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

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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)

- 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
- 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

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

- 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

- Why low-latency?

- 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

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:

- 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

- 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

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

B reports to C here!!!

B collects data here!!!

Latency from B to C is at mostone active portion !!!

- 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

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

- 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

- 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

- 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

- 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

- 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.

- Proof:

- 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

- 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.

- 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.

- 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

- 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

- 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

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

- 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

- 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.

- Node v sends an association request to the beacon sender.

Each router tries to find a slot that induces the least report latency to its parent

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

- 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

- 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

- 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

- 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