Lecture 5: Topology Control

1. Lecture 5: Topology Control Anish Arora CIS788.11J Introduction to Wireless Sensor Networks Material uses slides from Paolo Santi and Alberto Cerpa

2. Problems affected by link quality • Topology Control • Neighborhood Management • Routing • Time Synchronization • Aggregation • Application Management

3. References • Topology Control tutorial, Mobihoc’04, Paolo Santi • SPAN, Benjie Chen, Kyle Jamieson, Robert Morris, Hari Balakrishnan, MIT • GAF/CEC, Y. Xu, S. Bien, Y. Mori, J . Heidemann & D. Estrin, USC/ISI – UCLA • ASCENT, Alberto Cerpa and Deborah Estrin, UCLA • GS3: Scalable Self-configuration and Self-healing in Wireless Networks, PODC 2002, Hongwei Zhang, Anish Arora • M. Demirbas, A.Arora, V.Mittal, FLOC: A Fast Local Clustering Service for Wireless Sensor NetworksDIWANS 2004

4. Why Control Communications Topology • High density deployment is common • Even with minimal sensor coverage, we get a high density communication network (radio range > typical sensor range) • Energy constraints • When not easily replenished • Power usage • Observation: radios consume about the same power in idle state than Tx and Rx state • Chicken & egg problem: to save energy, radios must be turned off (not simply reduce packet transmissions); but if radios are turned off, nodes cannot receive messages

5. Problem Statement(s) • Find an MCDS, i.e. a minimum subset of nodes that is both: • Set cover • Connected • Choose a transmit-power level whereby network is connected • per node or same for all nodes • with per node there is the issue of avoiding asymmetric links • cone-based algorithm: • node u transmits with the minimum power ρu s.t. there is at least one neighbor in every cone of angle x centered at u • k-neighbors algorithm: • each node chooses nearest k neighbors for its subgraph • k is chosen s.t. the graph generated is connected w.h.p.

6. Problem Statement(s) • Find a minimum subset of nodes that provides some density • in each geographic region  connectivity • we’ll look at the examples of GAF, SPAN, GS3, ASCENT • Given a connected graph G, find a subgraph G’ which can route messages between nodes in energy-efficient way • both unicast and broadcast spanners • reduces interference as well Sub-problems: • Prune asymmetric links • Tolerate node perturbations • Load balance

7. Where should TC be positioned in the protocol stack? No clear answer in the literature One view: Routing Layer TC Layer MAC Layer Routing protocol may trigger TC execution (to get better routes) • Routing (structure) involves only active nodes MAC protocol may trigger TC execution (if neighborhood changes) • TC controls coarse-grain duty-cycling, MAC controls fine-grain • Mode changes need to be coordinated to avoid conflicts

8. Assumptions: Radio/MAC • Circular or Isotropic Models: GS3 • Grid-based connectivity: GAF, GS3 • Radio/MAC dependencies: • 802.11 Power Saving mode: Span • Promiscuous mode: ASCENT, CEC

9. Assumptions: Neighbor Information • Locality: • 1-hop neighbor: GS3, ASCENT • n-hop neighbor (with various n > 1): GAF, CEC, Span … • Dependency on routing: GS3, Span • Measurement-based: ASCENT, CEC

10. Properties: Reactivity to dynamics & load balancing • Local re-calculation of state: GS3 • Global re-calculation of state: Span • Local recovery: GS3, GAF, CEC, ASCENT • Explicit load balancing mechanisms: GS3, Span, GAF, CEC

11. SPAN • Goal: preserve fairness and capacity & still provide energy savings • SPAN elects “coordinators” from all nodes to create backbone topology • Other nodes remain in power-saving mode and periodically check if they should become coordinators • Tries to minimize # of coordinators while preserving network capacity • Depends on an ad-hoc routing protocol to get list of neighbors & the connectivity matrix between them • Runs above the MAC layer and “alongside” routing

12. Coordinator Election & Announcement • Rule: if 2 neighbors of a non-coordinator node cannot reach each other (either directly or via 1 or 2 coordinators), node becomes coordinator • Announcement contention is resolved by delaying coordinator announcements with a randomized backoff delay • delay = ((1 – Er/Em) + (1 – Ci/(Ni pairs)) + R)*Ni*T Er/Em: energy remaining/max energy Ni: number of neighbors for node i Ci: number of connected nodes through node i R: Random[0,1] T: RTT for small packet over wireless link

13. Coordinator Withdrawal • Each coordinator periodically checks if it should withdraw as a coordinator • A node withdraws as coordinator if each pair of its neighbors can reach each other directly of via some other coordinators • To ensure fairness, after a node has been a coordinator for some period of time, it withdraws if every pair of nodes can reach each other through other neighbors (even if they are not coordinators) • After sending a withdraw message, the old coordinator remains active for a “grace period” to avoid routing loses until the new coordinator is elected

