1

Theory of Distributed Systems (TDS)

Group Leaders: Nancy Lynch, Idit Keidar

PhD students: Victor Luchangco, Josh Tauber, Roger Khazan, Carl Livadas, Rui Fan

Meng and UROP students: Laura Dean, Andrej Bogdanov, Michael Tsai, Chris Luhrs,

Affiliates: Alex Shvartsman (U. Conn.), Alan Fekete (U. Sydney), Paul Attie (Northeastern), Ziv Bar-Joseph

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Research Overview

Algorithms Applications

Math Models, Proof and Analysis Methods

Building blocksProject (AFOSR)

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Math Models, Proof and Analysis

Methods• I/O Automata

– Mathematical model for asynchronously interacting system components.

• Timed I/O Automata, Hybrid I/O Automata [Lynch, Segala, Vaandrager], Probabilistic [Segala], Dynamic [Lynch, Attie]

• Invariant assertions• Levels of abstraction (simulation relations)• Compositional reasoning• Conditional performance analysis• Object inheritance [Keidar, Khazan, Shvartsman]

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IOA Language and Toolset

• Language design [Garland, Lynch]• Front end [Garland]• Simulator [Chefter, Ramirez, Dean]• Code generator [Tauber, Tsai]• Theorem prover [Garland, Fan, Bogdanov]• Test examples [Luhrs, Dean, Rosen, Karlovich]

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Algorithms

• Communication [Keidar, Khazan, Livadas, Bar-Joseph, Lynch]

• Distributed data management [Keidar, Shvartsman, De Prisco, Lynch]

• Consensus [Bar-Joseph, Keidar]• Load balancing [Shvartsman, Khazan, Fekete]

• Lower bounds, impossibility results

• Distributed algorithms => Distributed systems– Generating code from models [Tauber, Tsai]

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Applications

• Multiprocessor memories [Luchangco]• Hybrid systems

– Automated transportation: Planes (TCAS), Trains (Raytheon PRT), and Automobiles (California PATH) [Livadas]

– Mobile computing

• Middleware (building blocks) for fault-tolerant distributed computing [Keidar, Shvartsman, Fekete, De Prisco, Khazan]

• Communication [Livadas, Bar-Joseph]• Object-oriented programming [Fekete, Lynch]• Agents [Attie, Luchangco, Lynch, Keidar]

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8

Reliable Group Communication: a Mathematical Approach

Nancy Lynch

Theory of Distributed Systems

MIT LCS

AFOSR Review

November 15, 2000GC

…

9

Dynamic Distributed Systems

• Modern distributed systems are dynamic.• Set of clients participating in an application

changes, because of: – Network, processor failure, recovery– Changing client requirements

• To cope with changes:– Use abstract groups of client processes

with changing membership sets.– Processes communicate with group members by

sending messages to the group as a whole.

? ?

?? ?

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Group Communication Services

• Support management of groups• Maintain membership info • Manage communication• Make guarantees about ordering, reliability of

message delivery, e.g.:– Best-effort: IP Multicast

– Strong consistency guarantees: Isis, Transis, Ensemble

• Hide complexity of coping with changes

GC

…

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This Talk

• Describe– Group communication systems

– A mathematical approach to designing, modeling, analyzing GC systems.

– Our accomplishments and ideas for future work.

• Collaborators: Idit Keidar, Alan Fekete, Alex Shvartsman, Roger Khazan, Roberto De Prisco, Jason Hickey, Robert van Renesse, Carl Livadas, Ziv Bar-Joseph, Kyle Ingols, Igor Tarashchanskiy

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Talk Outline

I. Background: Group Communication

II. Our Approach

III. Projects and Results1. View Synchrony

2. Ensemble

3. Dynamic Views

4. Scalable Group Communication

IV. Conclusions

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I. Background: Group Communication

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The Setting

• Dynamic distributed system, changing set of participating clients.

• Applications:– Replicated databases, file systems

– Distributed interactive games

– Multi-media conferencing, collaborative work

– …

? ?

?? ?

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Groups

• Abstract, named groups of client processes, changing membership.

• Client processes send messages to the group (multicast).

• Early 80s: Group idea used in replicated data management system designs

• Late 80s: Separate group communication services.

