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Formalizing the Resilience of Open Dynamic Systems. Kazuhiro Minami (ISM) , Tenda Okimoto (NII), Tomoya Tanjo (NII), Nicolas Schwind (NII), Hei Chan (NII), Katsumi Inoue (NII), and Hiroshi Maruyama (ISM) October 26, 2012 JAWS 2012.

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formalizing the resilience of open dynamic systems

Formalizing the Resilience of Open Dynamic Systems

Kazuhiro Minami (ISM), TendaOkimoto (NII), TomoyaTanjo (NII), Nicolas Schwind (NII), Hei Chan (NII), Katsumi Inoue (NII), and

Hiroshi Maruyama (ISM)

October 26, 2012

JAWS 2012

Kazuhiro Minami

many disastrous incidents show that we cannot build systems that fully resist to unexpected events
Many disastrous incidents show that we cannot build systems that fully resist to unexpected events

Lehman financial shock

3.11 nuclear disasters

9.11

2003 Northeast blackout

we should aim to build a resilient system
We should aim to build a resilient system

Recovery

Resistance

+

Taoi-cho, Miyagi Pref.

http://www.bousaihaku.com/cgi-bin/hp/index2.cgi?ac1=B742&ac2=&ac3=1574&Page=hpd2_view http://fullload.jp/blog/2011/04/post-265.php

Kazuhiro Minami

we formalize bruneau s resilience triangle based on dynamic constraint satisfaction problems dcsps
We formalize Bruneau’s ``Resilience Triangle’’based on Dynamic Constraint Satisfaction Problems (DCSPs)

100

Degree of damage

Service Level

50

Time for recovery

0

Time

why dcsp
Why DCSP?
  • Model open systems
    • Members join or go away dynamically
  • Model changing conditions

f(X1)

Land height

Sea level

Ct

X1

Ecological environment

dcsp a time series of csps
DCSP – A time series of CSPs

Variables

Constraint

Domains

#Variables, domains, and a constraint all change over time!

configuration and fitness
Configuration and fitness
  • Each variable takes a value from domain
    • I.e.,
  • A set of value assignment

is a configuration of the system at time t

  • A configuration is fit

iff

k recoverable
K-Recoverable
  • A configuration sequence

in dynamic system is k-recoverable

if there is no subsequence

where all the configurations are unfit

Event 1

Event 2

fit

fit

fit

Unfit

Unfit

example resilient spacecraft rs 1
Example: Resilient Spacecraft RS-1

Components:

Value Domain: {Green, Red}

Fitness: Every component is Green

  • Conditions on external Events:
  • Each event affects at most k components
  • Next event is at least kdays apart
  • Adaptation Strategy:
  • The engineer fixes one component a day

RS-1 is k-Recoverable

we actually need formal ways to represent accidental failures and adaptation strategies
We actually need formal ways to represent accidental failures and adaptation strategies

Capture laws causality, and non-deterministic events

Transitional

Constraint

(TC)

Adaptation

Strategy

(AS)

configuration

v

Represent actions taken by the system itself

spacecraft example again
Spacecraft Example again

Transitional

Constraint

Component

failures

Adaptation

Strategy

Transitional

Constraint

Nothing

happened

Adaptation

Strategy

we can easily integrate the notion of l resistance to get our resilience definition
We can easily integrate the notion of l-Resistance to get our resilience definition
  • Express a constraint Ct as the intersection of multiple Cti for i =1 to Mt
  • Define the service level as a weighted sum of satisfied constraint Cti
  • l-Resistance ensures the upper bound of the service degradation
what s next
What’s Next?
  • Proactive resilience verification algorithm
    • Find stable solutions by utilizing knowledge of transitional constraints
  • Another formalization based on Distributed Constraint Optimization Problems (DCOPs)
    • Defining multiple utility functions might be more practical
  • Study common resilience strategies:
    • Diversity, Adaptability, Redundancy and Altruism
adaptability example ant colony on the shore
Adaptability Example:Ant Colony on the Shore

f(X1)

X1: Location of the colony

Fitness: fit if f(X1)>Ct

Sea level Ct goes up every l days

Land height

Sea level

Ct

X1

Adaptation Strategy:

if (unfit)

Otherwise

This ant colony is 1-resilient if

diversity example space colony
Diversity Example: Space Colony
  • Each robot has ten binary features (e.g., 2-leg/4-leg, flying/non-flying, …)
  • E.g., <0110111011>

Colony of n robots

  • Resource Reserve R
    • Fit robots contribute to build up R
    • A robot consumes one unit for reconfiguring its one feature
  • The colony is resilient if robots can survive a series of changing constraints C1, C2, …, Ct, …

Resource

  • Constraint C
    • A Subset of 2(set of all 1,024 configurations)
    • A robot is fit if its configuration is in C

C: “fit” configurations

notes on adaptation strategies
Notes on Adaptation Strategies
  • Local vs Global
    • Local: Each robot makes its own decision independently from others
    • Global: There is a global coordination. Every robot must follow the order
    • Mixed
  • Complete vs Incomplete knowledge on C
    • Complete knowledge: max 10 steps to become fit again
    • Incomplete knowledge: probabilistic (max 1023 steps if the landscape is stable)
notes on constraints
Notes on Constraints
  • Topological continuity
    • If x, y ∈ C, there is x1 (=x), x2, …, xk (=y) s.t. xi ∈ C and the humming_distance(xi, xi+1) = 1
  • Semi continuity
    • There are only a small number of isolated regions
  • Small change vs disruptive change
    • Small: only neighbors are added/deleted
    • Disruptive: non-small
conclusions
Conclusions
  • Formal definition of resilience based on DCSPs
    • Integrate the notions of Resistance and Recoverability
    • Represent open systems in a changing environment
  • Need to develop additional formalism to define various classes of transitional constraints and adaptation strategies
  • Plan to apply our model to systems in different domains

Kazuhiro Minami

slide19

Any Questions?

For more information, please visit our project web site at

systemsresilience.org

Hiroshi Maruyama