Edge-Based Beaconing Schedule in Duty- Cycled Multihop Wireless Networks

Edge-Based Beaconing Schedule in Duty- Cycled Multihop Wireless Networks Quan Chen, Hong Gao, Yingshu Li, Siyao Cheng, and Jianzhong Li Harbin Institute of Technology, China Quan Chen@ Harbin Institute of Technology

Contents Motivation The Need For Beaconing Schedule Beaconing Schedule in Duty-Cycled WSNs Previous Work Problem Definition The Edge-based Scheduling Framework Beaconing Schedule under Protocol Interference Model Beaconing Schedule under Protocol Interference Model Evaluation Conclusions

The Need For Beaconing Schedule Beaconing is an essential operation for many networking protocols in which each node broadcasts a packet to all of its one-hop neighbors, e.g. Discovering network topology Data collection Data dissemination Routing, Multicasting, Broadcasting Multipath routing Network coding

Beaconing Schedule in Duty-Cycled WSNs Duty-Cycled WSNs Each node works cyclically with two states: active and dormant Each node can only receive packet in active state a b c A working period (WP) WP1 e 0 ab 1 WP2 0 1 Active State 2 2 Dormant State 3 3

Beaconing Schedule in Duty-Cycled WSNs Duty-Cycled WSNs Each node works cyclically with two states: active and dormant Each node can only receive packet in active state a b c e ab WP 0 Beaconing Schedule e ba e bc e cb 1 2 3 Active State Dormant State

Beaconing Schedule in Duty-Cycled WSNs Duty-Cycled WSNs Each node works cyclically with two states: active and dormant Each node can only receive packet in active state a b c Beaconing Schedule e ab e ba e bc e cb WP1 WP2 0 1 2 3 0 1 2 3 Active State Dormant State

Related Work Existed solution L. Wang, P. J. Wan and K. Young, "Minimum-Latency Beaconing Schedule in duty-cycled multihop wireless networks," in Proc. of IEEE INFOCOM, 2015. This method assumes each node has only one active time slot per working cycle, and exploits a node-based schedule! a b c e.g., at time slot 1 Conflict graph a conflicting c Coloring a with 0 Coloring c with 1 This node-based schedule cannot assign its active time slot among neighbors intelligently!

Problem Definition Network Model Let T denote a working period Let W(u) denote nodes working plan, i.e. the active time slot in a working period An example of duty-cycled WSNs, Where T =4

Problem Definition INPUT A duty-cycled sensor network G=(V, E); The working plans for all nodes, {W(u) v V}. OUTPUT The edge based schedule S={(e uv, t uv ) e uv E },which satisfies: 1) For (e uv, t uv ) S, t uv =C T +t 0,C 0, t 0 W(v); 2) S is conflict free; 3) BL(S)=min{ t uv } is minimized. The MLBSDCA problem is NP-hard under protocol interference model.

Edge-based Scheduling Framework Constructing super conflict graph (SCG) G i (0 i T -1): the induced subgraph of G at time slot i, is formed by the nodes that are active at time slot i and their neighbors. H i : the conflict graph of G i For example, the induced subgraph G 0 and H 0 G G 0 H 0

Edge-based Scheduling Framework Constructing super conflict graph (SCG) Super conflict graph H S = {H i 0 i T 1} G H s Beaconing Schedule Label Coloring Problem!

Edge-based Scheduling Framework Label Coloring Problem Coloring all the labels in H S, not all the vertexes in H S Coloring and deleting technique

Beaconing under Protocol Interference Model Scheduling by time slot Main idea:exploit the coloring method to color H 0 ~H T -1 simultaneously First-Fit coloring: each vertex is colored and assigned the first color it fits WP 1 WP 2 Depends on a fixed order! Massive Data Computing Research Center @HIT

Beaconing under Protocol Interference Model Scheduling by time slot Main idea:exploit the coloring method to color H 0 ~H T -1 simultaneously First-Fit coloring: each vertex is colored and assigned the first color it fits WP 0 WP 1 WP 2 WP 3 Depends on a fixed order! Massive Data Computing Research Center @HIT

