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Int. J. Sensor Networks, Vol. 1, Nos. 3/4, 2006

179

Fuzzy preserving virtual polar coordinate space sensor networks for mobility performance consideration Wally Chen and Sy-Yen Kuo Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan, ROC E-mail: [email protected] E-mail: [email protected]

Han-Chieh Chao* Department of Electronic Engineering, National Ilan University, I-Lan, Taiwan, ROC E-mail: [email protected] *Corresponding author Abstract: One of the major problems in sensor networks is how to build a topology aligned to the practical environment. This paper presents a novel method for building a logical tree using Virtual Polar Coordinate Space (VPCS). This tree structure gives every node a pair of IDs representing an included angle. The angle range is a characteristic that indicates the relationship between the current node and the destination node. In such a structure, efficient routing strategies for utilising cross-links are provided without additional information. The maintenance of tree structure in a mobile environment is considered. This tree-like architecture is suitable for organising in sensor networks; however, it is a challenge to maintain the tree-like architecture, especially in sensor networks, each node can only provide limited functions. The essential point of this paper is to preserve the angle range for handling node’s variations and a fuzzy system is adopted to estimate the preserving range. Keywords: Virtual Polar Coordinate Space (VPCS); mobile; sensor; fuzzy. Reference to this paper should be made as follows: Chen, W., Kuo, S-Y. and Chao, H-C. (2006) ‘Fuzzy preserving virtual polar coordinate space sensor networks for mobility performance consideration’, Int. J. Sensor Networks, Vol. 1, Nos. 3/4, pp.179–189. Biographical notes: Wally Chen received his MSE from Electrical Engineering Department at National Dong-Hwa University, Hualien, Taiwan, ROC, in 2006. Currently he is a PhD student in the Electrical Engineering Department at National Taiwan University, Taipei, Taiwan, ROC. His research interests include wireless network, topology control, application of algorithms, computer architecture and logic synthesis. Sy-Yen Kuo is a Professor at the Department of Electrical Engineering, National Taiwan University and was the Chairman from 2001 to 2004. He received a PhD in Computer Science from the University of Illinois at Urbana-Champaign in 1987. He is an IEEE Fellow. He is heading the Dependable Distributed System and Networks Laboratory in the Department of Electrical Engineering at NTU, which focuses on the research of fault tolerant computing. Currently, the more and more complicated development of hardware/software systems and wired/wireless networks has made fault tolerance a very important issue in designing information systems to provide services with high dependability and high availability. His current research interests are mobile computing and networks, dependable distributed systems, software reliability and optical WDM networks. Han-Chieh Chao is a Full-time Professor of the Department of Electronic Engineering, the Dean of the College of the Electrical Engineering and Computer Science, National Ilan University, I-Lan, Taiwan, ROC. His research interests include high-speed networks, wireless networks, IPv6-based networks, digital creative arts and digital divide. He received an MS and a PhD in Electrical Engineering from Purdue University in 1989 and 1993, respectively. He is an IEEE Senior Member and Fellow for both IET (IEE) and BCS.

Copyright © 2006 Inderscience Enterprises Ltd.

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W. Chen, S-Y. Kuo and H-C. Chao

