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Self-stabilization and Virtual Node Layer Emulations

Self-stabilization and Virtual Node Layer Emulations. Tina Nolte, Nancy Lynch (MIT CSAIL). Main Topics. Virtual Node layer emulations: VSA layer. Example VSA layer application. VSA layer emulation. Stabilization and Self-stabilization: Def. for TIOA setting.

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Self-stabilization and Virtual Node Layer Emulations

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  1. Self-stabilization and Virtual Node Layer Emulations Tina Nolte, Nancy Lynch (MIT CSAIL) TDS seminar

  2. Main Topics • Virtual Node layer emulations: • VSA layer. • Example VSA layer application. • VSA layer emulation. • Stabilization and Self-stabilization: • Def. for TIOA setting. • Application to VN layer emulations.

  3. Mobile Networks • Increasingly common and important. • Ad hoc network scenarios: • Rescue workers • Soldiers in battle • Robots in novel location • Cooperative driving • Mobile object tracking

  4. Motivation • But application design is hard! • No infrastructure • Unpredictable reliability • Unpredictable motion • Unpredictable communication

  5. Virtual Node Layers • Q: How do we simplify application design for mobile ad hoc networks? • A: Virtual node infrastructure: • Virtual timed automata • Fixed virtual automata locations Application Virtual Node Layer

  6. Prior Virtual Node Work • Virtual Storage: GeoQuorums [DGLSW’03] • Atomic read/write memory • Virtual Mobile Nodes [DGLSSW’04, DGSSW’05] • Untimed automata • Mobile • Virtual Stationary Automata • Timed automata • Stationary

  7. Virtual Infrastructures

  8. GeoCast [DLLN’05] • Route message to a geographical region.

  9. Timed I/O Automata (TIOA) [KLSV’06] • Nondeterministic state machine whose state can change via discrete transitions or according to trajectories. • A TIOA consists of: • X: internal variables • Q ≤ val(X): states • Θ ≤Q: start states, nonempty • I: input actions • O: output actions E=I+O • H: internal actions A=I+O+H • D ≤ QxAxQ: discrete transitions • T ≤ trajectories of Q: trajectories

  10. TIOA cont. • Composition A||B of compatible A and B • (A,V)-sequence: act1, traj1, act2, traj2, … • Executions and execution fragments • Traces and trace fragments • (A’,V’)- restriction of an (A,V)-sequence

  11. Physical Layer Model • Carve space up into regions w/ids in U. • Physical layer (mobile node) assumptions: • TIOAs • Local Broadcast communication (only): • Atomic broadcast within a region. • Guaranteed timely delivery. • Might fail and restart. • Access to RW.

  12. RW • Source of consistency: • Location/ region information. • Synchronized real-time clocks. • Refreshed at each node every εsampletime and whenever node changes region or fail status. • Reasonable assumption.

  13. VSA Layer • Mobile nodes. • Virtual Stationary Automata (VSAs): • Timed. • Predetermined regions and programs. • V-bcast service: • VSAs and mobile nodes in same and neighboring regions can communicate. • Similar comm guarantees as with physical nodes. • RW’

  14. What is a VSA? • Implemented by the underlying real mobile nodes and their broadcast services. • What abstract machines can we emulate? • Automata with real-time clocks. • Necessary for many control applications. • Can broadcast and receive messages. • Can crash, restart. • We provide delay-augmented VSAs: • Abstract machines with delayed broadcasts.

  15. RW’ • RW augmented with region fail/restart. • Region failure predicates over RW’ exe history: • failprec[u]: an alive region is allowed to fail • failstop[u]: an alive region must fail • Region restart predicates over RW’ exe history: • restartprec[u]: a failed region is allowed to restart • restartstop[u]: a failed region must restart

  16. Physical and virtual layer diagrams RW ’ GPSupdate(u,now)p failv failp restartq GPSupdate(u,now)p restartv restartp failq failu restartu GPSupdate(u,now)q C / Pp C / Pq Vu Vv … … bcast(m)p bcast(m)q bcast(m)u bcast(m)v brcv(m)v brcv(m)u bcrcv(m)p bcrcv(m)q P-bcast V /

  17. VSA Layer programs • A V-algorithm, alg, is a mapping from: • Mobile node ids to client TIOAs • Region ids to VSA TIOAs • Valgs is the set of all V-algorithms • Vlayer[alg] is the instantiation by alg of the abstract VSA layer. • Vlayer[alg] is composition of V-bcast, Dout[e]u for u in U, and alg(q) for q in P+U, with bcast action between VSA and Dout hidden.

