FranckPetit Self-StabilizationandMANET

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Dynamic networks Best-eort algorithms Group service maintenance Conclusion

Self-Stabilization and MANET

Franck Petit

[email protected]UPMC

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MANET

I Network

I computing nodes

I communication links

I topology;graph G(V,E)

I Ad hoc network

I uniform nodes: all equivalent, all routers

I Wireless network

I mutual exclusion in the neighborhood:

a message sent by a neighbor is received only if no other neighbor is sending

I message passing or register model

I Wireless ad hoc networks

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Dynamic MANET

I Dynamic network : the topology is not xed

; sequence of graphs

G0(V0,E0),G1(V1,E1),G2(V2,E2),G3(V3,E3). . . 1. Dynamic links

I adding links

I deleting links temporarily or denitively 2. Dynamic nodes

I adding nodes

I deleting nodes temporary or denitively

I ;adds and deletes links 3. Moving nodes

I 6=deleting node + adding node elsewhere memory of the node

I ;adds and deletes links temporarily 4. Dynamic and moving nodes. . .

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Dynamic MANET

wired network

mobile terminal mobile

user

mobile network

mobile ad hoc networks

dynamic ad hoc networks

hand-over... virtual structures management (tree...) MobileIP

with infrastructure without infrastructure

dynamic

Cellular MANET VANET

Internet, IP

routers, fixed servers

?

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Metrics for Dynamic

I Percentage of nodes or links aected

I Mean percentage of a neighborhood aected

I Frequency of changesUnit of time?

I Frequency of changes vs. eciency of the com.

Nodes could move very fast without impact on the algorithm if the communication protocol is ecient.

I Algorithmic metric

I δ-dynamic system: any node that experiments a neighborhood change is able to send a message to all its neighbors untilδ hops before the next topology change

I 1-dynamic system: a minimal requirement for allowing local exchange in a dynamic network

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Examples of Dynamic MANET

I Large networks are generally dynamic

I Social networks

I Peer-to-peer networks

I Network of laptops

IEEE working group MANET: Mobile Ad hoc NETworks I Network of pedestrian with personnal devices

I Network of embedded computers

I Robots networks

I Vehicular networks

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VANET

I Intelligent Transport Systems (ITS)

I infrastructure oriented applications

for optimizing the infrastructure management(transit, freeway, freight, emergency organization...)

I vehicle oriented applications for increasing the road safety

(crash prevention, alerts, visibility distance...)

I driver oriented applications for improving the road usage

(trac jam and road work information, traveler payment, ride duration estimate...)

I passenger oriented applications for oering new services on board

(Internet access, distributed games, chat, touristic information...)

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VANET

I Example of scenario

from Car 2 Car Communication Consortium

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VANET

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VANET

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VANET

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VANET

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Coping Dynamic

Global Data Structure I Backbones, spanning trees, clusters...

I using such structures as in non-dynamic networks

I updating the structures when the topology changes

I But:

I require control messages to be updated

I when the dynamic increases, too much control messages are required

I diverge

I Thus:

I useful only when the dynamic is low

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Coping Dynamic

Global Data Structure I Backbones, spanning trees, clusters...

I using such structures as in non-dynamic networks

I updating the structures when the topology changes

I But:

I require control messages to be updated

I when the dynamic increases, too much control messages are required

I diverge

I Thus:

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Coping Dynamic

Redundancy I Important data are replicated

I critical system

I A node's disappearance is then supported

I But:

I replicated data should be coherent

I pessimistic replicationrequires consensus

I consensus is unsolvable in unreliable asynchronous networks [FLP85]

I alternative: failure detectors[CT96]

I optimistic replicationwill eventually converge

I working with non up-to-date data I Thus:

I strong conditions on the network

I or weak conditions on the replicas

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Coping Dynamic

Redundancy I Important data are replicated

I critical system

I A node's disappearance is then supported

I But:

I replicated data should be coherent

I pessimistic replicationrequires consensus

I consensus is unsolvable in unreliable asynchronous networks [FLP85]

I alternative: failure detectors[CT96]

I optimistic replicationwill eventually converge

I working with non up-to-date data I Thus:

I strong conditions on the network

I or weak conditions on the replicas

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Coping with Dynamic

Self-Stabilization I Self-stabilizing algorithms:

I recover after a transient fault aecting a memory, a message

I neighborhood change

;some memories are not up-to-date

I topology change↔transient fault

I But:

I duration of the convergence phase vs. dynamic

I the system doesn't know whether the stabilized phase is reached or not

I Thus:

I and for non critical applications

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Coping with Dynamic

Self-Stabilization I Self-stabilizing algorithms:

I recover after a transient fault aecting a memory, a message

I neighborhood change

;some memories are not up-to-date

I topology change↔transient fault

I But:

I duration of the convergence phase vs. dynamic

I the system doesn't know whether the stabilized phase is reached or not

I Thus:

I and for non critical applications

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Best-eort algorithms

Principle I The dynamic aects the algorithms

When the dynamic increases, it becomes illusory to expect that an application continuously ensures the service for which it has been designed.