Introduction

There are two fundamental architectures in the Basic Service Set (BSS) for wireless networks. The first is the infrastructure BSS. The second is the independent BSS or so called ‘mobile ad hoc network’ (MANET) (Internet Engineering Task Force, 2003). A sensor network is one application in the MANET for wide deployment, a changeable environment and limited energy. The Internet Engineering Task Force (IETF) provided an experimental RFC for routing protocol specifications in MANET (i.e. AODV, DSR, OLSR and TBRPF; Wu et al., 2003). However, this RFC is too complex to apply to sensor networks. In sensor networks, the major problems are how to pass messages between nodes and how to maintain networks while nodes are frequently joining and leaving. Good network structure and proper routing strategy will bring advantages of time and energy saving. Numerous solutions are associated with Graph techniques. Routing in sensor networks is related to geographic information; however, sensor nodes may not get the necessary information (e.g. location coordinate) for some routing approaches due to their lack of functionality. This paper proposes a solution for this dilemma. Considering the reality of sensor networks, we propose building a network topology as a ringed tree graph based on Virtual Polar Coordinate Space (VPCS). The VPCS is the same as a normal polar coordinate system, using degrees to present a radius and a pair of IDs to present an included angle, which indicates the relation between each node. This tree structure is good for building a topology, searching nodes, passing messages and aggregating data (Madden et al., 2002). The proposed method is easy to implement and analyse. In order to cooperate with sensor networks, there are two important features in sensor networks must be considered. Firstly, the computing resources in a sensor node are very limited. The cost of addressing nodes is great because the node’s geographic position must be identified first. In sensor networks, energy consumption is the first priority. Numerous researches have addressed this topic (Chen et al., 2001; Kim et al., 2003; Schurgers et al., 2002; Shrisathapornphat and Shen, 2003). Traditionally, people used triangulation to locate objects in space. This has led to developments such as directional antennas (Huang et al., 2002). However, it is not necessary for a sensor node to compute its actual location. We propose a model that only utilises the neighbour existence (or so call signal) between each neighbour node and base station as their relevant position. Generally, base stations have greater computing resources than nodes. The proposed method lowers the computing demands on sensor nodes and reduces the manufacturing cost of sensor networks. There are numerous mature techniques for maintaining tree structures; however, not all methods are suitable for sensor networks. In normal data structure cases, there is no geographic relation between the data. For example, if a node is deleted from a tree, it is easy to choose one of the deleted node’s children and promote the child in

the deleted node’s place. However, this may not work in the real world because the communication radius limits the responsible area of each node. We use the degree and angle range to present a reference position in VPCS. Moreover, the cost for a new node joining this network is great. For this issue, we propose preserving interspaces for VPCS in a changeable environment. A simple fuzzy model is adopted to estimate the suitable angle range for each preserved space. In that case, node adding only causes very little effect to a constrained area. The following features are introduced in this work: •

We build topology aligned reality network without a physical node location measurement.

•

Principles are determined for assigning the degree and included angle in VPCS. This method facilitates passing message in sensor networks.

•

We propose preserving the angle range in every spanning tree to make it easier to maintain the network.

•

A simple Fuzzy system takes charge of estimating the suitable preserving angle range and prolongs the life time of the tree.

We focus on building, routing and maintaining the network topology. A brief description of related works is given in Section 2. The basic VPCS and how VPCS works is also addressed in Section 2. Section 3 shows how to build a topology without physical locations and how the network architecture is planned. In Section 4, we discuss a routing scenario in the proposed network. In Section 5, the problem of maintaining tree structure in sensor networks and the solution- Fuzzy preservation is introduced. Section 6 shows how preservation spaces are used to maintain the tree. Section 7 discusses several design models for analysing the proposed system and presents some simulation results.

2

Related work

We assumed that a sensor network system would gather information and forward that information to the sink nodes (or base stations). It is reasonable for the sink nodes to be located at the edge of the sensor network. As seen in Figure 1, there may be hundreds of nodes in the network cloud. The data flow through the network would move towards the sink nodes. The data flow volume would be related to the distance to the base station. Figure 1

Scenario for sensor networks application

Fuzzy preserving VPCS sensor networks for mobility performance consideration A brief description of some relevant researches is given before discussing the proposed method.

2.1 Geographic random forwarding Geographic Random Forwarding (GeRaF), is a MAC scheme technique based on the geographical location of nodes and the random selection a relay node. In group communication, GeRaF provides good collision avoidance and it provides a protocol for transition frameworks (Zorzi and Rao, 2003a,b). Earlier, sensor networks were considered wireless local area networks. MAC layer routing was reasonable in such a scenario. Recently, the scale of networks has increased, making layer 2 routing insufficient in large networks. High reliability in sensor networks is not demanding, and making the IP protocol too complicated. For these reasons, a label routing was proposed that is easy to practise and provides efficient routing. GeRaF is good for communication infrastructure and the label work provides help for improving routing efficiency.

