Genuine atomic multicast in asynchronous distributed systems Rachid - - PDF document

Genuine atomic multicast in asynchronous distributed systems

Workshop on Distributed Algorithms '97

Rachid Guerraoui, Andre Schiper

ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE

Introduction

• This%paper%addresses%the%problem%of%atomic'mul*cas*ng%messages%in%

asynchronous%distributed%systems.%

• Be8er%understand%the%characteris9cs%of%the%atomic%mul9cast%problem,%

and%in%par9cular%to%whether%the%possibility%and%impossibility%results%stated% for%atomic%broadcast,%also%apply%to%atomic%mul9cast.%

• Atomic%broadcast%=%simply%by%atomic%mul9cas9ng%every%message%to%all%the%

processes%in%the%system.%A%consequence%of%this%transforma9on,%together% with%the%FLP%result,%and%the%equivalence%of%atomic%broadcast%and% consensus%[Chandra],%is%that%atomic%mul9cast%is%impossible%to%solve%in% asynchronous%systems%if%one%process%can%crash.%

• Lower%bound%result%on%the%knowledge%about%failure%detec9on%needed%to%

solve%atomic%broadcast,%directly%applies%to%atomic%mul9cast%

Problem

• Could%we%solve%atomic%mul9cast%in%asynchronous%systems%augmented%with%

failure%detectors,%even%if%such%failure%detectors%are%unreliable%?%%

Solution ?

• Could%we%solve%atomic%mul9cast%in%asynchronous%systems%augmented%with%

failure%detectors,%even%if%such%failure%detectors%are%unreliable%?%

• Yes,%as%a%simple%atomic%mul9cast%algorithm%can%be%obtained%from%any%

atomic%broadcast%algorithm%

Solution ?

• Could%we%solve%atomic%mul9cast%in%asynchronous%systems%augmented%with%

failure%detectors,%even%if%such%failure%detectors%are%unreliable%?%

• Yes,%as%a%simple%atomic%mul9cast%algorithm%can%be%obtained%from%any%

atomic%broadcast%algorithm%

• No,%the%above%algorithm%is%a%“feigned”%mul9cast%
• a%mul9cast%to%a%small%subset%turns%out%to%be%as%costly%as%a%broadcast%and%

the%benefit%of%a%mul9cast%is%in%this%case%lost.%

Why not the previous solution ?

• “Minimality”%reflects%the%scalability%of%a%mul9cast,%and%we%require%from%

any%genuine%mul9cast%that%it%sa9sfies%this%property.%

• The%“Minimality”%property%states%that%only%the%sender%and%the%addressees%
• f%a%message%should%be%involved%in%the%protocol%needed%to%deliver%the%

message.%

• A%system%with%at%least%two%processes,%among%which%one%can%crash,%there%

exists%no%genuine%atomic%mul9cast%algorithm%using%a%failure%detector%that% can%be%wrong%about%at%least%two%processes.%

• A%corollary%of%this%result%is%that%genuine%atomic%mul9cast%is%strictly%harder%

than%atomic%broadcast.%

Key techniques and insights

• An%algorithm%A%is%an%atomic%mul9cast%algorithm,%if%in%every%run%R%of%A,%the%

following%proper9es%are%sa9sfied:%%

• %Agreement:%If%a%correct%process%TORdelivers%a%message%m,%then%every%correct%

process%in%Dst(m)%eventually%TORdelivers%m.%%

• %Validity:%If%a%correct%process%TORmul9casts%a%message%m,%then%every%correct%

process%in%Dst(m)%eventually%TORdelivers%m.% %•%Integrity:%For%any%message%m,%every%correct%process%p%TORdelivers%m%at%most%

• nce,%and%only%if%p%%Dst(m)%and%m%was%TORmul9cast%by%some%process%

Orig(m).% %•%Pairwise:%total%order:%If%two%correct%processes%p%and%q%TORdeliver%messages%m% and%m%,%then%p%TORdelivers%m%before%m%if%and%only%if%q%TORdelivers%m%before% m.% %•%Minimality:%If%a%correct%process%p%sends%or%receives%a%(non%null)%message%in%run% R,%then%some%message%m%is%TORmul9cast%in%R,%and%p%%{Orig(m)}%%Dst(m).%

Intuition of Proof

• The%basic%idea%of%the%proof%is%by%contradic9on%
• Assume%that,%there%is%some%genuine%atomic%mul9cast%algorithm%A%using%a%

