1

On the problem of placing Mobility Anchor Pointsin Wireless Mesh Networks

Wu; LeiSchool of Information Technologies

and National ICT Australia

Abstract Over the past few years, wireless mesh networks areemerging as a strong technology for cheap wireless coverage.Despite recent advances in wireless mesh networking, manyresearch challenges remain in all protocol layers. Since a meshnetwork usually has very different characteristics than those ofcurrent fixed mobile networks, traditional fixed deploymentssuch as those in Cellular IP and HMIP will not perform well. Inwireless mesh networks, the topology is usually an unplannedgraph and there are no root nodes for the placements ofmobility anchor points (MAP). Furthermore, the connectionsbetween mesh routers are wireless and have very highvariability which make the MAP placement problem evenharder as the changes of the topology have to be adhered to.In this paper, we will explore the MAP placement problem in agraphic model. We point out the factors that have to beconsidered in the placement problem and give a simple solution.

Index Terms-Wireless Mesh network, Anchor Points,Centrality, Mobility Management, HMIP

I. INTRODUCTIONWs,rLAN has become a standard to provide wireless access

within a small area and it's becoming very popular inboth residential and commercial areas because of its

mobility and flexible reconfiguration. As laptop andhandheld computer devices become more popular and globalnetworking ubiquitous, the demand to provide wide areanetwork access to mobile users is growing rapidly. There arecurrently many different technologies under research anddevelopment to provide wireless coverage (WiMax, 3G), andwireless mesh networks are emerging as a strong candidateamong them due to its low cost. Even though research in thisspace is relatively immature, the ideas underpinning thesystems came from industry and products are already on themarket [6].Wireless mesh networks consist of wireless routers, whichmay also operate as radio access points (AP). These wirelessrouters are called mesh nodes. Similar to ad-hoc networknodes, mesh nodes spontaneously form multi-hop wirelessnetworks capable of finding routing paths through an

Manuscript received July 17th, 2006.

Bjorn LandfeldtSchool of Information Technologies

and National ICT Australia

unplanned graph network. However, as opposed to ad-hocnetwork nodes, mesh network nodes are stationary. Thisbounds many of the aspects of ad-hoc networks and createssystems that can be deterministically modeled. Specifically,the most discouraging features of ad-hoc networks areremoved in terms of losses and throughput constraints.The mesh networks also consist of mesh clients, which are theconventional nodes (laptops, PDAs, desktops, phones, etc.)that connect directly to the mesh routers. These mesh clientsmay mobile in the wireless mesh network and connect todifferent mesh routers. Thus many mobility managementfunctions are needed to maintain the appropriate operations.Both the distributed [9] and hierarchical [10, 11] mobilitymanagement schemes developed for ad hoc networks maynot perform well due to the specific feature of WMNs:

* The mesh nodes do not exhibit as high mobility asthe mobile nodes in ad hoc networks.

As the mesh nodes are stable, the mobility managementschemes developed for cellular or mobile IP networks couldbe useful for WMNs. However, current centralized schemessuch as cellular IP [7] and hierarchical Mobile IP [8] for fasthandover were designed for fixed networking paths withstructured tree hierarchies. The possible wireless access(base station) is usually attached at the last hop. Theseschemes assume that the fixed networking paths are stableand the hierarchies can be deterministically created followingthe network layout at deployment thus the MAPs can beplaced at the root nodes in the hierarchies. In WMNs theseassumptions do not hold true because of another two specificfeatures ofWMN:

* The topologies of WMNs are usually unplannedgraphs instead of trees so there exist no root nodesto place the mobility anchor points (MAPs)

* Two geographically neighboring nodes may not bedirectly connected and can be very far from eachother in the mesh network.

All these properties make appropriate placements of mobilityanchor points in wireless mesh networks an interestingproblem.In this paper, we make the following contributions: Weanalyse the problem mathematically in a graph model andfind the most important factors for placing the MAPs. Basedon the mathematical model, we develop a simple solution forthe MAP placement problem. We also compare our solution

1-4244-0692-7/06/$20.00 ©2006 IEEE.