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yet joined the tree system. Later generation nodes chose suitable nodes as their parents before joining the tree. In VPCS, the parent assigns each child a subset of its own angle range. The size of this angle range depends on each child’s proportion in the parent’s subtree. Children inherit their angle range from their parents in this way, see as Figure 2. However, this method produces a few problems. This process recurs until every node has its own angle. Here are the problems incurred in this process: Figure 2

Angle range assignment according to the size of subtree

2.2 Data-centric storage There are three categories for data storage in sensor networks: local storage, external storage and data-centric storage (Shenker et al., 2002). These three approaches have their own advantages and disadvantages. Data-centric storage is more acceptable in most practices. The original data-centric storage concept comes from the internet. The Geographic Hash Table (GHT) is designed for data-centric storage (Ratnasamy et al., 2002). GHT hashes keys in a geographic coordinate and stores a key value pair at each sensor node. This system architecture replicates data locally to prevent damage if nodes fail and enhances network stability.

2.3 Graph EMbedding for routing The Graph EMbedding for sensor networks use the Graph Embedding Method (GEM). VPCS is used to build a labelled ringed tree graph that is embedded in the network topology (Newsome and Song, 2003). The GEM also presents a routing for VPCS, called the VPCR, which checks if its neighbourhood is closer to the destination than the current node. VPCS provides an efficient alignment to the real environment, but it is expensive to maintain this tree-like structure. VPCR uses cross-links in the ringed tree to route laterally through the tree structure. However, it is limited to nodes with the same degree. Our proposal focuses on solving these problems. The following is a brief description of the VPCS.

2.4 Virtual polar coordinate space The proposed polar coordinate system chooses the tree root as the original reference in building the graphic topology. The VPCS has a tree-like architecture with a link process that is accessed from root to leaf. Earlier generation nodes were aware of neighbours that had not

Firstly, if a parent node has only one child, that child will have the same angle range as the parent. If there are several generations with only one child, they will all have the same angle range. In this situation, a node located in the middle generation will be confused about the direction of its destination. Mobility in such a compact tree structure will incur great cost, especially when nodes are added. When a new node is added into this system, there will be no space for it to occupy. Under current solutions, this new node will try to find its neighbours and choose a suitable one as its parent. The parent assigns a degree to the new node by taking away a part of the angle range from one or more of its other children. This movement causes a variation change flow down to the leaves in this tree, thereby expending lots of energy. To solve this problem, we propose some interspaces between two neighbouring subtrees, which means that some angle ranges should be reserved. When a node tries to join the tree, this additional movement will not affect the angle degrees of other nodes. We will discuss how to choose the preserved area and how this system works in a mobile environment.

3

Building graph topology

The nodes at the edge of the networks are chosen as the tree root nodes. We will describe how topology grows up in an application of Breadth-first search algorithm.

3.1 Preliminary Assuming that we have a connected, undirected graph G = (V, E). V is the vertex set representing sensor nodes and E ⊂ V × VE is the edge set. (u,v) ∈ E denotes two

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nodes could communicate with each other. We try to find a spanning tree T = (V, E’) for G where T is rooted at a vertex we selected and contains no circle. We denote π[v] = u if u is predecessor or parent of v in tree T, of course, π[root] = NIL. Tree (v) denotes the subtree rooted at vertex v ∈ V, and we denote the size of Tree (v) by n[v]. c[v] denotes the number of children of vertex v ∈ V, for example, c[v] = 0 if v is a leaf node in T. We try to locate nodes by polar coordinates. Degree of a node v in the tree represented the radius in the polar coordinate system, denoted by d[v]. We denote the included angle, shown in Figure 2, by a[v] = [a1[v], a2[v]].