14. Performance Results

15. GAF/CEC: Geographical Adaptive Fidelity • Each node uses location information (provided by some orthogonal mechanism) to associate itself to a virtual grid • All nodes in a virtual grid must be able to communicate to all nodes in an adjacent grid • Assumes a deterministic radio range, a global coordinate system and global starting point for grid layout • GAF is independent of the underlying ad-hoc routing protocol

16. Virtual Grid Size Determination • r: grid size, R: deterministic radio range • r2 + (2r)2 R2 • r  R/sqrt(5)

17. Parameters settings • enat: estimated node active time • enlt: estimated node lifetime • Td,Ta, Ts: discovery, active, and sleep timers • Ta = enlt/2 • Ts = [enat/2, enat] • Node ranking: • Active > discovery (only one node active per grid) • Same state, higher enlt --> higher rank (longer expected time first) • Node ids to break ties

18. Performance Results

19. CEC • Cluster-based Energy Conservation • Nodes are organized into overlapping clusters • A cluster is defined as a subset of nodes that are mutually reachable in at most 2 hops

20. Cluster Formation • Cluster-head Selection: longest lifetime of all its neighbors (breaking ties by node id) • Gateway Node Selection: • primary gateways have higher priority • gateways with more cluster-head neighbors have higher priority • gateways with longer lifetime have higher priority

21. Network Lifetime

22. ( ( ) ( ) ) ( ) cascading ) ( ) ( ) ( ) ( A B new node Challenges for local healing of solid-disc clustering • Equi-radius solid-disc clustering with bounded overlaps is not achievable in a distributed and local manner

23. FLOC protocol • Solid-disc clustering with bounded overlaps is achievable in a distributed and local manner for approximately equal radius • Stretch factor, m≥2, produces partitioning that respects solid-disc • Each clusterhead has all the nodes within unit radius of itself as members, and is allowed to have nodes up to m away of itself • FLOC is locally self-healing, for m≥2 • Faults and changes are contained within the respective cluster or within the immediate neighboring clusters

24. FLOC program … • By taking unit distance to be reliable comm. radius & m be maximum comm. radius, FLOC • exploits the double-band nature of wireless radio-model • achieves communication- and energy-efficient clustering • FLOC achieves clustering in O(1) time regardless of the size of the network • Time, T, depends only on the density of nodes & is constant • Through simulations and implementations, we suggest a suitable value for T for achieving fast clustering without compromising the quality of resulting clusters

25. Model • Geometric network, e.g., 2-D coordinate plane • Radio model is double-band * • Reliable communication within unit distance = in-band • Unreliable communication within 1 < d < m = out-band • Nodes have i-band/ o-band estimation capability • RSSI-based using signal-strength as indicator of distance • Statistics-based using average link quality as an indicator • Fault model • Fail-stop and crash • New nodes can join the network

26. Problem statement • A distributed, local, scalable, and self-stabilizing clustering program, FLOC, to construct network partitions such that • a unique node is designated as a leader of each cluster • all nodes in the i-band of each leader belong to that cluster • maximum distance of a node from its leader is m • each node belongs to a cluster • no node belongs to multiple clusters

27. ( ( ) ( ) ) ( ) ) ( ) ( ) ( ) new node subsumed Justification for stretch factor > 2 • For m≥2 local healing is achieved: a new node is • either subsumed by one of the existing clusters, • or allowed to form its own cluster without disturbing neighboring clusters ) ( ( ) ( ( ) ) ( ) new cluster

28. Basic FLOC program • Status variable at each node j: • idle : j is not part of any cluster and j is not a candidate • cand : j wants to be a clusterhead, j is a candidate • c_head : j is a clusterhead, j.cluster_id==j • i_band : j is an inner-band member of a clusterhead j.cluster_id; a clusterhead itself is an i_band member • o_band :j is an outer-band member of j.cluster_id • The effects of the 6 actions on the status variable:

29. FLOC actions • idle Λ random wait time from [0…T] expired  become a cand and bcast cand msg • receiver of cand msg is within in-band Λ its status is i_band  receiver sends a conflict msg to the cand • candidate hears a conflict msg  candidate becomes o_band for respective cluster • candidacy period Δ expires  cand becomes c_head, and bcasts c_head message • idle Λ c_head message is heard  become i_band or o_band resp. • receiver of c_head msg is within in-band Λis o_band  receiver joins cluster as i_band

30. FLOC is fast • Assumption: atomicity condition of candidacy is observed by T • Theorem: Regardless of the network size FLOC produces the partitioning in T+Δ time • Proof: • An action is enabled at every node within at most T time • Once an action is enabled at a node, the node is assigned a clusterhead within Δtime • Once a node is assigned to a clusterhead, this property cannot be violated • action 6 makes a node change its clusterhead to become an i-band member, action 2 does not cause clusterhead to change

31. FLOC is locally-healing • Node failures • inherently robust to failure of non-clusterhead members • clusterhead failure detected via “lease” mechanism, the orphaned nodes execute clustering ---see node additions • Node additions • either join existing cluster, or • form a new cluster without disturbing immediate neighboring clusters