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Group Communication Service

• Communication middleware

• Manages group membership, current views

View = membership set + identifier

• Manages multicast communication

among group members– Multicasts respect views

– Guarantees within each view:

• Reliability constraints

• Ordering constraints, e.g., FIFO from each sender, causal, common total order

• Global service

GC

…AB

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Group Communication Service

GCS

new-view

new-viewmcast

mcastreceive

receive

Client A Client B

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Isis [Birman, Joseph 87]

• Primary component group membership• Several reliable multicast services, different ordering

guarantees, e.g.:– Atomic Broadcast: Common total order, no gaps

– Causal Broadcast:

• When partition is repaired, primary processes send state information to rejoining processes.

• Virtually Synchronous message delivery

A B

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Example: Interactive Game

• Alice, Bob, Carol, Dan in view {A,B,C,D}• Primary component membership– {A}{B,C,D} split;

only {B,C,D} may continue.

• Atomic Broadcast– A fires, B moves away;

need consistent order

A B C D

A B C D

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Interactive Game

• Causal Broadcast– C sees A enter a room; locks door.

• Virtual Synchrony– {A}{BCD} split; B sees A shoot; so do C, D.

A B C D

A B C D

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Applications

• Replicated data management– State machine replication

[Lamport 78] , [Schneider 90]

– Atomic Broadcast provides support

– Same sequence of actions performed everywhere.

– Example: Interactive game state machine

• Stock market• Air-traffic control

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Transis [Amir, Dolev, Kramer, Malkhi 92]

• Partitionable group membership

• When components merge, processes exchange state information.

• Virtual synchrony reduces amount of data exchanged.

• Applications– Highly available servers

– Collaborative computing, e.g. shared whiteboard

– Video, audio conferences

– Distributed jam sessions

– Replicated data management [Keidar , Dolev 96]

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Other Systems• Totem [Amir, Melliar-Smith, Moser, et al., 95]

– Transitional views, useful with virtual synchrony

• Horus [Birman, van Renesse, Maffeis 96]

• Ensemble [Birman, Hayden 97]– Layered architecture– Composable building blocks

• Phoenix, Consul, RMP, Newtop, RELACS,…• Partitionable

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Service Specifications

• Precise specifications needed for GC services– Help application programmers write programs that use the

services correctly, effectively

– Help system maintainers make changes correctly

– Safety, performance, fault-tolerance

• But difficult:– Many different services; different guarantees about

membership, reliability, ordering

– Complicated

– Specs based on implementations might not be optimal for application programmers.

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Early Work on GC Service Specs

• [Ricciardi 92]• [Jahanian, Fakhouri, Rajkumar 93]• [Moser, Amir, Melliar-Smith, Agrawal 94]• [Babaoglu et al. 95, 98] • [Friedman, van Renesse 95]• [Hiltunin, Schlichting 95]• [Dolev, Malkhi, Strong 96]• [Cristian 96]• [Neiger 96]

• Impossibility results [Chandra, Hadzilacos, et al. 96]

• But still difficult…

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II. Our Approach

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Approach

• Model everything:– Applications

• Requirements, algorithms

– Service specifications

• Work backwards, see what

the applications need

– Implementations of the services

• State, prove correctness theorems:– For applications, implementations.

– Methods: Composition, invariants, simulation relations

• Analyze performance, fault-tolerance.

• Layered proofs, analyses

Application

Application Algorithm

Service

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Math Foundation: I/O Automata

• Nondeterministic state machines

• Not necessarily finite-state

• Input/output/internal actions (signature)

• Transitions, executions, traces

• System modularity:– Composition, respecting traces

– Levels of abstraction, respecting traces

• Language-independent, math model

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Modeling Style• Describe interfaces, behavior• Program-like behavior descriptions:

– Precondition/effect style– Pseudocode or IOA language

• Abstract models for algorithms, services• Model several levels of abstraction,

– High-level, global service specs

…

– Detailed distributed algorithms

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Modeling Style

• Very nondeterministic:– Constrain only what must be constrained.

– Simpler

– Allows alternative implementations

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Describing Timing Features

• TIOAs [Lynch, Vaandrager 93] – For describing:

• Timeout-based algorithms.

• Clocks, clock synchronization

• Performance properties

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Describing Failures

• Basic or timed I/O automata, with fail, recover input actions.