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to the average performance and MIP performance throughsimulation and conclude that our solution does give betterperformance in the studied cases.

needed to MAP. When the client moves from one subnet toanother, a global handover is needed.

The rest of this paper will be organized as follows. In section2, we will discuss the MAP selection problem in detail. Insection 3, we will provide some relevant work. In section 4,we will study the problem in a graph model. In Section 5, wewill propose our simple approach together with somealternative approaches. In section 6, we validate ourapproach through simulation. In Section 7, we will discusssome future work and section 8 will finally conclude.

II. PROBLEM DESCRIPTION

Mobile IP [3] has been designed to provide seamlessconnectivity for a new class of mobile Internet computers.Although the Mobile IP solution meets the goals ofoperational transparency and handover support [4], it'sdesigned for slowly moving hosts and may becomeinefficient in the cases of frequent migrations [5].Several hierarchical mobility management schemes havebeen designed [7][8] in order to provide faster handover formore frequent migrations. In these schemes, mobility ismanaged differently at different networking levels. As inHMIP [8], mobility anchor points (MAPs) are deployed togroup access points into different subnets so that when amobile client is moving within the same subnet, only a localbinding update to the MAP is required. These schemes workwell in traditional fixed mobile networking where paths areusually fixed [12].

BS]IT BS3 -T- ~BS4 BS5BS2

Mobile Node La o l - - Global Mobility - * <9Mobile Node (Position 2) Mobile Node (Position 3)

Figure 1. Local and global mobility in traditionalhierarchical networkFigure 1 shows a traditional network where the root nodes actas routing nodes (MAPs). As can be seen from the figure, thetopology of the traditional mobile network is structured like atree and the placement of rooting nodes (MAPs) are usuallypredetermined to be the root nodes in the tree structure.Access points (base stations) are connected together to theMAPs using wired and stable links. When a mobile clientmoves within the same subnet, only a local handover is

(S5

MN2

................... ((T') ...N.,

M1MN

13

.........

>4j

MN2

-- 1

15

(i)

Figure 2. Mobility in a Wireless Mesh Network

These hierarchical mobility management schemes can also beuseful in wireless mesh networks. However, it is very hard tofind appropriate placement of MAPs as the backbone ofWMNs usually has a graph topology instead of tree topologyand the mesh network topology is usually unplanned wheretwo geographically neighboring nodes may not be directlyconnected and can be very far from each other in the meshnetwork. Figure 2 shows such an example of wireless meshnetwork where determining the placement of mobility anchorpoints is very difficult. As can be seen from the figure, MN1moves from node 6 to node 13 and then to node 15 and thennode 14, it's extremely hard to find the appropriate MAPplacements as node 6 and 13 are 6 hops away and node13 is 3hops away from node 5. In addition, the wireless connectionsbetween mesh nodes can have high variability. For example,as shown in figure 3, when MN2 is moving from node 6 tonode 7, theoretically, node 3 might be a good node to placeMAP. However, node 3 might have very high delay in somecircumstances as it actually has 5 neighbors. In this case,other nodes such as node 4 or node 2 might be betterplacements for MAPs.All these properties make MAPs placement an interestingand challenging problem in wireless mesh network.

III. RELATED WORK

Because the problem of MAPs placements in traditionalnetworks is a fairly easy problem, there has been rarely anyresearch regarding the placement of MAPs. However, [13]compares HMIPv6 to MIPv6 and proved that HMIPv6 givesbetter performance in a Wireless LAN scenario. Twodifferent MAP placements in the same network scenario arealso compared and the results demonstrate that differentplacements of MAPs do result in different handover delays.There have also been a number of interesting studies onplacing different servers at different locations in the Internet