  18. Application: algGeo [DLLN’05] • Timed channel automaton allowing geocast, georcv. • Say geocast by client in u to region v at time t is serviceable if exists >= 1 path of non-failed regions from u to v over entire interval [t,t+ttlgeo]. If client performs geocast(v,m) at time t, and the geocast is serviceable, then all nonfailed clients in region vgeorcv(m) by time t+ttlgeo. • If a client in region v performs georcv(m), a geocast(v,m) was performed within last ttlgeo time.

  19. VNLayer GeoCast implementation (alggeo) • Uses VSA layer and a greedy DFS algorithm. • If non-destination VSA receives message m (via V-bcast): • It forwards m to a neighboring VSA closer to the destination. • If it does not receive an ack that m was received in bd’d time, it reforwards to the next closest neighbor, etc. • Greedy DFS. • Persistent greedy DFS. • If destination VSA receives the message: • It tells the forwarder that the message has arrived. • That forwarder tells the VSA that forwarded m to it that m has arrived, etc.

  20. Example: VSA u sending m to v • 1. VSA u wants to send m to v. Geocast(v, m)

  21. Example: VSA u sending m to v • 2. Message is forwarded to nbr closest to v. bcast(<forward, <m, u, v, now>, u, u’>)

  22. Example: VSA u sending m to v • 3. Message continues to be forwarded closer… bcast(<forward, <m, u, v, now>, u”, u”’>)

  23. Example: VSA u sending m to v • 4. If a hole is reached, the forwarding will time out.

  24. Example: VSA u sending m to v • 5. The next closest nbr is then forwarded to.

  25. Example: VSA u sending m to v • 6. The message finally arrives at the destination. bcast(<forward, <m, u, v, now>, u””, v>) Georcv(m)

  26. Example: VSA u sending m to v • 7. Found messages are forwarded backwards to prevent reforwarding. bcast(<found, <m, u, v, now>>)

  27. VSA Layer emulation • An emulation (amap, tmap) of the VSA layer is:

  28. A VSA Emulation Algo [DGLLN’05] • Replicated state machine approach: • Uses a totally ordered regional broadcast service. • Emulates deterministic timed state machine. • Each mobile node maintains state and processes messages as if it was the VSA. • Leader-based: • Only leader broadcasts on behalf of the VSA. • Leader handles joins of new emulators to maintain consistency. • Provides real-time clock to VSA.

  29. VSA Emulation + Geocast algorithm • Q: What happens if we run the VSA layer emulation algorithm instantiated with the Geocast program? • A: We get a trace that maps to look just like a trace of a “real” VSA layer running Geocast, minus the region fails and restarts.

  30. Stabilization motivation • What if a system could get started in an arbitrary state? • What if system components could suffer from corruption faults?

  31. Stabilization preliminaries • A state-matched t-suffix of an (A,V)-sequence α: • More than one state-matched t-suffix can exist. • If t < α.ltime, or t=α.ltime and α is closed, then a state-matched t-suffix of α exists. α’ α” α: t

  32. Stabilization • Let B be a set of (AB,V)-sequences, C be a set of (AC,V)-sequences, t be a non-negative real. • B stabilizes in time t to C if each state-matched t-suffix of each sequence in B is a sequence in C. α” .: α’ α” t . . . . . . . . C B

  33. Stabilization results • Lemma (Restriction). Let A be a set of actions, V be a set of variables, and let B stabilize to C in time t. {α┌(A,V)|α in B} stabilizes to {α┌(A,V)|α in C} in time t. • Lemma (Transitivity). Let B stabilize to C in time t1, and C stabilize to set D in time t2. Then B stabilizes to D in time t1+t2.

  34. Self-stabilization . t state in L

  35. Self-stabilizing emulation

  36. Self-stabilizing emulation traces b trace: t tmap[alg](b) Mtrace: t

  37. Proof of Theorem 1 Proof sketch:

  38. Self-stabilization of emulation algo • Previously described emulation algorithm has been made self-stabilizing: • Local checking. • Periodic checksums.

  39. Htraces

  40. S-s emulations + s-s VLayer applications

  41. Self-stabilization of Geocast • Messages and versions of the DFS are identified with real-time timestamps. • Local checking allows the clean-up of expired or too early DFS attempts.

  42. S-s emulation + s-s geocast VLayer algo

  43. Relate back to VSA failure model… • Assume the example VSA fail/restart predicates. • Can describe what it means for a region to be definitely non-failed through traces of physical nodes interacting with RW. Can describe weak physgeo spec. • Conclude that traces of U(amap[alggeo])||R(RW) stabilize to traces satisfying physgeo.

  44. Conclusions • The VSA programming layer: • Provides a stationary, timed overlay network. • Makes building other applications easier. • Self-stabilizing emulations allow us to write self-stabilizing applications over the VSA layer, and know we will eventually observe good behaviour.

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