1 The Orphan Problem in ZigBee- based Wireless Sensor Networks IEEE Trans. on Mobile Computing (also in MSWiM 2007) Meng-Shiuan Pan and Yu-Chee Tseng Department

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The Orphan Problem in ZigBee-based Wireless Sensor Networks

IEEE Trans. on Mobile Computing (also in MSWiM 2007)Meng-Shiuan Pan and Yu-Chee Tseng

Department of Computer ScienceNational Chiao Tung University, Taiwan

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Outline

Introduction Problem definition The proposed algorithm

Algorithm for the BDDTF problem Algorithm for the EDMM problem

Simulation results Conclusion

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Introduction

ZigBee is a developing standard which is considered to satisfy the needs of WSN

In ZigBee, when forming a network, devices are said to join the network if it can receive a network address Each device tries to associate to the ZigBee coordinator or a

ZigBee router A ZigBee coordinator or router will decide whether to accept

devices according to its capacity The capacity of a ZigBee device relates to the ZigBee address

assignment

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ZigBee address assignment

In ZigBee, network addresses are assigned to devices by a distributed address assignment scheme

ZigBee coordinator determines three network parameters the maximum number of children (Cm) of a ZigBee router the maximum number of child routers (Rm) of a parent node the depth of the network (Lm)

A parent device utilizes Cm, Rm, and Lm to compute a parameter called Cskip which is used to compute the size of its children’s address pools

Real implementation

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Assuming Cm=Rm,49 nodes on a 360x360 cm2 sending fieldTX range is 100 ~ 200 cm

Although small Rm can lead to fewer orphans,it also results in longer end-to-end delay

Large-scale tests by simulations

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(Rm, Lm) are equal to (a) (4, 7), (b) (3, 9), and (c-d) (2, 15).There are 461, 341, 120, and 351 orphan nodes, respectively

Assume Cm = RmA router at depth d serving as a left

There exists a loss of address spaces

This is why a larger part of network at (d) is unable to join the network

Rm

Rm dLm

1

1 1

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An ZigBee address assignment example

Cm = 5Rm = 3Lm = 2

ZigBee coordinator ZigBee router

ZigBee router-capable deviceZigBee end device

Tree link Communication link

Addr = 0Cskip = 6

CE

BD

A

Addr = 1Cskip = 1

Addr = 2

Addr = 3Addr = 5

Addr = 8

Addr = 7Cskip = 1

Addr = 9Addr = 10

Addr = 19

Addr = 15 Addr = 13Cskip = 1

Addr = 14

Addr = 17

Addr = 18

Addr = 11

Addr = 12

0 1 7 13

Cskip=6 Total:21

19For coord.

7node B

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A becomes an orphan node !!

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Orphan Problem:A better assignment

This example shows that a better assignment can effectively reduce orphan devices A better assignment can connect more zigbee devices

Cm = 5Rm = 3Lm = 2

Addr = 0Cskip = 6

CE

BD

A

Addr = 1Cskip = 1

Addr = 2

Addr = 3Addr = 5

Addr = 7Cskip = 1

Addr = 9Addr = 10

Addr = 19

Addr = 15 Addr = 13Cskip = 1

Addr = 14

Addr = 17

Addr = 18

Addr = 11

Addr = 12

Addr =8Addr =4

Addr =8

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Contributions

Model an orphan problem in ZigBee networks by two subproblems The Bounded-Degree-and-Depth-Tree Formation (BDDTF)

problem The End-Device Maximum-Matching (EDMM) problem

Prove the BDDTF problem is NP-complete Propose a network formation algorithm, which can

effectively reduce the number of orphan devices

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Outline




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Problem definition

Given Cm, Rm, and Lm and coordinator t , we model the orphan problem by two subproblems: BDDTF (for routers) EDDM (for end devices)

In the BDDTF problem, we consider only router-capable devices Given Gr=(Vr, Er) The goal is to assign parent-child relationships to nodes

such that as many nodes can join the network as possible A node in Vr can have at most Rm child devices and The depth of the tree should be smaller than Lm

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NP Completeness for BDDTF problem

It has been shown that the Degree-Constrained Spanning Tree problem is NP-C

Given G = (V, E) and a positive integer K≦|V|, the Degree-Constrained Spanning Tree (DCST) problem is to find a spanning tree T of G such that no vertex in T has a degree larger than K

THEOREM 1. The BDDTF problem is NP-complete PROOF.

1) Given a tree T in Gr, we can check if T satisfies the constraints of Rm and Lm and if T contains more than N nodes in polynomial time

2) The DCST problem can be reduced to a special case of the BDDTF problem when Rm = K, Lm∞, and N = |Vr|

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The EDMM problem

Goal: to connect end devices to the tree T constructed earlier satisfying the ZigBee definition. The goal is to connect as many end devices to T as

possible We model the sensor network by a graph

Gd = ({ V’r ∪Ve }, Ed)

Routers, excluding the ones at depth Lm, in T

Comm. link between V’r and Ve

All end devices

Cm = 4Rm = 2Lm = 2

Original T

Gd

V’r∪Ve

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The EDMM problem

Based on T, each vertex v∈V’r can accept at most Cv≧(Cm-Rm) end devices

From Gd, we construct a bipartite graph Gb=({ V’br∪Vbe }, Ebd) as follows Rule 1: From each vertex v∈V’r , generate Cv vertices in V’br