2Runreliable%failure%detector.%

• A%message%m%R>%TORmul9cast%to%a%des9na9on%set%Dst(m)%%
• A%message%m'%R>%TORmul9cast%to%a%des9na9on%set%Dst(m')5
• And%Dst(m)∩5Dst(m')5=%{q1;%q2}.%%
• A%par9al%run%R%of%A%in%which%no%process%crashes.%
• (1)%the%processes%of%Dst(m)%think%that%q2%has%crashed%and%then%TORdeliver%

m,%whereas%(2)%the%processes%of%Dst(m')5think%that%q1%has%crashed%and% then%TORdeliver%m'.%

• As%a%consequence,%process%q1%TORdelivers%m%but%not%m',%whereas%q2%TOR

delivers%m'%but%not%m,%viola9ng%the%proper9es%of%atomic%mul9cast.%

Failure scenario Failure scenario

Solution to the problem

• %Restrict%this%model%by%considering%TORmul9cast%to%sets%of%nonRintersec9ng%

process%groups.%

Solution to the problem

• Solu*on,1,:%one5consensus5per5group5g5to5compute5the5group5<mestamp5tsg(m)5
• Consider%m%TORmul9cast%to%Dst(m),%where%Dst(m)%is%a%set%of%nonR

intersec9ng%groups:%%

– Every%group%g%in%Dst(m)%;first%computes%a%group%9mestamp%tsg(m);%% – The%sequence%number%sn(m)%is%then%set%to%the%maximum%of%all%the%group% 9mestamps%tsg(m).5

Solution to the problem

• Solu*on,2:%one5consensus5in5Dst(m)5to5compute5the5sequence5number5sn(m)55
• Consider%m%TORmul9cast%to%Dst(m),%where%Dst(m)%is%a%set%of%nonR

intersec9ng%groups:%%

– %Each%member%p%of%a%group%g%in%Dst(m),%when%receiving%m,%a8aches%a% 9mestamp%tsp(m)%to%m.% – Once%a%process%p%has%its%9mestamp%tsp(m),%p%then%sends%tsp(m)%to%all%the% processes%in%Dst(m).%Process%p%then%waits%to%get%the%9mestamp%tsx(m)%from%a% majority%of%processes%of%every%group%in%Dst(m).%These%9mestamps%are%used%by% p%to%define%its%ini9al%value%prop@snp(m)%for%a%consensus%protocol%to%decide%on% the%sequence%number%sn(m):%prop@snp(m)%is%set%to%the%maximum%of%all% 9mestamps%tsx(m)%received%by%p.% – The%sequence%number%sn(m)%is%the%decision%of%the%consensus%protocol%among% the%processes%in%Dst(m).%5

What should everyone remember about this paper?

• In%contrast%to%atomic%broadcast,%genuine%atomic%mul9cast%is%impossible'to'

solve'with'failure'detectors'that'are'unreliable.%

• Discuss%a%way%to%circumvent%the%impossibility%result,%by%restric9ng%the%

des9na9ons%of%mul9casts%to%sets%of%disjoint%process%groups,%each%group% behaving%like%a%logically%correct%en9ty.%

Appendix (Dr. Skeen)

• When%a%process%p%TORmul9casts%a%message%m5to%Dst(m),%p%sends%the%

message%to%every%member%of%Dst(m).%Every%process%q55Dst(m)%that% receives%m,%stores%m%in%a%pending5buffer,5and%sends%back%to%p%a%9mestamp% tsq(receive(m))%corresponding%to%q’s%current%logical%clock.%

• Process%p%then%collects%the%9mestamps%from%all%the%processes%in%Dst(m),%

defines%a%sequence%number%sn(m)%as%the%maximum%of%the%9mestamps,% and%sends%sn(m)%to%every%member%of%Dst(m).%

• Every%process%q55Dst(m)%that%receives%sn(m),%removes%m%from%its%

pending%buffer%and%stores%it%in%a%delivery%buffer.%

• Process%q%TORdelivers%m%when%(1)%there%is%no%message%m5=5m%in%its%pending%

buffer%for%which%tsq(receive(m))<sn(m)%and%(2)%there%is%no%message%m”%=5m% in%its%delivery%buffer%for%which%sn(m”)5<%sn(m).%5