後卓越計畫進度報告 Quick Convergecast in ZigBee/IEEE 802.15.4 Tree-Based Wireless Sensor Networks

1. 後卓越計畫進度報告Quick Convergecast in ZigBee/IEEE 802.15.4 Tree-Based Wireless Sensor Networks 2006.12.06 交通大學 High-Speed Communication & Computing Laboratory 指導教授:曾煜棋教授

2. Minimum delay beacon scheduling problem • Given G=(V,E),GI=(V,EI), and k slots: • A ZigBee router i can be assigned slots s(i), where • The report latency form node i to node j is defined as • dij=( S(j)-S(i) ) mod k • The report latency of ZigBee router i is the sum of report latencies of the links on the shortest path form i to the sink. • L(G): the latency of the convergecast is the maximum of all router’s report latency. 6 6 k=8 4 4 5 j 3 Hop Latency: (4-7)%8 = 5 0 Report Latency: 3 2 i i j 7 Convergecast Latency: 7+5+2 = 14 3 3 Hop Latency: 2 1 i 0 0 1

3. Definition ofMinimum Delay Beacon Scheduling (MDBS) problem • Definition: Given G=(V,E), G’s interference graph GI=(V,EI), 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 is minimized. • We have proved that the MDBS problem is NP-Complete, and propose a heuristic algorithm for MDBS problem .

4. A Centralized Tree-Based Assignment • phase 1: • From G, we first construct a BFS tree T rooted at sink t. • phase 2: (bottom-up assignment) • We traverse vertices of 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: • set t(v) to the minimal nonnegative integer l such that for each vertex u that has been visited and .(choose non-interference slot) • If v is an in-tree node: • set t(v) to the minimal nonnegative integer l such that for each vertex u that has been visited and .(choose non-interference slot) • and t(v) > m , where m = max{ t( child(v) ) }, where child(v) is the set of v’s children. • After every vertex v is visited, we make the assignment s(v) =t(v) mod k. • phase 3: (top-down slot compact) • each vertex v 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 , if possible. Then we reassign s(v) = l.

5. Centralized tree-based assignment Phase1: construct a BFS tree T Phase2: bottom-up assignment Phase3: top-down slot compact 6 Reduce report Latency form 6 4 4 5 Interference neighbors’ slots 0 and 1 4 3 E 2 0 2 s(C) must be larger than s(A) 3 C D 2 1 3 A B 0 1 0 Convergecast Latency: 6

6. 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

7. 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) ∈ EIand s(u) ≠NULL. Then v chooses s(v) = (s(par(v)) − l) mod k as its slot. • Then, v broadcasts HELLOsfor a time period twait. If it finds that s(v) = s(u) for any (u, v) ∈ EIsuch 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 twait, 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

8. Distributed slot assignment 7  Need to find another slot  Start to send its beacon t ID 1 ID 10 5 6 beacon Asso. req. 6 A B I choose 6!! 5 4 beacon 2 3 4 3 0 1 2 Convergecast Latency: 7