[PPT] - In Search of Lost Time Bernadette Charron-Bost CNRS / Ecole PowerPoint Presentation

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In Search of Lost Time

Bernadette Charron-Bost CNRS / Ecole Polytechnique, France Martin Hutle EPFL, Switzerland Josef Widder TU Wien, Austria tubs.CITY Symposium / Braunschweig July 1, 2009

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failure detector approach

◮ consensus

◮ solvable in synchronous systems ◮ not solvable in asynchronous systems [FLP85]

◮ FD approach: an effort to establish intermediate assumptions

that allows solving consensus

◮ motivation: in an async. system, a slow process cannot be

distinguished from a crashed one

◮ replace timing assumptions ◮ provide processes with information about failures 2/32

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intermediate assumptions

◮ [DDS87] study 5 synchrony parameters

◮ 32 models ◮ coarse frontier between models where consensus is solvable and

not

◮ FD models allows a comparatively fine grained classification of

models [CHT96]

◮ this advantage is widely accepted ◮ disadvantages mostly ignored / not investigated

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consensus algorithm with partial synchrony

t good period partial synchrony [DLS88] Paxos [Lam98] (established 1989): A finite good period is sufficient to solve Consensus.

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consensus algorithm with partial synchrony

t good period partial synchrony [DLS88] Paxos [Lam98] (established 1989): A finite good period is sufficient to solve Consensus. consensus is solvable in practice

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lower bound for consensus with FDs [CHT96]

t good period Ω: “There is a time after which all the correct processes always trust the same correct process.” By the proof in [CHT96]: Ω is necessary! A good period which lasts forever is necessary for Consensus.

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lower bound for consensus with FDs [CHT96]

t good period Ω: “There is a time after which all the correct processes always trust the same correct process.” By the proof in [CHT96]: Ω is necessary! A good period which lasts forever is necessary for Consensus. consensus is not solvable in practice

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What we do

◮ explain the paradox

◮ the problem is inherent to the model

◮ in parallel we found fundamental problems with the relation to

compare FDs

◮ both problems have the same origin ◮ we will discuss this origin in this talk

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The Model

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The FD model

◮ set Π of n processes

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The FD model

◮ set Π of n processes ◮ discrete time base T

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The FD model

◮ set Π of n processes ◮ discrete time base T

(we employ T = I N)

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The FD model

◮ set Π of n processes ◮ discrete time base T

◮ failure pattern F : T → Π such that F(t) ⊆ F(t + 1) 8/32

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The FD model

◮ set Π of n processes ◮ discrete time base T

◮ failure pattern F : T → Π such that F(t) ⊆ F(t + 1)

◮ and two layers. . .

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failure detector layer

◮ history H : Π × T → R

(range R)

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failure detector layer

◮ history H : Π × T → R

(range R)

◮ defined for every time

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failure detector layer

◮ history H : Π × T → R

(range R)

◮ defined for every time

Example: R =

,

, ,

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failure detector layer

◮ history H : Π × T → R

(range R)

◮ defined for every time

Example: R =

,

, ,

t

H(r, ) H(q, ) H(p, )

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failure detector layer

◮ history H : Π × T → R

(range R)

◮ defined for every time

Example: R =

,

, ,

t

H(r, ) H(q, ) H(p, )

◮ failure detector D : F → D(F) = {H1, H2, . . . }

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provide information about failures?

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provide information about failures? yes

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provide information about failures? yes

◮ Ω [CHT96] has range R = Π ◮ q = H(p, t): at time t, Ω “tells” p that q is correct ◮ from some time on

◮ Ω provides the same information to all correct processes, and ◮ this information is correct

∀F ∈ E, ∀H ∈ Ω(F), ∃t0 ∈ T , ∃q ∈ correct(F), ∀p ∈ correct(F), ∀t > t0 : H(p, t) = q.

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provide information about failures?

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provide information about failures? no

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provide information about failures? no

failure detector C

◮ range R = I

N

◮ HC : ∀p, ∀t, HC(p, t) = t ◮ C : F → {HC}

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provide information about failures? no

failure detector C

◮ range R = I

N

◮ HC : ∀p, ∀t, HC(p, t) = t ◮ C : F → {HC} ◮ perfect global clock is a FD ◮ reason:

◮ FDs are defined via histories ◮ a history is a function of time 11/32

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