• Included in traces, can use them in specs.

failrecover

fail

recover

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Using I/O Automata for Group Communication Systems

• Use for global services + distributed algorithms• Define safety properties separately from

performance/fault-tolerance properties.– Safety:

• Basic I/O automata; trace properties

– Performance/fault-tolerance:

• Timed I/O automata with failure actions; timed trace properties

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III. Projects and Results

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Projects

1. View Synchrony

2. Ensemble

3. Dynamic Views

4. Scalable Group Communication

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1. View Synchrony (VS) [Fekete, Lynch, Shvartsman 97, 00]

Goals:• Develop prototypes:– Specifications for typical GC services

– Descriptions for typical GC algorithms

– Correctness proofs

– Performance analyses

• Design simple math foundation for the area. • Try out, evaluate our approach.

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View Synchrony

What we did:• Talked with system developers (Isis, Transis)• Defined I/O automaton models for:– VS, prototype partitionable GC service– TO, non-view-oriented totally ordered bcast service– VStoTO, application algorithm based on

[Amir, Dolev, Keidar, Melliar-Smith, Moser]

• Proved correctness• Analyzed performance/ fault-tolerance.

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VStoTO Architecture

VS

VStoTO VStoTO

TObcast

brcv

gpsnd

gprcvnewview

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TO Broadcast Specification

Delivers messages to everyone, in the same order.Safety: TO-Machine

Signature: input: bcast(a,p) output: brcv(a,p,q) internal: to-order(a,p)State: queue, sequence of (a,p), initially empty for each p: pending[p], sequence of a, initially empty next[p], positive integer, initially 1

TO

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TO-Machine

Transitions:

bcast(a,p)Effect:

append a to pending[p]

to-order(a,p)Precondition:

a is head of pending[p]Effect:

remove head of pending[p]append (a,p) to queue

brcv(a,p,q)Precondition:

queue[next[q]] = (a,p)Effect:

next[q] := next[q] + 1

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Performance/Fault-Tolerance

TO-Property(b,d,C): If C stabilizes, then within time b, a point is reached after which any message sent or received anywhere in C is received everywhere in C, within time d.

stabilize

b

send

d

receive

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VS Specification

• Partitionable view-oriented service• Safety: VS-Machine– Views presented in consistent order, possible gaps

– Messages respect views

– Messages in consistent order

– Causality

– Prefix property

– Safe indication

• Doesn’t guarantee Virtual Synchrony • Like TO-Machine, but per view

VS

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Performance/Fault-Tolerance

VS-Property(b,d,C):

If C stabilizes, then within time b, a point is reached where views known within C are consistent, and messages sent in the final view v are delivered everywhere in C, within time d.

mcast(v) receive(v)

d

stabilize

b

newview( v)

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VStoTO Algorithm• TO must deliver messages in order, no gaps.• VS delivers messages in order per view.• Problems arise from view changes:

– Processes moving between views could have different prefixes.– Processes could skip views.

• Algorithm: – Real work done in majority views only– Processes in majority views totally order messages, and deliver

to clients messages that VS has said are safe.– At start of new view, processes exchange state, to reconcile

progress made in different majority views.

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Correctness (Safety) Proof

• Show composition of VS-Machine and VStoTO machines implements TO-Machine.

• Trace inclusion

• Use simulation relation proof:– Relate start states, steps of composition

to those of TO-Machine– Invariants, e.g.: Once a message is ordered everywhere in some majority view, its order is determined forever.

• Checked using PVS theorem-prover, TAME [Archer]

TO

Composition

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Performance Analysis• Assume VS satisfies VS-Property(b,d,C):– If C stabilizes, then within time b, views known

within C become consistent, and messages sent in the final view are delivered everywhere in C, within time d.

• And VStoTO satisfies:– Simple timing and fault-tolerance assumptions.

• Then TO satisfies TO-Property(b+d,d,C):– If C stabilizes, then within time b+d, any message

sent or delivered anywhere in C is delivered everywhere in C, within time d.

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Conclusions: VS• Models for VS, TO, VStoTO• Proofs, performance analysis• Tractable, understandable, modular • [PODC 97], [TOCS 00]• Follow-on work:

– Algorithm for VS [Fekete, Lesley]– Load balancing using VS [Khazan]– Models for other Transis algorithms [Chockler]

• But: VS is only a prototype; lacks some key features, like Virtual Synchrony

• Next: Try a real system!