Step 1 Degree assignment: The root node is assigned the degree 0. A node is an orphan if it has not been assigned a degree. The root broadcasts a message to announce its degree to its neighbour nodes. The announcement message will assign every orphan node the degree 1. After receiving the acknowledgement from those node with degree 1, root add those neighbours into its adjacency-list, denoted by Adj[root] and those neighbours will set root as their father. NEIGHBOUR-SEARCH (G, v) V’ Å V[G] while (u Å Find-neighbour (V’, v)) ≠ Ø do ADD-ADJ (Adj[v], u)

3.2 Assumption

if state[u] = Orphan then state[u] Å Announce d[u] Å d[v] + 1 π[u] Å v V’ Å V’ – {u}

We make the following assumptions in our model. •

It is possible for a node to measure the existence of its neighbour.

•

Communication radius for each node is equal.

•

We only use the information of adjacent nodes, and it is unreachable for other nodes where there are two or more hops away (or out of communication radius).

•

Any isolated node will be ignored because it is unreachable, and we do not consider isolated nodes as a part of our network.

state[v] Å Wait subtree account for each u ∈ Adj[ v] do if state[u] = Announce then NEIGHBOUR-SEARCH (G, u) Nodes with the degree 1 then broadcasts messages. These messages carry information about the current nodes and their parent nodes. In this way, these announcements accomplish four functions:

3.3 Process of tree spanning

•

There are seven states for this process as shown in Figure 3, state of node v is denoted as state [v].

Assign their neighbour nodes to be the next degree if they are orphans.

•

Receive acknowledgement and memorise their child.

Figure 3

•

Nodes with the same degree as the parent (we call them uncle) will memorise their nephew node.

•

Nodes with the same degree as the announcer will mark the cross-link. If the cross-link belongs to a different tree, these nodes become bridge nodes.

Action of building VPCS

The announcement message will propagate until all nodes have joined the tree or the remaining nodes are unreachable. Thus, all available nodes become connected into the tree structure. Step 0 Initialise: We assumed that every sensor node is an orphan until it receives an announcement, which we will describe later. INITIALISE (G, root) state[root] Å Announce d[root] Å 0 π[root] Å NIL n[root] Å 0 for each node u ∈ V [G ] − {root} do state[u] Å Orphan d[u] Å ∞ π[u] Å NIL n[u] Å 0

Step 2 Backward subtree account: After a node being assigned a degree, there is a simple method to count the size of a subtree. If a node sends out the announcement but it does not receive the acknowledge message from its child for a period of time, the node will assume itself to be a leaf in the tree and report to the size of subtree as 1 to its parent node. When a node receives an announcement from its child, it will wait for its child’s response. Until it receives subtree account reports from all of its children, this node sums the children’s subtree account numbers plus one. This number constitutes the parent node’s subtree account number. The node then reports to his parent node and the data aggregates in this way throughout the tree. Every node will get its subtree account before the root receives it.

Fuzzy preserving VPCS sensor networks for mobility performance consideration This means that the next step occurs only after the root receives all of the children’s responses. REPORT-SUBTREE-ACCOUNT (G, v) if c[v] = 0 then n[π[v]] Å n[π[v]] + n[v] else if REPORT-COUNT (v) = c[v] then REPORT (π[v], n[v]) else WAIT-NEXT-CYCLE() Step 3 Angle range assignment: This step is a kernel process in our method. Parent nodes determine the size of the angle range according to the children’s number and their subtree account. Figure 4 explains how the orders are determined between children with the same parent. As the tree structure shows in the figure, node A is the root with degree 0 and its angle range is [0:90]. B group has degree 1 and C group has degree 2. Because B1 and B2 have the same parent and no other conditions; their orders will be randomly assigned. We assume B1 = [10:40], B2 = [50:70] and we see that there are a few angle ranges reserved. In the next stage, B1 divides his angle range for his children into three parts, [12:18], [21:27] and [30:36]. How is a suitable node chosen to inherit each angle? Let us examine points C3 and C4. There is a cross-link between C3 and C4 and they memorised one another as bridge nodes during step 1. They know their parent’s ID and they could exchange messages about their parent information. Once they are aware that they have different parents, it is clear that they belong to different subtrees. In the B1 subtree, C3 is the only node that can contact the B2 subtree. Intuitively, C3 is closer to the B2 subtree than C1 and C2. It is, therefore, reasonable to choose C3 to inherit the angle range [30:36] because B2 > B1. The same scenario plays in the B2 subtree and C4 inherits the angle range [53:59]. Figure 4