I impossibility results?

I weak specications?

I conditions on the dynamic

I What we can only expect from the distributed algorithms is to behave as "the best" as possible, the result depending on the dynamic.

I Abest eort algorithm fullls its specications if the dynamic of the network allows it, and fullls them few time after the network allows it, otherwise.

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Best-eort algorithms

Using self-stabilization?

I Self-stabilization can help face to the dynamic

Neighborhood change

;some memories do not reect the neighborhood

;similar to a transient failure

I However, it is implicitly assumed that the convergence time is smaller than the delaybetween two topology changes

I General case:

self-stabilization property must be completed

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Best-eort algorithms

Neighborhood change

I General case:

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Best-eort algorithms

Neighborhood change

I General case:

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Best-eort algorithms

Denition

I Continuity predicate Π_C on successive cong.:

False if the quality of successive outputs decreases

depends on the problem

I Topological predicate Π_T on successive cong.:

False if the topological change is important

depends on the problem

I Best-eort requirement: Π_T ⇒Π_C

While the system is converging to a correct behavior, the result is better and better, as long as the dynamic allows it.

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Best-eort algorithms

Enhancing stabilization for dynamic systems I How to complete self-stabilization?

I Fault-containing network protocols Gosh, Gupta, Pemmaraju, SAC '97

I Stabilizing time adaptive protocols

Kutten, Patt-Shamir. Theor. Comp. Sci. 1999

I Superstabilizing protocols for dynamic distributed systems Dolev, Herman. PODC 1995

I Superstabilization

I self-stabilization + passage predicate

I after a legitimate state is reached, if a single topology change occurs, the predicate passage holds until a new legitimate state is reached

I but:

I what before stabilization?

I important in a dynamic system

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Best-eort algorithms

I but:

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Best-eort algorithms

I but:

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Groups service

Requirements: groups in vehicular networks I Intelligent Transport Systems

I infrastructure oriented applications

I vehicle oriented applications

I driver oriented applications

I passenger oriented applications

I Some services are based on collaboration

I driving, diagnostic, perception, infotainment...

I collaboration;group

I Vehicular networks: a kind of dynamic networks

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Groups service

Requirements: constraints on the groups I Maintaining the running service

I the aim is not to optimize the partition of the vehicles into groups

I it is much more important to not split existing groups

I ;keeping the existing groups as long as possible

I Diameter constraint

I delay vs. number of hops

I no collaboration with far vehicles

either useless (driving, diagnostic, perception...) or inecient (chat, games...)

I ;bound on the diameter depending on the applications

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Example

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Groups service for inter-vehicles applications

Specications I Groups: disjoint subgraphs of G(V,E)

I subgraphsH_i(V_i,E_i)withV_i∩V_j =∅

Vi ⊂V and∀(u,v)∈E,(u,v∈Vi)⇒(u,v)∈Ei I view^c_v: knowledge of v about its own group

at conguration c

I Agreement Π_A(c): views dene groups

(u∈V_i and v ∈V_i)⇔view_u^c =view_v^c =V_i Ω^c_v =view_v^c ifΠ_A(c) holds, ∅else

I Safety Π_S(c): groups are well formed

connected and bounded diameter (dΩcv: distance inΩ^c_v)

∀v∈V,maxx,y∈Ω^c_vdΩ^c_v(x,y)≤Dmax

I Maximality Π_M(c): groups cannot merge more

∀u,v∈V with Ω^c_u 6= Ω^c_v

∃x,y ∈Ω^c_u∪Ω^c_v such that dΩc

u∪Ω^c_v(x,y)>Dmax

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Groups service for inter-vehicles applications

Best-eort specication I Topological predicate Π_T:

The distance between members of a group will remain smaller than Dmax

∀v∈V,max_x,y∈Ω^ci_v d_Ω^cⁱ⁺¹ci

v (x,y)≤Dmax

I Continuity property Π_C:

No node disappear from a group

∀v ∈V,Ω^c_vⁱ ⊂Ω^c_vⁱ⁺¹

I Best-eort specication: Π_T ⇒Π_C:

As long as the diameter of a group remains smaller than Dmax, the algorithm should ensure that no node will disappear

I ; An application can work with the current knowledge of the group (view) even if the convergence did not happend

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Groups service for inter-vehicles applications

v (x,y)≤Dmax

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Groups service for inter-vehicles applications

v (x,y)≤Dmax

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Groups service for inter-vehicles applications

v (x,y)≤Dmax

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Groups service for inter-vehicles applications

