1 Quick Convergecast in ZigBee/IEEE Tree-Based Wireless Sensor Networks Yu-Chee Tseng and Meng-Shiung Pan Department of Computer Science National Chiao Tung University, Taiwan (in ACM MobiWac, 2006, candidate of best paper award)

2 Outline Introduction Minimum delay beacon scheduling (MDBS) problem Algorithms for the MDBS problem  Optimal solutions for special cases  Centralized tree-based assignment  Distributed slot assignment Simulation results Conclusions

3 Outline Introduction Minimum delay beacon scheduling (MDBS) problem Algorithms for the MDBS problem  Optimal solutions for special cases  Centralized tree-based assignment  Distributed slot assignment Simulation results Conclusions

4 Introduction In many surveillance applications, convergecast is an important operation  sensors periodically report sensed environmental events to a sink ZigBee is a developing standard which is considered to satisfy the needs of WSN sink sensor

5 Goal To design protocols to achieve low-latency convergecast in ZigBee tree-based wireless sensor networks  Why low-latency? The late-arrived sensory readings are meaningless  Why ZigBee tree-based network? Devices in ZigBee tree-based network can operate in low-power mode

6 Contributions Define a minimum delay beacon scheduling (MDBS) problem for ZigBee tree-based WSNs Prove MDBS problem is NP-complete Find special cases in MDBS Propose centralized and distributed algorithms, which are compliant to the ZigBee standard

7 Network scenario In a tree network, routers can send regular beacons to support low duty cycle operations A’s beacon sche: A wakes up to hear C’s beacon and report data To C Zzz.. Zzz …. Zzz.. C’s beacon sche: ZigBee coordinator

8 Superframe structure in a ZigBee tree network According to ZigBee standard, beacons are scheduled in the front of non-overlapped active portions Superframe structure of IEEE A superframe can contain 2 BO-SO non-overlapped active portions (slots) Beacon interval = u × 2 BO 1 Active portion = u × 2 SO 232 BO-SO ★ In WSN, beacon interval >> active portion u=aBaseSuperframeDuration

9 Schedule beacons in a ZigBee tree network When choosing a slot, routers should consider interferences from other routers  Indirect interference Two routers have indirect interference if they have at least one common neighbor  Direct interference Two routers have direct interference if they can hear each other’s beacons A B A B C

10 A beacon schedule example Latency from B to C is almost one beacon interval !!! Can up to 4 min. in ZigBee B collects data here!!! B reports to C here!!!

11 A better beacon schedule example Latency from B to C is at most one active portion !!! B collects data here!!! B reports to C here!!!

12 Outline Introduction Minimum delay beacon scheduling (MDBS) problem Algorithms for the MDBS problem  Optimal solutions for special cases  Centralized tree-based assignment  Distributed slot assignment Simulation results Conclusions

13 Minimum delay beacon scheduling problem Given G = (V, E), G I = (V, E I ), and k slots A router i can be assigned to slot a s(i), where  s(i) ∈ [0, k-1] (choosing a proper active portion)  s(i) ≠ s(j) if (i, j) ∈ E I (avoiding direct and indirect nterference) 6 s(i)=? k=8 routers comm. link Interference relationship

14 Minimum delay beacon scheduling problem (hop latency) The latency from i to j, where (i, j) ∈ E, is defined as  d ij = (s(j)-s(i)) mod k (difference of slot number between i and j) Hop Latency: 2 k=8 i j 3 1 i j Hop Latency: (4-7)%8 = 5

15 Minimum delay beacon scheduling problem (report latency of a node) The report latency of router i is the sum of per hop delay from i to the sink i Report Latency: 3 k=8

16 Minimum delay beacon scheduling problem (convergecast latency) The convergecast latency is the maximum report latency between all routers  L(G) Convergecast Latency: = 14 k=8 critical path

17 Minimum delay beacon scheduling problem Definition of Minimum Delay Beacon Scheduling (MDBS) problem  Given G=(V, E), G’s interference graph G I =(V, E I ), and k available slots, the MDBS problem is to find an interference-free slot assignment s(i) for each i ∈ V such that the convergecast latency L(G) is minimized Definition of Bounded Delay Beacon Scheduling (BDBS) problem  Given G = (V,E), G’s interference graph G I = (V, E I ), k available slots, and a delay constraint d, the BDBS problem is to decide if there exists an interference-free slot assignment s(i) for each i ∈ V such that the convergecast latency L(G) ≤ d

18 Minimum delay beacon scheduling problem Theorem 1: The BDBS problem is NP-complete  Proof: 1. Given a solution, we can check if L(G) ≤ d in polynomial time. 2. We then prove that the BDBS problem is NP-hard by reducing the 3 conjunctive normal form satisfiability (3-CNF-SAT) problem to a special case of the BDBS problem in polynomial time.