Example of angle range assignment

4

Fuzzy preserving engine

Several policies were designed for preserving interspaces: •

if the current node spans a large subtree, it should preserve more angle range

•

if the current node has a large angle range (that imply its location near to root), it should preserve more angle range

•

if the current node has fewer children, it should preserve more angle range and

•

if the current node has no cross-link, it should preserve more angle range at the side that lacks traffic.

Before we talk about fuzzy variables, let us analyse our system first. We assumed that the nodes are distributed in a circle. The width of a degree distribution area is associated with the communication radius of a node. Figure 5 shows a model of the node distribution. The problem how many nodes exist in each degree is equal to calculate the proportion of each band area delineated by those concentric circles. Figure 5

Node distributed model for analysis

The intersection area of two circles is calculated as An, giving the band area Bn = An − An-1. Figure 6 shows the networks deployment radius as R and the radius of the concentric circles with degree n is r, where r = n × Rc (communication radius). Figure 6

We use a simple diagram to present these steps in Figure 2. After these steps, we build a tree structure with graph embedding information. We will show how these angle ranges are used for efficient routing in Section 4. We discuss how to preserve interspaces for easy maintenance later.

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Model for intersection calculation

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The intersection area is divided into two parts. The height function is expressed as

h1 ( x ) = R − ( R − x ) 2

Table 1

2

Nodes versus reserve space

System degree

10

20

50

100

1000

Total nodes

78

314

1963

7853

785K

405

3398

54K

440K

1T

Reserve space

h2 ( x ) = r − x 2

2

In this case, every preserved space will have the capacity to generate another subtree as large as the total network. In this way, 16-bits ID will be suitable for a system with a scale of about 2000 nodes. 32 bit ID will be competent to handle a system with more than one million nodes. This is a greedy method for reserving space, however, we did not intend to use such a brutal method. Instead of reserving a fixed amount of angle range, we propose using a fuzzy system to estimate how many preserved spaces are needed (Yager, 1988; Yager and Filev, 1994). We design a fuzzy engine, which helps each node to estimate suitable preservation spaces that does not cost a lot in our sensor node. In this way, our sensor network architecture has been competent in a changing environment. Finally, we explain how to maintain networks using these resources.

Using the law of cosine, r 2 = R 2 + R 2 − 2 R × R × cos θ 2 R2 − r 2 2 R2 d = R − R cos θ