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for better performances which have some similarities to ourMAP placement problem. [15] examines the placementproblem for Internet instrumentation and [14] proposed away to find the optimized placements of gateway points inwireless mesh networks. These previous works cannot beapplied to our problem as their focus is on maximizing thecapacity of the network rather than minimizing the latency.It is also worth mentioning that the MAP placement problemcan be considered as a centrality type of problem. Firstintroduced in social network analysis [16], centrality indiceshave been used to determine the ability to provide efficientcommunication in a variety of networks. Examples of thesenetworks include co-citation networks, scientific cooperationnetworks, etc [18]. Based on different centrality indices, thecentrals of the networks which indicate the most influentialnodes in these networks can be determined for variouspurposes. In the co-citation networks, this usually indicatesthe most important authors in the area, and in the scientificcooperation network, the central nodes usually indicates themost important and famous scientists.The improvement of communication network using centralityindices is first found in [17] where the author applies theknowledge of human networks into the design of computernetwork topologies. [19] proposes a general framework fordecentralized algorithms which can be used to calculate thecentrality indices dynamically.All these previous works are not directly related to ourproblem, but we can still borrow some of their ideas in oursolution.

IV. MATHEMATICAL MODELINGA wireless mesh network consists of a set of mesh nodes thatare connected by radio channels within a given distance. Bydescribing these mesh nodes as vertices v and theconnections between two adjacent nodes as edges e, thewireless mesh network can be modeled as a simple graphG = (V,E) with undirected edges, without multi-edgeswhere (v e V, e e E). For simplicity, we can assume thegraph is always connected and all edges are always two way(the mesh network is always connected and there is no oneway connection between any two mesh nodes). Every edgee = (vI, v2) e E represents a direct communication

between vl, V2. Two nodes are directly connected if andonly if there is an edge between these two nodes. Nodes v andw are neighbors if and only if they are directly connected.The number of n nodes is defined as the cardinality of V(The number of mesh nodes). The number of edges is definedas the cardinality of E (the number of mesh connections).We can assume that each node maintains a list N(v) of itsneighbouring nodes and a list of the edges to its neighbouringnodes. Degree Degi (v) represents the number of nodesthat can be reached by v in i hops.A path P(V1 I VM ) from a source node v1 to a target node

vn is defined as a set of nodes {V,IV2, ...'Vm} such that

there is an edge eiJ+1 between any pair of nodes {vi, vi+1 }.

In our case, the edge delay De = Dvi vj is the cost on an

edge e between any adjacent nodes vi, v1 andd

DP = E De is the cost of the shortest path from vs to Vds

passing a sequence of edges.

The handover delay for any mobile node can be broken downinto the following four parts:

1. Movement detection delay2. Router advertisement delay3. Address configuration delay4. Binding update delay

The first three delays are local delays caused by registrationwith the new access point and won't be affected by theplacement of MAPs. We assume these delays are constant inour calculation and define them together to be D . We can

also assume the processing time required for localregistration, local and global binding updates to be constantand define it to be Dproc .The last delay is caused by the binding update and is of ourmain interest. It includes two parts in HMIP, local bindingupdate delay and global binding update delay. Local bindingupdate delay is the delay between the mobile node (MN) andthe MAP. Global binding update delay is the delay betweenthe MN and the Home Agent (HA). We use DBBUL and

DBUG to represent these two delays.The total handover delay can be defined as:

DglobalHO DconSt + DBUL + DBUG (1)

DIocalHO DCOnSt + DBUL (2)for global handover (1) and local handover (2) respectively.In the formula, the local and global binding up delays can beformulated as:

MAP

DBUL = 2x ZDeMN

HA

DBUG = 2xZDeMN

MAP= 2xDMN,AR +2x ZDe

AR

MAP

=2XDMNAR +2xZDe +AR

where the constant cost Dconst contains two parts:

const =Dreg + proc -

We can then simplify formula (1) and (2) to get the handoverdelays in terms of edge delays:

MAP

DiocalHO =2XDMN,AR +2x De +DconstAR

(3)