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2. Ensemble [Hickey, Lynch, van Renesse 99]

Goals:• Try, evaluate our approach on a real system • Develop techniques for modeling, verifying,

analyzing more features, of GC systems, including Virtual Synchrony

• Improve on prior system validation methods

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Ensemble

• Ensemble system [Birman, Hayden 97]– Virtual Synchrony– Layered design, building blocks– Coded in ML [Hayden]

• Prior verification work for Ensemble and predecessors: – Proving local properties using

Nuprl [Hickey]– [Ricciardi], [Friedman]

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Ensemble• What we did:– Worked with developers

– Followed VS example

– Developed global specs for key layers:

• Virtual Synchrony

• Total Order with Virtual Synchrony

– Modeled Ensemble algorithm spanning between layers

– Attempted proof; found logical error in state exchange algorithm (repaired)

– Developed models, proofs for repaired system

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Conclusions: Ensemble

• Models for two layers, algorithm • Tractable, easily understandable by developers• Error, proofs• Low-level models similar to actual ML code (4 to 1)• [TACAS 99]• Follow-on:

– Same error found in Horus.– Incremental models, proofs [Hickey]

• Next: Use our approach to design new services.

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3. Dynamic Views [De Prisco, Fekete, Lynch, Shvartsman 98]

Goals:• Define GC services that cope with both:– Long-term changes:• Permanent failures, new joins• Changes in the “universe” of processes

– Transient changes

• Use these to design consistent total order and consistent replicated data algorithms that tolerate both long-term and transient changes.

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Dynamic Views

• Many applications with strong consistency requirements make progress only in primary views:– Consistent replicated data management – Totally ordered broadcast

• Can use static notion of allowable primaries, e.g., majorities of universe, quorums– All intersect.– Only one exists at a time.– Information flows from each to the next.

• But: Static notion not good forlong-term changes

A B C D E

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Dynamic Views

• For long-term changes, want dynamic notion of allowable primaries.

• E.g., each primary might contain majority of previous:

• But: Some might not intersect.Makes it hard to maintain consistency.

FA B C D E

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Dynamic Views

• Key problem: – Processes may have different opinions about which

is the previous primary

– Could even be disjoint.

• [Yeger-Lotem, Keidar, Dolev 97] algorithm– Keeps track of all possible previous primaries.

– Ensures intersection with all of them.

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Dynamic Views

What we did:

• Defined Dynamic View Service, DVS, based on [YKD]

• Designed to tolerate long-term failures

• Membership:– Views delivered in consistent order, with possible gaps.

– Ensures new primary intersects all possible previous primaries.

• Communication: Similar toVS– Messages delivered within views,

– Prefix property, safe notifications.

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Dynamic Views

• What we did:– Modeled, proved implementing algorithm

– Modeled, proved TO-Broadcast application

– Distributed implementation [Ingols 00]

DVS

TO

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Handling Transient Failures: Dynamic Configurations

• Configuration = Set of processes plus structure, e.g., set of quorums, leader,…

• Application: Highly available consistent replicated data management:– Paxos [Lamport], uses leader, quorums

– [Attiya,Bar-Noy, Dolev], uses read quorums and write quorums

• Quorums allow flexibility, availability in the face of transient failures.

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Dynamic Configurations [De Prisco, Fekete, Lynch, Shvartsman 99, 00]

• Combine ideas/benefits of– Dynamic views, for long-term failures, and– Static configurations, for transient failures

• Idea:– Allow configuration to change (reconfiguration).– Each configuration satisfies intersection properties with

previous configuration

• Example:– Config = (membership set, read quorums, write quorums)– Membership set of new configuration contains read quorum

and write quorum of previous configuration

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Dynamic Configurations

What we did:• Defined dynamic configuration service DCS,

guaranteeing intersection properties w.r.t. all possible previous configurations.

• Designed implementing algorithm, extending [YKD]• Developed application: Replicated data

– Dynamic version of [Paxos]– Dynamic version of [Attiya, BarNoy, Dolev] – Tolerate

• Transient failures, using quorums• Longer-term failures, using reconfiguration

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Conclusions: Dynamic Views

• New DVS, DCS services for long-term changes in set of processes

• Applications, implementations• Decomposed complex algorithms into tractable pieces:

– Service specification, implementation, application– Static algorithm vs. reconfiguration

• Couldn’t have done it without the formal framework.• [PODC 98], [DISC 99]

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4. Scalable Group Communication [Keidar, Khazan 99],

[Keidar, Khazan, Lynch, Shvartsman 00]

Goal: • Make GC work in wide area networks

What we did:• Defined desired properties for GC services • Defined spec for scalable group membership service

[Keidar, Sussman, Marzullo, Dolev 00], implemented on small set of membership servers

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Scalable Group Communication

What we did:• Developed new, scalable GC algorithms:

– Use scalable GM service

– Multicast implemented on clients

– Efficient: Algorithm for virtual synchrony uses only one round for state exchange, in parallel with membership service’s agreement on views.