cos θ =

=

r2 2R

The area is then calculated as: An = 2 ∫

d

= 2∫

R

R 2 − ( R − x )2 dx + 2 ∫

0

r

d

R 2 − x 2 dx + 2 ∫

R−d

r

r 2 − x 2 dx

d

= 2 R2 ∫

π /2

sin

−1

r 2 − x 2 dx

π /2 cos 2θ + 1 cos 2θ + 1 dx + 2r 2 ∫ −1 dx sin d / r R−d / R 2 2 π /2

⎛ sin 2θ ⎞ ⎛ sin 2θ ⎞ = R2 ⎜ +θ ⎟ + r2 ⎜ +θ ⎟ 2 2 − 1 ⎝ ⎠ sin R − d / R ⎝ ⎠ sin−1 d / r ⎛π ⎛ R − d ⎞⎞⎞ ⎛ R−d⎞ 1 ⎛ = R 2 ⎜ − sin −1 ⎜ − sin ⎜ 2 sin −1⎜ ⎟⎟⎟ ⎟ ⎝ R ⎠⎠⎠ ⎝ R ⎠ 2 ⎝ ⎝2 ⎛π ⎛d⎞ 1 ⎛ ⎛ d ⎞⎞⎞ + r 2 ⎜ − sin −1 ⎜ ⎟ − sin ⎜ 2 sin −1 ⎜ ⎟ ⎟ ⎟ ⎝r⎠ 2 ⎝ ⎝ r ⎠⎠⎠ ⎝2

According to those policies, the preservation area is a proportion to subtree account. We use this area to present a number of nodes in the following discussion: Our system is a tree with N degrees, and Rc. The calculus parameters previously discussed are represented as follows: R=

NRc , 2

r = nRc ,

d=

r2 2R

The worst case is considered and the amount is reserved in each node. We assume that every node reserves an angle range equal to all subtree accounts. A rough estimation of the total number reserved is: N

E reserve = π R 2 ∑ ( Bn + 1) n =1

⎛ N ⎞ = π R 2 ⎜ ∑ Bn + N ⎟ ⎝ n =1 ⎠

(

= π R2 =π2

)

2

+ Nπ R 2

( NRc ) 16

5

Routing policy

π /2

4

+ Nπ R 2

The total number of nodes is πR2. Table 1 gives a general idea using an actual numbers:

In our network, every node has a table with neighbourhood information that contains several relationships as Parent, Uncle, Brother, Friend, Children and Nephew. •

parent and children are logically connected

•

children’s angle ranges are totally contained by the Parent’s

•

an Uncle has a lower degree than a Nephew and they could contact each other. This is a multi-tree concept but there is no overlap between their angle ranges and

•

brother and friend are cross-linked in the same degree. Brothers inherit their angle ranges from the same parent and friends belong to different parents. Note that the distance from the current node to its father is probably closer than the distance to its uncle. It does not imply that the distance to children will be closer than the distance to a Nephew because a Nephew may choose a closer node to be its parent. In the same logic, the distance between Brothers is not necessarily closer than the distance between friends. It won’t cause confusion in our system, because we did not measure the actual distance. Only Parents and their Children are logically directly connected. Uncles, Friends, Brothers and Nephews are within communications radius to each other. According to these conceptions, we defined our routing policies as follows. •

a direct path between ancestor and descendents could be the best choice in a tree structure

•

if the direct relative node is not available, moving to a different subtree closer to the destination is desirable and

•

if the current node lacks traffic ability, pushing the data up to the Parent is a safe route.

Fuzzy preserving VPCS sensor networks for mobility performance consideration If the network density is adequate, cross-links will exist between neighbouring subtrees. This advantage tells us that a straight routing path is always possible if we have enough sensor nodes existing in the tree structure. Figure 7 shows the proposed routing policy flow chart. Figure 7

Routing policies in VPCS

For this reason, they have high priority for path decisions. If there is no Uncle or Friend available, the packet is pushed up to the Parent to insure that the message will arrive at the destination. When the destination has a different degree from the current node, the message is passed to a node with the nearest degree first. In our method, Parent nodes often have wider angle ranges than their children. This also causes them to have closer angle ranges because of the preservation spaces at the edges. This is an advantage because actual networks are fan-shaped rather than triangle-shaped. If the destination is in the same degree to the current node, forwarding the packet to an earlier generation would be helpful in finding a closer path to the destination. This is called transverse routing, as shown in Figure 8. Figure 8

