initial decrease of capacity followed by anincrease. Even though load balancing improves with increasein growth factor, highest capacity is achieved at f = 1 incase of grid topology. This is because highest spatial reuse isachieved at f= 1 in case of grid and spatial reuse gradually

978-1-4244-5638-3/10/$26.00 2010 IEEE



6/6

using centrality-based power control for hot-spot mitigation in wireless networks.pdf

Documents