Summary

I Self-stabilizing algorithm forΠ_A∧Π_S∧Π_M

I C: set of all the congurations

I L ⊂ C: set of congurations c satisfying Π_A(c)∧Π_S(c)∧Π_M(c)

I prove, on a xed topology, that

I Lis an attractor forC

I Lis close I Best-eort requirement

I assuming a dynamic network sequence of graphs

I considering two consecutive congurations ci,ci+1in any execution, prove thatΠ_T(ci,ci+1)⇒Π_C(ci,ci+1)

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Example: A Best-Eort Group Service Algorithm

Overview: diusion of lists I Candidates for a group: neighbors up toDmax

I Lists of close nodes:

I diusion at timer expiration

I merging of the received lists

I lists of nodes ordered by the distance: ({d},{b},{a,c})

I lists truncated toDmax

I Lists ltering:

I only symmetric links

Three-way handshake by marking nodes: v

I malformed lists ignored

I arrival list accepted only if the diameter remains smaller than Dmax after the merge

I if merging is impossible, the neighbor is double-marked(v)

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Example: A Best-Eort Group Service Algorithm

I lists of nodes ordered by the distance:

({d},{b},{a,c})

I Lists ltering:

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Example: A Best-Eort Group Service Algorithm

I lists of nodes ordered by the distance:

({d},{b},{a,c})

I Lists ltering:

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Example: A Best-Eort Group Service Algorithm

Overview: merging lists

I S: set of lists of nodes' sets ({d},{b},{a,c})∈S

I Operator ⊕on S that merges two lists while deleting useless members:

({d},{b},{a,c})⊕({c},{a,e},{b}) = ({d,c},{b,a,e},{a,c,b}) = ({d,c},{b,a,e})

I Endomorphism r ofS, that inserts an empty set at the beginning of a list

r({d},{b},{a,c}) = (∅,{d},{b},{a,c})

I l1/l2 =l1⊕r(l2), l1,l2 ∈S strictly idempotent r-operator

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Example: A Best-Eort Group Service Algorithm

r({d},{b},{a,c}) = (∅,{d},{b},{a,c})

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Example: A Best-Eort Group Service Algorithm

r({d},{b},{a,c}) = (∅,{d},{b},{a,c})

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Example: A Best-Eort Group Service Algorithm

r({d},{b},{a,c}) = (∅,{d},{b},{a,c})

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Example: A Best-Eort Group Service Algorithm

Overview: priorities I Conict:

I deciding between far nodes in a too large list

I Node priority:

I oldness of the node in its group

I local logical clock increased until the node belongs to a group

I Group priority:

I smallest priority of its members

I Usefull to avoid loops of merging groups

I Quarantine:

I waiting for Dmax timers before entering into the view

I allowing to broadcast its identity in the whole group, and then resolve conicts(using priorities)

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Sketch of Proof

1. lists bounded

2. lists contain only existing nodes

3. propagation until double-marked edges

4. if d(u,v)>Dmax, each path from u to v contains a double-marked edge

5. if d(u,v)>Dmax, u, v not in the same subgraph

6. Agreement: convergence to similar views inside each subgraph

; groups

7. Safety: group'diameters smaller than Dmax 8. The number of external edges does not increase 9. The number of external edges decrease

10. Maximality: if new merge, safety is false

11. Best-eort: a node leaves a group only if the safety becomes false

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Sketch of Proof

1. lists bounded

2. lists contain only existing nodes 3. propagation until double-marked edges

; groups

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Sketch of Proof

1. lists bounded

; groups

7. Safety: group'diameters smaller than Dmax

8. The number of external edges does not increase 9. The number of external edges decrease

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Sketch of Proof

1. lists bounded

; groups

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Sketch of Proof

1. lists bounded

; groups

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Experiences

Platform

I Airplug: Same tools for simulation, prototyping, implementation

VIS ALT CTD

FTP

NBH

DIF

GPS

PTH MSG

MVS

AIRPLUG CTL HOP CNV

WTR JEUX ALT CTD

NBH

DIF

GPS

PTH MSG

MVS

AIRPLUG CTL HOP CNV

WTR JEUX

IMG

VIS

FTP IMG

TNL TNL

IO IO

TST TST

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Experiences

I On Road: airplug-road

I Six vehicles (with Orange R&D)

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Experiences

I In the lab: airplug-lab

I Possibility to reuse GPS data recorded on road

I New scenarios

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Experiences

I In the lab: airplug-lab

I Simulation: airplug-sim

I Network Simulator

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Conclusion

I Dynamic ad hoc network:

I a next step in distributed computing?

I How to build distributed applications?

I Best-eort approach:

I algorithms do their best

I the result depends on the dynamic

I Best-eort algorithm:

I self-stabilizing + continuity in the outputs

I depending on the dynamic

I Application:

I Group Service in vehicular networksCode and videos:

http://www.hds.utc.fr/∼ducourth/airplug

I Unison in vehicular networks