1. 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 of Computer Science National Chiao Tung University, Taiwan

2. 2 Outline Introduction Problem definition The proposed algorithm  Algorithm for the BDDTF problem  Algorithm for the EDMM problem Simulation results Conclusion

3. 3 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

4. 4 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 C skip  which is used to compute the size of its children’s address pools

5. Real implementation 5 Assuming Cm=Rm, 49 nodes on a 360x360 cm 2 sending field TX range is 100 ~ 200 cm Although small Rm can lead to fewer orphans, it also results in longer end-to-end delay

6. Large-scale tests by simulations 6 (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 = Rm A 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

7. 7 An ZigBee address assignment example 01713 C skip =6 Total:21 19 For coord. 7 node B 20 A becomes an orphan node !!

8. 8 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 Addr =8Addr =4 Addr =8

9. 9 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

10. 10 Outline Introduction Problem definition The proposed algorithm  Algorithm for the BDDTF problem  Algorithm for the EDMM problem Simulation results Conclusion

11. 11 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 G r =(V r, E r )  The goal is to assign parent-child relationships to nodes such that as many nodes can join the network as possible A node in V r can have at most Rm child devices and The depth of the tree should be smaller than Lm

12. 12 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 G r, 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 = |V r |

13. 13 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  G d = ({ V’ r ∪ V e }, E d ) Routers, excluding the ones at depth Lm, in T Comm. link between V’ r and V e All end devices Cm = 4 Rm = 2 Lm = 2 Original T GdGd V’ r ∪ V e

14. 14 The EDMM problem Based on T, each vertex v ∈ V’ r can accept at most C v ≧ (Cm- Rm) end devices From G d, we construct a bipartite graph G b =({ V’ br ∪ V be }, E bd ) as follows  Rule 1: From each vertex v ∈ V’ r, generate C v vertices in V’ br Cm = 4 Rm = 2 Lm = 2 Can accept 2 child end devices Can accept 3 child end devices G F C D A B E V’ br

15. 15 The EDMM problem  Rule 2: From each vertex u ∈ V e, generate a vertex u in V be  Rule 3: From each edge (v, u) in E d, connect each of the C v vertices generated in rule 1 with the vertex u generated in rule 2. These edges form the set E bd 5 47 6 3 2 G F C D A B E 1 A B C D E F G 1 2 3 4 5 6 7 V’ br ∪ V be G b =({V’ br ∪ V be }, E bd )

16. 16 Outline Introduction Problem definition The proposed algorithm  Algorithm for the BDDTF problem  Algorithm for the EDMM problem Simulation results Conclusion

17. 17 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 G r 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

18. 18 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

19. 19 Centralized Algorithm for the BDDTF problem t Communication link  Start Span phase: form a BFS tree T’ rooted at t Rm=3 Lm=3 Rm=3 Lm=3 t T’ Initially, only t in T

20. 20 Start prune phase: Compare association priorities of t’s 5 children in T’ Then check this node  no need to prune Centralized Algorithm for the BDDTF problem t T’ Rm=3 Lm=3 Has more than 3 child routers will be pruned The result of this iteration

21. 21 Centralized Algorithm for the BDDTF problem Rm=3 Lm=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

22. 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() 22

23. 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 23

24. 24 Centralized Algorithm for the EDMM problem Given a G d = ({ V’ r ∪ V e }, E d ), a solution for the EDMM problem can be obtained by applying a bipartite maximum matching algorithm A B C D E F G 1 2 3 4 5 6 7 A B C D E F G 1 2 3 4 5 6 7 A maximum matching on G b

25. 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 25

26. 26 Outline Introduction Problem definition The proposed algorithm  Algorithm for the BDDTF problem  Algorithm for the EDMM problem Simulation results Conclusion

27. 27 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

28. 28 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

29. 29 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

30. 30 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