HA

2 x E DeMAP

4

MAP HA

DglobalHO - X MN,AR +4xEDe +2xEDe +DconstAR MAP

(4)With the above settings, the anchor point placement problemcan be mathematically described as the problem of selecting aset of nodes {vmapl, Vmap2 Vmapn I from V and a set of

sub-graphs {G1,G2,...,Gn} from G so that each vmapi

acts as the root of Gi to give the minimum possible averagehandover delays. Figure 3 shows an example of suchselections. As can be seen in the graph, the originalunplanned random graph with 18 nodes can be transformedinto 4 sub-graphs {{2,1,6,3,9,4}, {7,10,9,4,8,5,12},{11,15,13,4,16,5,12}, {13,18,17,16,12}} with 4 MAPs {2,7, 11, 14}. With this transformation, we can get a beautifultree structure with 4 root nodes and 11 nodes 1 hop awayfrom roots (for nodes with more than one paths to MAPs , weonly count the shortest one) and 3 nodes 2 hops away.

3

\4 5

10 11 15

1216

13

17

14\

18

movement of a MN. We assume ki is the same forevery node.

1. In the first case we analyse when there is only one MAP inthe graph and the only sub-graph Gi is G itself. In this case,there won't be any global handover. With the assumptions,the average handover delay for a selected MAP and any ARcan be formulated as:

MAP

avg(Dhandoff) E X (2 XDMNAR + 2 x E De +DAR AR

n MAP

2ZZDe= 2avg(DMN AR) + Dconst + AR=1 AR

n

n MAP

2E EDe/Note the major part of this formula AR=1 AR

actually represents two times the average shortest path delayor average round trip time (RTT) from any node to the MAP.This delay can be as small as 50% for the MAP in the centralof a graph comparing to the MAP at the edge of a graph.Figure 4 shows such an example when the delay on each edgeis 1, the average RTT for the central node is 1.2 and can betwice as high for some edge node.

RTT=2 0

MAPs

1 hop away

2 hops away

2 7

8<

10

,4/17

(RTI

5L

RTT=2 0

Figure 3. Forming sub-graphs with MAPs.

=1 2)

RTT 2 0CXIt is also important to notice that the selection actually has

two parts which can be performed in any order:* Formation of sub-graphs* Selection of the root nodes

Although it is very hard to derive a general formula for theaverage handover delay when the topology and themovement pattern are unknown, we can still analyse severalinteresting cases of the placements problem to find the mostimportant factors.First, we will make some assumptions:

* All mesh nodes are access routers (AR) and canprovide wireless connections to Mobile Nodes(MN)

* Each Mesh Node has the same possibility of being aHA.

* The possibility ki is the possibility that the current

point of attachment is node vi for a random

RTT=1 6 (RTT=2 4)

Avg(RTT)= 1 86

Figure 4. Average RTT for different nodes in a graphtopologyThis case proves that the correct placement of MAP in agraph topology can well reduce the handover delay.

2. In the second case we analyse the case where each AR is a

MAP, so each sub-graph Gi contains only 1 node. In thiscase, the delay between AR and MAP is 0. With theassumptions, the average handover delay for any MAP andany HA can be formulated as:

Z IE ki DglobalHOj

avg (Dhandoff ) = i

Yki

-7

5

HA

ZZE 4X DMN,AR +2x Z De const_ HA MAP MAP

n2n n HA

2Z Z De4aVg(D + Dconst + HA=1MAP= MAP

MO~VN,AR?' 2n

n n HA /2ZZZDe

Note again that only the last part HA MAPMAP 2 will

be affected by the placement ofMAP. And not surprisingly, itactually represents two times the average of the shortest pathdelays between any two nodes in the graph (average shortestroundtrip time).It is also worth noticing that, this case actually represents thedelay for MobileIP with an unnecessary local binding update.Specifically, if we remove DBUL = 2avg(DMN,AR) from

the above formula, we can get the formula for the averagehandover delay of MobileIP.