Cm = 4Rm = 2Lm = 2

Can accept 2 child end devices

Can accept 3 child end devices

GF

CD

AB

EV’br

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The EDMM problem

Rule 2: From each vertex u∈Ve, generate a vertex u in Vbe

Rule 3: From each edge (v, u) in Ed, connect each of the Cv vertices generated in rule 1 with the vertex u generated in rule 2. These edges form the set Ebd

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4 7

63

2

GF

CD

AB

E

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A

B

C

D

E

F

G

1

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V’br∪Vbe

Gb=({V’br∪Vbe}, Ebd)

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Outline




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Centralized BDDTF Algorithm (SP)

In our algorithm, we decide to connect or disconnect a node according to its association priority The priority assignment is based on forming BFS trees from

Gr

priority(x) > priority(y) if (subtree_size(x) > subtree_size(y)) priority(x) > priority(y) if (subtree_size(x) = subtree_size(y) and

potential_parents(x) < potential_parents(y)) A node takes a tree neighbor as its potential parent if this neighbor

has a smaller hop count distance to the root of the BFS tree than its

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Centralized BDDTF Algorithm (cont.)

Initially, T contains only the coordinator t Then in each iteration, there are two phases: Span

and Prune In the Span phase: we will pick a node in T, say x, and

span from x a subtree T’ to include as many nodes not in the tree T as possible. Then we attach T’ to T to form a larger tree

In the Prune phase: some of the newly added nodes in T’ may be trimmed to satisfy ZigBee definition

The resulting tree is then passed to the next iteration for another Span and Prune phases

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Centralized Algorithm for the BDDTF problem

t

Communication link

Start Span phase: form a BFS tree T’ rooted at t

Rm=3Lm=3

Rm=3Lm=3

t

T’

Initially, only t in T

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Start prune phase:

Compare association priorities of t’s 5 children in T’

Then check this node no need to prune


t

T’Rm=3Lm=3

Has more than 3 child routers

will be pruned

The result of this iteration

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Rm=3Lm=3

2nd iteration: Start Span phase from this node

Can connect this two nodes

3rd iteration: Start Span phase from this node

The resulting tree

Distributed algorithm for the BDDTF problem (DBS) Our distributed algorithm for BDDTF will do a Depth-first-

search followed by a Breadth-first-like Search Depth-first search tries to form some long, thin backbones, which are

likely to pass through high-node-density areas Depth Probing

The coordinator t will flood a Probe(sender_addr, current_depth, Lm) packet Each node will set its parent to sender_addr, and curretn_depth to

current_depth + 1 Probe Response

After the depth probing, each node reports to its parent a Report packet containing 1) the size of the subtree rooted by itself and 2) the height of the subtree rooted by itself

Backbone Formation After t receives all its children’s report, it will choose at most Rm children with

the larger subtree sizes as backbone nodes by sending Backbone() messages When a node receive a Backbone(), it further invites its child with the tallest

subtree into the backbone by sending Backbone()

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Distributed algorithm for the BDDTF problem (DBS) From these backbones, we span the tree in a

breadth-first-like manner BFS-like spanning

The coordinator can broadcast beacons to start the network A backbone node must associate with its parent on the

backbone, and its parent must accept the request For each non-backbone node

Compete with each other by its association priority Association priority is defined by the size of the subtree rooted by

this node

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Centralized Algorithm for the EDMM problem Given a Gd = ({ V’r ∪Ve }, Ed), a solution for the

EDMM problem can be obtained by applying a bipartite maximum matching algorithm

A

B

C

D

E

F

G

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A

B

C

D

E

F

G

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A maximum matching on Gb

Distributed Algorithm for the EDMM problem (Dist-Match) We proposed a simple distributed matching algorithm

Two phases: greedy phase followed by probing phase Each orphan router will try to probe a 3-hop alternative path

Greedy phase The routers will accept end devices which have less potential

associable routers Potential parent are the neighbor routers which still have capacity

to accept more end devices Probing phase

For an orphan end device e, it can send a Probe() packet to any neighboring router r

If r has a child end device having other potential parent, r will send another Probe() packet to disassociate it

If r receives Probe_Ack(), e will associate with r

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Outline




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Network scenario All router-capable devices Number of nodes: 800 Network radius: 200 m

Dotted nodes are orphan nodes !!

Tx range: 35 m Cm=Rm=2, Lm=8 Random vs. regular networks

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Network scenario All router-capable devices Number of nodes: 800 Network radius: 200 m Tx range: 35 m Vary Rm and Cm

The proposed scheme can effectively reduce the number of orphan routers with a smaller Rm or Lm

Increasing Lm can more effectively reduce orphan routers as opposed to increasing Rm !!

Impact of Rm and Lm on the BDDTF Problem

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Network scenario Number of nodes: 800 Number of end devices: 8000 Network radius: 200 m Tx range of routers: 35 m, Tx range of end devices: varied (15 ~ 30 m) Cm=15, Rm=3, and Lm=8 Use the proposed scheme to connect routers

all routers can join the network

The EDMM Problem

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Conclusions

In this paper, we have defined an orphan problem in ZigBee-based wireless sensor networks.

This is the first work that models the orphan problem in ZigBee networks

The proposed network formation strategy is compliant to the standard and can be implemented easily

Documents

1 The Orphan Problem in ZigBee- based Wireless Sensor Networks IEEE Trans. on Mobile Computing (also in MSWiM 2007) Meng-Shiuan Pan and Yu-Chee Tseng Department