19 Outline Introduction Minimum delay beacon scheduling (MDBS) problem Algorithms for the MDBS problem  Optimal solutions for special cases  Centralized tree-based assignment  Distributed slot assignment Simulation results Conclusions

20 Optimal solutions for special cases Regular linear network  Theorem 2. For a regular linear network, if k ≥ h + 1, a bottom-up slot assignment can achieve a report latency of |V | − 1, which is optimal. Each node has an interference relation with any node within h hops from it.

21 Optimal solutions for special cases Regular ring network  Theorem 3. For a regular ring network, assuming that k ≥ 2h and [(|V |−1) / 2] ≥ 2h, a heuristic slot assignment can achieve a report latency L(G) = [(|V |−1) / 2] + h, which is optimal within a factor of 1.5 [ ] means floor function

22 Centralized tree-based assignment Given G = (V,E), G I = (V, E I ), and k, our centralized slot assignment heuristic algorithm is composed of three phases:  Phase 1: From G, construct a BFS tree T rooted at sink t  Phase 2: Traverse T in a bottom-up manner. For each vertex v visited, we first compute a temporary slot number t(v) for v as follows. If v is a leaf node, we set t(v) to the minimal nonnegative integer l such that for each vertex u that has been visited and (u, v) ∈ E I, (t(u) mod k) ≠ l. If v is an in-tree node, let m be the maximum of the numbers that have been assigned to v’s children. We then set t(v) to the minimal nonnegative integer l >m such that for each vertex u that has been visited and (u, v) ∈ E I, (t(u) mod k) ≠ (l mod k). After every vertex v is visited, we make the assignment s(v) = t(v) mod k.  Phase 3: Traverse vertices from t in a top-down manner. When each vertex v is visited, we try to greedily find a new slot l such that (s(par(v)) − l) mod k < (s(par(v)) − s(v)) mod k, such that l≠s(u) for each (u, v) ∈ E I, if possible. Then we reassign s(v) = l. Each in-tree router tries to find a slot that induces the least report latency to its children To further reduce the report latency of routers

23 Centralized tree-based assignment: Example (k=8) E A DC B Interference neighbors’ slots 0 and Convergecast Latency: 6 Report Latency from 6  4 s(C) must be larger than s(A)

24 Distributed slot assignment Based on the observation that each router can consider the neighbors within 2r as interference neighbors  r is the default transmission range Each router uses larger transmission power to exchange HELLOs with its interference neighbors  The HELLO packet contains the sender’s slot information

25 Distributed slot assignment This algorithm is triggered by the sink t setting s(t) and then broadcasting its beacon. A router v≠t that receives a beacon will find itself a slot as follows.  Node v sends an association request to the beacon sender. If v fails to associate with the beacon sender, it stops the procedure and waits for other beacons.  If v successfully associates with a parent node par(v), it computes the smallest positive integer l such that (s(par(v))− l) mod k≠s(u) for all (u, v) ∈ E I and s(u) = NULL. Then v chooses s(v) = (s(par(v)) − l) mod k as its slot.  Then, v broadcasts HELLOs for a time period t wait. If it finds that s(v) = s(u) for any (u, v) ∈ E I such that u’s ID is larger than v’s ID, then v has to choose another slot assignment and going back to the above step.  After t wait, v can finalize its slot selection and broadcast its beacons. Each router tries to find a slot that induces the least report latency to its parent

26 Distributed slot assignment t A B beacon 7 Asso. req. 6 6 I choose 6!! ID 1 ID 10  Need to find another slot Start to send its beacon Convergecast Latency: 7

27 Outline Introduction Minimum delay beacon scheduling (MDBS) problem Algorithms for the MDBS problem  Optimal solutions for special cases  Centralized tree-based assignment  Distributed slot assignment Simulation results Conclusions

28 Simulation results We compare our algorithms to a random slot assignment scheme (RAN)  In RAN, each router randomly chooses a slot which does not interfere with its interference neighbors  CTB =centralized tree-based; DSA=distributed slot assignment Fixed tx rangeFixed network size Centralized algo. outperforms others The larger tx range implies the more interference neighbors 5 to 7x better 6 to 9x better

29 Outline Introduction Minimum delay beacon scheduling (MDBS) problem Algorithms for the MDBS problem  Optimal solutions for special cases  Centralized tree-based assignment  Distributed slot assignment Simulation results Conclusions

30 Summary We have define a new minimum delay beacon scheduling problem This is the first work that models the quick convergecast in ZigBee/IEEE based WSNs Our solution is compliant to the standard and can be implemented easily