Quick Convergecast in ZigBee/IEEE 802.15.4 Tree-Based Wireless Sensor Networks

Quick Convergecast in ZigBee/IEEE 802.15.4 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)

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

Introduction sink sensor • 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

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

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

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

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 802.15.4 • A superframe can contain 2BO-SO non-overlapped active portions (slots) Beacon interval = u × 2BO 1 2 3 2BO-SO u=aBaseSuperframeDuration Active portion = u × 2SO ★ In WSN, beacon interval >> active portion

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

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

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

Minimum delay beacon scheduling problem Interference relationship comm. link routers • Given G = (V, E),GI = (V, EI), 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)∈EI(avoiding direct and indirect nterference) 6 k=8 4 5 3 0 2 s(i)=? 7 3 1 0 1 0

Minimum delay beacon scheduling problem(hop latency) • The latency from i to j, where (i, j)∈E, is defined as • dij = (s(j)-s(i)) mod k (difference of slot number between i and j) 6 k=8 4 j 5 3 Hop Latency: (4-7)%8 = 5 0 2 i j 7 3 Hop Latency: 2 1 i 0 0 1

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 6 4 5 k=8 Report Latency: 3 3 0 2 7 i 3 1 0 0 1

Minimum delay beacon scheduling problem(convergecast latency) • The convergecast latency is the maximum report latency between all routers  L(G) 6 4 k=8 5 3 0 Convergecast Latency: 7+5+2 = 14 2 critical path 7 3 1 0 0 1

Minimum delay beacon scheduling problem • Definition of Minimum Delay Beacon Scheduling (MDBS) problem • 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 L(G) is minimized • Definition of Bounded Delay Beacon Scheduling (BDBS) problem • Given G = (V,E), G’s interference graph GI = (V, EI), 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

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.

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.

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

Centralized tree-based assignment • Given G = (V,E), GI= (V, EI), and k, our centralized slot assignment heuristic algorithm is composed of three phases: • Phase 1: From G, construct a BFS treeT 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 integerl such that for each vertex u that has been visited and (u, v) ∈ EI, (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 >msuch that for each vertex u that has been visited and (u, v) ∈ EI, (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) ∈ EI, 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

Centralized tree-based assignment:Example (k=8) 6 4 5 Interference neighbors’ slots 0 and 1 Report Latency from 6 4 4 3 E 2 0 2 s(C) must be larger than s(A) 3 C D 2 3 1 A B 0 1 0 Convergecast Latency: 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

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

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

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 range Fixed network size 5 to 7x better 6 to 9x better Centralized algo. outperforms others The larger tx range implies the more interference neighbors

Summary • We have define a new minimum delay beacon scheduling problem • This is the first work that models the quick convergecast in ZigBee/IEEE 802.15.4 based WSNs • Our solution is compliant to the standard and can be implemented easily

Quick Convergecast in ZigBee/IEEE 802.15.4 Tree-Based Wireless Sensor Networks