6

The first block is the original tree structure concept, the so called ‘naïve tree routing’. If the destination is an ancestor or a descendant of the current node, there is a direct way and that is probably the shortest path. If the destination is not a direct relative of the current node, we check the neighbour list if any node directly relates to the destination. If the angle of a neighbour node overlaps the destination node, the packet is passed to the neighbour. This is called smart tree routing. In practice, naïve tree routing has two problems. Firstly, it causes numerous detours by triangle routing and it will increase the network load. Secondly, earlier generation nodes will have a higher rate of energy drain and the network will break off once nearby root nodes have depleted their energy. The Smart tree method does not improve the naïve method problems by much. It works only when the source and destination belong to neighbour subtrees. The proposed method provides a solution in VPCS. If no neighbour is directly connected to the destination, that destination is in a different subtree. Uncle and Friend nodes are the immediate connections to another subtree.

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Transverse routing in VPCS

Dynamic network maintanence

Sensor networks are always changing due to node failure, node addition and node movement. Basically, we could classify these mobile problems into two categories: join and leave.

6.1 Nodes leaving Figure 9 explains how nodes leave the network. Figure 9

Partial network re-configuration during node failure

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When node B2 disappears for a while, the states of all children in the next degree, C3 in this case, suddenly become Orphans and broadcast the orphan’s call to find a new parent. C2 receives this message and forwards it to its Parent, asking the Parent to accept this request from the orphan group. Until the request is forwarded to the Parent of the crashed node, node A in this case, will give the angle range of B2 to B1 including the interspaces between B1 and B2. B1 will also deliver those angles to C2, passed on to C3. In this case, only B1 and C2 change their angle range, whereas the others maintain their original configuration. In practice, this method gives us the great advantage that only 3–4 nodes need to be re-configured. The greatest contribution is that no angle range reduction is necessary because there will be a chain reaction flow down to all subtree if a node must reduce its angle range. Our approach localises the variation between a smaller region.

6.2 Joining nodes Sensor networks desire high adaptability and more nodes may need to be added to the network to replace crashed nodes. There is no difference in building the network because there are always preservation spaces. The fuzzy system will manage the preservation spaces and modify the membership function for different network scales for longer system life-time.

7

Evaluation

The simulation environment parameters are described as follows: •

Communication radius of a node: 1 m

•

Number of nodes: 600

•

Region of networks: 20 m × 20 m

•

Network density: 3 nodes/m2

•

Number of routing tables: 10 (include Parent, Children and other neighbour nodes).

The following discussion involves four routing strategies: naïve tree routing, smart tree routing, transverse routing and greedy forwarding. Greedy forwarding is an approach for the shortest path routing analysis (Chen et al., 2001; Li et al., 2003). A greedy algorithm requires information from every node. This method is impossible for a sensor node. We take the greedy forwarding to compare and examine our routing strategy.

7.1 Routing curve Figure 10 is a typical example of comparing these four routing strategies. The scale for this scheme is 500 nodes. The white node is our sensor device and the light-gray line presents the logical links between the nodes. The yellow line is the routing path. The light-cyan dot is the system root and the circle presents the communication radius of a node.

Figure 10 Transition path example in the four routing strategy: (a) naive tree routing, (b) smart tree routing, (c) transverse routing and (d) greedy forwarding

Fuzzy preserving VPCS sensor networks for mobility performance consideration Figure 10 Transition path example in the four routing strategy: (a) naive tree routing, (b) smart tree routing, (c) transverse routing and (d) greedy forwarding (continued)

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7.3 Load balance In this simulation, a map was randomly built, generating 50,000 packet accounts. The top10 loads are shown in Figure 12. The top10 loads in naive and smart tree routing must be nodes near the root. The top10 loads in transverse and greedy routing were in the centre area. In transverse routing, the top load was about 21% and it is higher than our expectation. The load could be much more improved by using other mechanisms such as the Minimum Drain Rate (MDR) or Conditional Minimum Drain Rate (CMDR). Figure 12

Top10 load with 500 nodes scheme

Naive tree routing is no accident and must make detours. Smart tree routing only improves the turning region in triangle routing. Transverse routing uses cross-links and routes laterally through our system. Greedy forwarding chooses the neighbour, which is nearest to the destination.