– Processes can join during reconfiguration.

• Distributed implementation [Tarashchanskiy]

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S

A A’

S’

Scalable GC

What we did:

• Developed new incremental modeling, proof methods [Keidar, Khazan, Lynch, Shvartsman 00]– Proof Extension Theorem

• Developed models, proofs (safety and liveness) , using the new methods.

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Conclusions: Scalable GC

• Specs, new algorithms, proofs

• New incremental proof methods

• Couldn’t have done it without the formal framework.

• [ICDCS 99], [ICSE 00]

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IV. Conclusions

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Practical GC Systems: Current Status [Birman 99]

• Commercial successes: – Stock exchange (Zurich, New York)– Air-traffic control (France)

• Problems:– Performance, for strong guarantees like Virtual Synchrony– Not integrated with OO programming technologies.

• Trends: – Flexible services– Weaker guarantees; better performance– Integration with OO technologies

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Summary

• GC services help in programming dynamic distributed systems, though scalability, integration problems remain.

• Our contributions:– Modeling style: Automata + performance properties

– Techniques: Conditional performance analysis, incremental modeling/proof

– Models, proofs for key services

– Discovered errors

– New services: Dynamic views, scalable GC

• Mathematical framework makes it possible to design more complex systems correctly.

GC

69

Conditional Performance Analysis• Make conditional claims about system behavior, under

various assumptions about behavior of environment, network.

• Include timing, performance, failures.

• Benefits:– Formal performance predictions

– Says when system makes specific guarantees

• Normal case + failure cases

• Parameters, sensitivity analysis

– Composable

– Get probabilistic claims as corollaries

70

CP Analysis: Typical Hypotheses

• Stabilization of underlying network.

• Limited rate of change.

• Bounds on message delay.

• Limited amount of failure (number, density).

• Limit input arrivals (number, density).

• Method allows focus on tractable cases.

71

Future Work

• Consider more dynamic settings:– Join, leave requests– Processor failures: Volatile memory, Byzantine behavior– Communication failures– Changing network topology– Mobility

• Design, model, analyze more services, applications– Communication, data sharing services– Other services

• Lower bounds, impossibility results• Math foundations

72

Math Foundations• Models:– General models for timing behavior, hybrid

continuous/discrete behavior, failures, probabilistic behavior, process creation,…

– Models for mobility (based on Hybrid I/O Automata)

– Combined models

• Proof and performance analysis methods:– Measures– Conditional performance analysis– Incremental modeling, proof

73

Communication: View-oriented GC

• Scalable GC– Experiments

– CP analysis

– Compare predicted, observed performance

– Applications

• Dynamic views, dynamic configurations– Experiments, Analysis, …

• Self-stabilization• Lower bounds, impossibility results

GC

74

Scalable Reliable Multicast [Floyd, Jacobson, et al. 95]

• IP Multicast+ retransmission protocol• Modeling, analysis [Livadas, Keidar, Lynch]

IPMcastSRM

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Other communication services

• Bimodal Multicast [Birman, Hayden, et al. 99]

• Compare GC services with SRM, Bimodal Multicast

• Study tradeoffs between strength of ordering and reliability guarantees vs. performance

• Multicast with QoS [Bar-Joseph, Keidar, Anker, Lynch 00]

– Models for:

• Bandwidth reservation service

• TO Multicast service with QoS (latency, bandwidth)

– Algorithms implementing TO-QoS using reservation service

76

Data Sharing

• Coherent– Analyze, compare implementations

– Lower bounds, impossibility results

• Less coherent• Tradeoffs between coherence guarantees and

performance

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Other services for dynamic systems:

• Registry/location services• Leader election • Consensus• Resource allocation• Establishing spanning trees, overlay networks• Load-balancing• …

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Mobility

• Mobile system models– Ad hoc, cellular, mixed (Oxygen)

– Failure models

– Formalized using Hybrid I/O Automata

• Mobile system services– Location services

– Group membership, group communication

– Data sharing

– Applications: Games, military operations