Beaconing under Protocol Interference Model Scheduling by working period Main idea: Schedule as much vertexes as possible in a working period Each vertex has 3 states: White, Yellow and Black White: vertexes can be scheduled at current WP C Black: Vertexes can not be scheduled at current WP C Yellow: Vertexes scheduled at current WP C

Beaconing under Protocol Interference Model Scheduling by working period 1) Isolated vertexes iterative scheduling and removing 2) Dynamic largest degree first scheduling Vertexes Scheduling at WP 0

Beaconing under Protocol Interference Model Scheduling by working period 1) Isolated vertexes iterative scheduling and removing 2) Dynamic largest degree first scheduling

Beaconing under Protocol Interference Model Performance analysis Theorem 4. The lower bound on the latency of any optimal beaconing schedule for MLBSDCA under the protocol interference model is at least l ( W G)+1m T, where (G) denotes the maximum degree in G, and W denotes the maximum number of active time slots in a working cycle. Theorem 5. The approximation ratio of the DLFBS algorithm is at most (ρ + 1) 2 W. When W =ρ = 1, the approximation ratio is only 4, which is better than 10 in [Wang, INFOCOM 2015]!

Beaconing under Protocol Interference Model Performance analysis Discussion of [Wang, INFOCOM 2015] s Lower Bound Analysis The reason is that they construct the conflicted graph based on nodes, not on edges, which may result in inaccuracy.

Beaconing under Physical Interference Model Physical Interference Model Node v can receive the messages from node u successfully if only if where α is the path-loss exponent which usually belongs to [2, 4], η is a positive reference loss parameter of power, ξ is the background noise, and node w denotes any other transmitting nodes at the same time slot.

Beaconing under Physical Interference Model Physical Interference Model Lemma 3. [18] Assume E = { e uv } is a set of transmissions. If for any e uv and e mn in E (u m), d(u, m) > ρ,then all transmissions in E can transmit successfully under the physical interference model. Construct the SCG according Lemma 3, and then use the coloring and deleting method in GFFC and DLFBS.

Beaconing under Physical Interference Model Improvement for DLFBS algorithm If two vertexes are connected in Hs, it does not means it is really conflicted. Each vertex has 3 states: White, Yellow and Black When a vertex is scheduled, its neighbors do not need to be marked Black. A vertex marked Black if once it is scheduled at current WP it causes collisions.

Beaconing under Physical Interference Model Performance analysis Theorem 6. The lower bound on the latency of any optimal beaconing schedule for MLBSDCA under the physical interference model is at least l ( W G)+1m T, where (G) denotes the maximum degree in G, and W denotes the maximum number of active time slots in a working cycle. Theorem 7. The approximation ratio of the DLFBS-ph and DLF algorithm is at most ( ρ)2 W.

Evaluation Baseline algorithm Beaconing under protocol interference model FFBSD [Wang,INFOCOM 2015] SCBSD [Wang,INFOCOM 2015] Beaconing under physical interference model FFBSD-ph [Wang,INFOCOM 2015] Network Topology Random generated in a 200m 200m field Networkx generated Graph

Beaconing Latency Protocol Interference Model 20% 200% Random Deployed Network

Beaconing Latency Protocol Interference Model 1.6 times 1.5 times Networkx Generated Graph

Beaconing Latency Physical Interference Model 7.7 times 7.5 times Random Deployed Network

Throughput Protocol Interference Model 2.4 times Random Deployed Network

Throughput Protocol Interference Model 1.7 times Networkx Generated Graph

Conclusions This paper proposes an edge-based scheduling framework for beaconing in duty-cycled WSNs. A novel kind of coloring problem, named label coloring problem, is proposed. Under the protocol interference model, a (ρ + 1) 2 * W approximation algorithm is designed. Under the physical interference model, a ( ρ) 2 * W approximation algorithm is designed Evaluation reveals our design can greatly reduce the beaconing latency.