2avg(DMN,AR) + Dconst +

n n i

2ZZZDei=l j=l j

2n

(5)

3. In the third case we analyse selecting g MAPs from thegraph topology where g can be any number. With previousassumptions remains the same, we make several furtherassumptions:

* Each sub-graph has just the same n/g nodes* The possibility that a movement is a local movement

is m% and is the same for all sub-graphs.* With all these assumptions, it also holds true that the

possibility for a movement to happen in anysub-graph is the same and equals to l/g

The handover delayfor a selectedAR and a selected HA can

then be formulated as:

Dhandoff =m%DLocalHO (I- m%)DGlobalHO

Simplifying this formula we get:

Dhandoff DCOnst + 2(2-m%)DMN,ARMAP

+2(2-m%) ZDeAReMAPHA

+ 2(1-m%)ZDeMAP

For any AR and any HA, the average handover delay is

Dhandoff

avg(Dhandoff AR HA2

n

Because we only have to calculate the delays between the

ARs and their own MAPs, E is the same as n E forAR MAP

the MAPs and E is the same as E for the ARs.AR AReMAP

Simplifying the formula for average handover delay, we getformula (6):

avg(Dhandoff)=D const + 2(2 - m%)avg(DMN,AR) (a)MAP

Z ZDe+ 2(2-m%) AReMAP AR (b)

nHA

+ 2(l-m%)MAP HA MAPng

Formula 6 has the following three parts:1. Part (a) of this formula is the registration delay and

the transmission delay between MN and AR. It isnot directly affected by the placement of MAP.However, this part can be reduced by increasing m.

That is, increasing the possibility of local movementcan reduce this delay.

2. Part (b) of this formula is affected by thetransmission delay between AR and MAP.

MAP

ZDe

AReMAP AR constitutes the averagen

shortest path delay between any AR and its MAP. Itcan also be interpreted as the shortest path delaybetween any node in a sub-graph to the MAP of thesub-graph. As mentioned in case 1, the selection ofa good MAP can reduce this delay by up to 50%.This part can also be reduced with a bigger m.

3. Part (c) of this formula is affected by thetransmission delay between any MAP and any HA.

HA

MAP HA MAP constitutes the average

ng

shortest path delay between any MAP and any HA.As mentioned in case 1, good selections of MAPscan greatly reduce this delay. This part can also bereduced by a larger m.

(6) can also be used to derive the formulas in the first twocases. In particular, when m= 100 and g=l, (6) becomesexactly the same as the formula in case 1. When m=O, g=n,we get the same formula as in case 2.We can also compare (6) with the formula (5) for MobileIP.Assume there are 36 ARs and 6 MAPs and 60% of themovement are local movement (n=36, g=6 and m=60). Alsoassume avg (DMN,AR) = D,o,st = 1 and the average delay

between any two nodes is 6 times the avg(DMN AR) . With

these values, it is also reasonable to assume that:

(c)

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* The average local shortest path delay between anyAR and its MAP is one third of the average shortestpath delay between any two nodes. (The sub-graphis 1/6 the size of the whole graph)

* The average shortest path delay between any MAPand any HA is two thirds of the average shortestpath delay between any two nodes (As shown infigure 4)

Then simple calculation can show that the average delayusing 6 MAPs is 12.2 and using MIP is 15. The delay isreduced by more than 18%.

In this section we used mathematical models to analyse theproblem of placing MAPs in WMN. We showed that theplacement of MAPs is actually a problem of selectingsub-graphs and roots in the sub-graphs. We also showed thata good selection of MAP can reduce the delay by up to 50%in a simple graph. By analysing the general case of selecting gMAPs in a WMN, we proved mathematically that HMIP withwell selected MAPs can reduce the handover delaycomparing to MIP. We also identified the following mostimportant factors for placement of MAPs:

* Large local mobility possibility (m)* Small local average RTT

MAP

Z ZDe2(2-m%) AReMAP AR

n* Small global average RTT

HA

AL ADe2(1- m%) MAP HA MAP

ng

V. OUR APPROACHBased on the mathematical model derived in the last section,we propose a simple solution for the MAP placementproblem. As suggested in formula (6), the local handoverpossibility m is the most important factor as it actually affectsall parts of the formula. This suggests that we should findsubnets based on pre-gathered user mobility information firstand then select the MAP for each subnet.When selecting these subnets, we don't want them to be toobig or too small. If they are too big, the local handover delaywill be well increased; and if they are too small, the localmovement possibility will be decreased. Both of them willincrease the total handover delay, thus we define the size ofeach subnet to be larger than the maximum one hop degreeand smaller than the maximum two hops degree in thetopology graph. Our solution has the following steps:

1. Gather user mobility information.2. Based on the mobility information gathered, group

the mesh nodes into subnets (one node can be in twodifferent subnets) with the number of nodes in eachsubnet to be larger than Max(Deg, (v) v E V)

and smaller thanMax(Deg2 (v) v E V) .Estimate the average local movement possibility mand record the number of subnets g.

3. Calculate the combined closeness centrality [20]value for every node using half the average roundtrip time as the delay on each link (based on theinformation gathered during the warm up time).

Cc (v) =1

v v

2(2-m%)gl],De+2(1-m%)ZZDeteS t teV t

4. Select the node with largest combined closenesscentrality in each subnet as the MAP in that subnet.

Apart from our solution, there are also some other alternativeapproaches that can be used to determine the locations ofMAPs.One of the alternative approaches is to use the integrationpoints (gateways) as MAPs and form subnets around thesegateways. Because most correspondent nodes are actually inthe Internet rather than in the mesh networks, this approachmight be good for optimized routing. However, this approachdoes not count the user mobility pattern and it gives somenew problems like how many gateways there should be andwhere they should be placed. The schemes for efficientplacement of integration points proposed in [14][23] focuseson minimizing the number of gateways and maximize thecapacity because the gateways are much more expensive todeploy compared to other types of mesh nodes. Theseassumptions do not hold for MAPs, which are less expensiveand are delay sensitive rather than capacity or throughputsensitive. Thus, gateways are not best places to put MAPs.Another simple approach is to select MAPs randomly. Aftersubnets are determined, a mesh node can be randomlyselected to be MAP in each subnet. This approach is easy toimplement and takes into account user mobility pattern.

However, this approach only has I I1 n ( n is the size

of ith subnet) possibility to find the best combination ofMAPs. This approach is neither a good approach to be used,but ifwe average the performance of this approach over manyruns, it can actually give the average selection performance,which can be used as a good benchmark for our solution.

VI. SIMULATION VALIDATION

To validate our solution, we compare our approach forselecting MAPs to the random selection approach and MIP.The simulation tool we use is OMNeT++ [21] with INETFramework [22]. We use wireless hosts with multiplewireless network interfaces as mesh nodes that act as bothrouters and access points. We also modified the code so thatthe wireless links between mesh nodes do not interfere withthe links to the mobile nodes. For a more accuratecomparison, all route discovery delay is removed from thehandover delay.

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The simulation set up is as follows: The wireless interfaceshave a transmission range of 150 meters. 15 mesh nodes are

randomly positioned and grouped into 3 subnets with 5 nodesin each subnet. 1 server (CN) is placed in each of the subnetsand is connected to a random mesh node. Mobile Nodes are

randomly placed and randomly connects to one of the servers.

UDP traffic of 1000 bytes transmitted in an interval of lOmsis selected as the traffic between the server and the MobileNodes. A modified Random WayPoint (RWP) user mobilitymodel is used so that the possibility for a mobile node tomove to a different subnet is 30% and mobile nodes willnever move out of the network. The maximum movementspeed is 4 m/s. All simulations are given a 1Os warm up time.