32. Extensions to basic FLOC algorithm • Extended FLOC algorithm ensures that solid-disc property is satisfied even when atomicity of candidacy is violated occasionally • Insight: Bcast is an atomic operation • Candidate that bcasts first locks the nodes in the vicinity for Δ time • Later candidates become idle again by dropping their candidacy when they find some of the nodes are locked • 4 additional actions to implement this idea

33. Simulation for determining T • Prowler, realistic wireless sensor network simulator • MAC delay 25ms • Tradeoffs in selection of T • Short T leads to network contention, and hence, message losses • Tradeoff between faster completion time and quality of clustering • Scalability wrt network size • T depends only on the node density • In our experiments, the degree of each node is between 4-12 • a constant T is applicable for arbitrarily large-scale networks

34. Tradeoff in selection of T

35. Constant T regardless of network size

36. Implementation • Mica2 mote platform, 5-by-5 grid • Confirms simulation

37. Sample clustering with FLOC

38. GS3: Scalability via locality • Locality is hard for some graph problems • e.g., self-configuration and self-healing of routing tree • An ideal goal for locality: self-healing should be a function of the size of perturbation (in time, space, and energy) • Locality depends on model

39. System model • System • multiple “small” nodes and one “big” node, on a plane • node distribution • density: ( Rts.t. with high probability, there are multiple nodes in any circular area of radius Rt) • localization: relative location between nodes can be estimated • Perturbations • dynamic nodes • joins, leaves (deaths), state corruptions • mobile nodes

40. Problem: Geography-aware self-configuration • Geographic radius of clusters is crucial • for communication quality, energy dissipation, data aggregations & applications • Problem statement • Given R: ideal cell radius (R > Rt) • Construct a set of cells , connected via a “head” node in each cell s.t. • radius of each cell is in [ R-c , R+c ] , where c = f (Rt) • each node belongs to only one cell • cells and the connectivity graph over head nodes self-heal locally

41. Static networks • An ideal case: • In reality: no node may exist at some geometric centers (ILs), but, with high probability there are nodes no more than Rt away from any IL (IL = Ideal Location)

42. How to find the set of cell heads • Bottom-up ? • hard to guarantee the placement and size of clusters • Top-down w.r.t. big node • use diffusing computation • but, accumulation in deviation of head location from IL is a problem i

43. Organizing neighboring clusters & heads Deviation problem is handled locally • instead of using real locations, node i uses its and its parent’s ILs • i calculates the ILs of next band cells in its search region < LD , RD > • big node: <0o , 360o> • other nodes: <-60o-a , 60o+a> , where a Sin-1(Rt / R) • for each IL, i ranks nodes within Rt radius of the IL (by <D, A>), and selects the highest ranked node as the corresponding cluster head

44. Summary: static networks • Cell structure is hexagonal • cell radius: • Time taken to form the structure is (Db), where Db = the maximum distance between the big node and the small nodes • Scalability in self-configuration: • local coordination: only with nodes within range • local knowledge: each node maintains info about a constant number of nearby nodes

45. Dynamic networks • Dynamics include: • node join, leave (death), state corruption • Common vs. rare • common perturbations: node density is preserved • rare perturbations: node density is destroyed • Scalable self-healing is achieved via locality in: • intra-cell healing • inter-cell healing • sanity checking of state (invariants)

46. Local intra-cell healing • Head shift • upon head leaving (death) • local in a radius of Rt • Cell shift • upon the death of all the nodes in an area of radius Rt • local in a radius of R • independent but consistent shift at individual cells sliding of the global head level structure

47. Local inter-cell healing & sanity checking • Local inter-cell healing : upon failure of intra-cell healing at head j, • first, the parent of j tries to find a new head j’ • if that fails, the children of j find new parents • Local sanity checking of state invariants : upon detecting violation of the hexagonality property, • node corrects itself after checking with its neighbors • when state perturbation includes several nodes, the perturbed region corrects itself from the outside going in, and all nodes are corrected within time proportional to size of perturbed region

48. Summary: dynamic networks • Cell radius • for cells not adjoining any gap: • for cells adjoining a gap: • Head tree is now minimum distance tree rooted at the big node • Stabilization time from perturbed state: (Dp), where Dp = diameter of the continuously perturbed area

49. Summary: dynamic networks (contd.) • Scalability in self-healing: • local fault-containment and healing • local knowledge • Local healing and fault-containment enables • stable cell structure • lengthened lifetime: (nc) , where nc = the number of nodes in a cell

50. Related work • Cellular hexagon structure (Mac Donald ’79) • Preconfigured & not considering self-healing • LEACH (Heinzelman et al’00) • No guarantee about the placement and size of clusters • Perturbations dealt with by globally repeating the whole clustering process • Logical-radius based clustering (in Banerjee ’01) • non-local cluster maintenance, and no consideration of state corruption • only logical radius  long links and link asymmetry are possible • multiple rounds of diffusion