7.2 Routing performance in networks scalability issue The network topology is built randomly with 100 nodes in a ringed tree. The construction method was described previously in this paper. In this environment, 5000 packets were generated with random sources and destinations. The map was then changed with another 100 nodes. The average hops count per packet in each strategy was 20. The network scale was then changed to 200 nodes and the simulation run again. Figure 11 shows the simulation result. The increasing transverse routing curve was less rapid than naïve and smart tree routing and closed to Greedy forwarding.

7.4 Adaptability in a changeable environment A simulation was developed to examine our method in varied environments shown in Figure 13. We randomly chose 5% of the nodes and erased them. An equal number of new were created to join the system. The routing performance was then recorded as before. This process was repeated until 50% of the original nodes were replaced. In this simulation, all strategies did not present clear responses. Success is attributed to the preservation spaces. After 50% of the nodes were replaced, VPCS with Fuzzy preservation still provides the geographic relation alignment to real networks. Figure 13

Figure 11

Routing performance to networks scalability

Routing performance to networks scalability

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7.5 Scalability in the fuzzy preservation system The pure binary tree architecture is the worst case in our preservation method and required the most preserved space. We analysed our system according to disadvantageous situations. Figure 14 indicates that less than 25% of the ID resources were used when the system scale exceeded 500 nodes. In practice, our simulation environment was equivalent to 2000 nodes. This scale was similar to current sensor networks. If it is necessary to increase system scalability, using 32-bit ID will have the capacity for one million nodes.

with the same nodes density. By this way, if that is a long way to get a new Parent in Section 6.1, it shall also work and ignore the Parent crashed while using other neighbour bridge to communicate. Figure 17 shows the routing path in the environment after we have removed 50 nodes from original networks. Figure 15

Networks life-time analysis

Figure 16

Average routing hops in dynamic networks

Figure 17

Routing in the multitrees

Figure 14 Account for utility ratio of ID resource

7.6 Network life-time analysis Further, energy parameter is taken into consideration for our networks. This simulation helps us to evaluate the network loading balance. Every node has the capacity to process 200 packets, and then crashed. We randomly pick a pair of source and destination nodes and decrease energy parameter of every node on the routing path. If any node has exhausted his energy, then all his neighbours will remove this relationship, Figure 15 shows the relation of nodes crashed in which packet sent. Figure 16 shows the routing average hops associated with Figure 15. The proposed network lost 32% node after 20000 packets. We observe our networks scale suddenly drop down after 8000 packets were processed. While 16% nodes have failed and routing-hop accounts also going down after this. About 27% nodes failure and networks scale reduced again after 16,000 packets were processed, then root lost all his children after 20,000 packets.

7.7 Routing in multitree On the other hand, we may ignore the self-healing in our tree, because the proposed system is a multi-tree structure. Uncle and Nephew are no different to Parent and Children in our routing decision and a node is not necessary to have a Parent after networks have built. The only thing we have to do is to remove the connection record in routing table while a neighbour node has crashed. In a practical simulation, such multi-tree structure provides the same performance for routing in networks

Fuzzy preserving VPCS sensor networks for mobility performance consideration

8

Conclusion

In this paper, we focused on building topology, routing strategies and maintaining a sensor network topology. We presented a simple method for building a sensor networks topology in VPCS. We proposed using preservation interspaces for VPCS that adopted Fuzzy models. In a dynamic environment, our system works well with self-healing and the area that must change configuration is minimised when nodes crash. We compared several routing strategies and provided several simulations. The simulation results show that our approach presents good performance with low maintenance costs. We consider tree-like topology as a proper architecture and we hope our research will give contributions for sensor network applications.

Acknowledgement This paper is a partial result of project no NSC 92-2219-E259-002 conducted by the National Dong Hwa University under the sponsorship of National Science Council, ROC.

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