Figure 5. Average Handover delay(ms) over No. ofhandovers.In the first scenario, we compare the average handover delayagainst the number of handovers. All three simulations have 5random mobile nodes and runs for 800s. The average

handover delays are calculated after each handover. Resultsare averaged over 500 runs with different seed values. Asshown in figure 5, the HMIP line is the result using our

approach. It is very clear that our approach almost alwaysperform better than MIP or the HMIP with randomly selectedMAP approach.In the second scenario, we compare the handover delayagainst the number of mobile nodes. We run the simulationsfor 500s with different number of mobile nodes. Results are

averaged over 100 runs with different seed values. As shownin figure 6, the average handover delay for our approach isalways smaller than the random selection approach and isbetter than MIP when the number of mobile nodes isrelatively small. When the number of Mobile nodes increasesto around 25, the delay of both HMIP approaches becomehigher than MIP. This is because traffic transmitted to themobile nodes in a foreign network always goes through theMAP, which becomes to have high delay with large numberof Mobile Nodes.In both scenarios, the results for the random selectionapproach are averaged through many different runs. Thus theresult of it can be treated as the average performance of allpossible selections. Thus our solution performs better thanthe average solution.

Figure 6. Average Handover delaymobile nodes increasing.

(ms) with number of

VII. FUTURE WORKAlthough our approach does give better performance in mostcases, there are still many issues left for future work.One of the assumptions for our approach is that the mobilitypattern can be predetermined and we can always group meshnodes together based on the mobility pattern. Thisassumption might be true in some cases (network in a

building, a park, etc.), but not in all cases. Thus a distributedscheme to dynamically form subnets based on the mobilityinformation gathered will be one important future work.In our approach, we did not consider the traffic throughMAPs. Traffic to mobile nodes in foreign networks alwaysgoes through MAPs and causes high delay when the numberof visiting mobile nodes becomes high (figure 6). Althoughthis might not matter too much as it has been shown in [2] thatthe handover rate for pedestrian users is low, it would beinteresting to consider routing and mobility managementtogether. In particular, as subnets can overlap with each otherand each mesh node can be in the more than one subnet, themobile nodes connects to the same access point can registerwith different MAPs for best routing. Thus a dynamic MAPregistration scheme based on the mobility prediction is alsoone of our future works.

VIII. CONCLUSIONIn this paper, we proposed an approach to use HMIP inwireless mesh networks. In particular, we analysed themobility anchor points placement problem in a mathematicalmodel. We find the most important factors for the placementproblem and proposed a simple solution based on thesefactors. We also validated our solution in simulation, whichshows that our approach performs better than MIP andrandom selection approach.Because it's only the starting point of our research, we havealso listed a number of interesting and challenging tasks forfuture works.

70-

60-

50 -Z

D 40 -*+ HMIP

a o MIP

n 30 HMIP(Random)

I

20

10

0-

5 10 15 20 30

No. of Mobile Nodes

Average Handover Delay

45

40

35

,, 30

aD 25-

> 0

I15

10

5

0

HMIPMIPHM IP(Random)

1 2 3 4 5 6 7 8 9 10 20

No. of Handovers

8

Our approach to solve the MAP placement problem can beseen as forming a tree structure in a random unplanned graphto minimize the handover delay. The idea is that some nodesin a mesh network are more important and more effectivethan other nodes for different evaluation criteria. These nodesshould then be chosen as the root nodes and the graph can betransformed into a hierarchical tree structure. As hierarchicaltree structures are always easier to analyse than random graphstructures, this idea can be adopted in many other researchareas such as routing, authentication, and security for findingoptimized solutions in wireless mesh networks.

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[19] K.A. Lehmann, M. Kaufmann, Decentralized algorithmsfor evaluating centrality in complex networks.

[20] Sabidussi, G. The centrality index of a graph.Psychometrika, 31, 581-603. (1966)

[21] OMNeT++

[22] INET Framework

[23] Y. Bejerano. Efficient integration of multi-hop wirelessand wired networks with QoS constraints. InACMMOBICOM, (2002)