《分布式算法实战指南》：理解与设计的关键

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《分布式算法：直观方法》是一本由Wan Fokkink编著的专业教材，由麻省理工学院出版社于2013年出版。该书针对分布式系统设计者提供了深入且实用的理论和实践指导，是理解和设计分布式算法的重要参考书籍。作者以其直观的方式，引导读者理解分布式计算中的核心概念和复杂问题，如负载均衡、通信协议、一致性模型等。在本书中，你将学习到一系列关键知识点，例如： 1. 分布式系统基础：书中首先概述了分布式系统的基本架构，包括客户端-服务器模型、对等网络以及分布式计算环境的组成部分，如节点、进程和消息传递。 2. 通信与消息传递：作者会详细介绍各种通信机制，如TCP/IP协议栈，以及消息队列、发布/订阅模式等，这些都是实现分布式算法的基础。 3. 一致性模型：书中讲解了不同的一致性模型，如强一致性、最终一致性、弱一致性，这对于处理分布式系统中的数据同步至关重要。 4. 分布式算法设计：涵盖了诸如分布式哈希表、Paxos和Raft协议，这些是分布式系统中常见的一致性算法，它们确保了数据在多台机器上的可靠存储和更新。 5. 负载均衡与分区容错：如何通过算法设计来分散系统负载，以及如何处理网络分区和故障转移，都是本书的重点内容。 6. 性能优化：涉及如何通过算法改进系统吞吐量、响应时间和资源利用率，以及如何应对网络延迟和不可预测性。 7. 案例研究与实践应用：书中提供实际案例分析，帮助读者了解如何在真实世界的应用场景中实施和优化分布式算法。 8. 附录与索引：包含了详细的参考文献和术语索引，便于读者进一步深入研究和查找相关信息。《分布式算法：直观方法》不仅适合计算机科学专业的学生和研究人员，也对软件工程师、系统架构师和云计算领域的从业人员具有很高的实用价值。它将复杂的分布式算法概念化繁为简，使得理解和掌握这些技术变得更加容易。

Message Passing

Preliminaries

In a message-passing framework, a distributed system consists of a ﬁnite network (or

graph) of N processes (or nodes). Each process in the network carries a unique ID.

The processes in the network are connected by channels (or edges), through which

they can send messages to each other. There is at most one channel from one process

to another, and a process does not have a channel to itself. Sometimes a process may

want to communicate a message to itself, but for this clearly no channel is needed.

We use E and D to denote the number of channels and the diameter of the network,

respectively.

A process can record its own state and the messages it sends and receives; pro-

cesses do not share memory or a global clock. Each process knows only its (direct)

neighbors in the network. The topology of the network is assumed to be strongly

connected, meaning that there is a path from each process to every other process.

Communication in the network is asynchronous, meaning that sending and re-

ceiving a message are distinct events at the sending and receiving process, respec-

tively. The delay of a message in a channel is arbitrary but ﬁnite. We assume that

communication protocols are being used to avoid that messages are garbled, dupli-

cated or lost. Channels need not be FIFO, meaning that messages can overtake each

other.

In a directed network, messages can travel only in one direction through a chan-

nel, while in an undirected network, messages can travel either way. Undirected

channels are required for distributed algorithms that use an acknowledgment scheme.

Acyclic networks will always be undirected, since otherwise the network would not

be strongly connected. A network topology is called complete if there is an undi-

rected channel between each pair of different processes.

A spanning tree of an undirected network is a connected, acyclic graph that con-

sists of all the nodes and a subset of the edges in the network. The edges of the

spanning tree are called tree edges, and all other edges are called frond edges. Often

the edges in a spanning tree are given a direction to obtain a sink tree, in which all

paths lead to the same node, called the root; each directed edge leads from a child to

its parent.

8 2 Preliminaries

At some places we will deviate from the assumptions mentioned so far and move

to, for instance, synchronous communication in which sending and receiving of the

same message form one atomic event, or unreliable processes or channels, or FIFO

channels, or processes without a unique ID, or processes with a probabilistic instead

of a deterministic speciﬁcation. This will then be stated explicitly.

Transition systems

A distributed algorithm, which runs on a distributed system, provides (usually deter-

ministic) speciﬁcations for the individual processes. The global state of a distributed

algorithm, called a conﬁguration, evolves by means of transitions. The overall be-

havior of a distributed system is captured by a transition system, which consists of:

• a set C of conﬁgurations,

• a binary transition relation → on C, and

• a set I⊆Cof initial conﬁgurations.

A conﬁguration γ is terminal if it has no outgoing transition: γ → δ for no δ ∈C.

An execution of the distributed system is a sequence γ

··· of conﬁgurations

that is either inﬁnite or ends in a terminal conﬁguration γ

, such that:

• γ

∈I, and

• γ

→ γ

i+1

for all i ≥ 0 (and in case of a ﬁnite execution, i<k).

A conﬁguration δ is reachable if there is a γ

∈Iand a sequence γ

···γ

with

→ γ

i+1

for all 0 ≤ i<kand γ

= δ.

States and events

The conﬁguration of a distributed system is composed from the local states of its

processes and the messages in transit. A transition between conﬁgurations of a dis-

tributed system is associated to an event (or, in case of synchronous communication,

two events) at one (or two) of its processes. A process can perform internal, send and

receive events. An internal event inﬂuences only the state at the process where the

event is performed. Typical internal events are reading or writing to a local variable.

Assignment of a new value to a variable is written as ←; for example, n ← n +1

means that the value of variable n, representing a natural number, is increased by

one. A send event in principle gives rise to a corresponding receive event of the same

message at another process. It is assumed that two different events never happen at

the same moment in real time (with the exception of synchronous communication).

A process is an initiator if its ﬁrst event is an internal or send event; that is, an

initiator can start performing events without input from another process. An algo-

rithm is centralized if there is exactly one initiator. A decentralized algorithm can

have multiple initiators.

2 Preliminaries 9

Assertions

An assertion is a predicate on the conﬁgurations of an algorithm. That is, in each

conﬁguration the assertion is either true or false.

An assertion is a safety property if it is true in each reachable conﬁguration of

the algorithm. A safety property typically expresses that something bad will never

happen. Examples of safety properties are:

– You can always count on me.

– The cost of living never decreases.

– If an interrupt occurs, a message will be printed within one second.

In particular, the last example states that never no message gets printed within one

second after an interrupt.

In general, it is undecidable whether a given conﬁguration is reachable. An as-

sertion P is an invariant if:

• P (γ) for all γ ∈I, and

• if γ → δ and P(γ), then P (δ).

In other words, an invariant is true in all initial conﬁgurations and is preserved by all

transitions. Clearly, each invariant is a safety property. Note that checking whether

an assertion is an invariant does not involve reachability.

An assertion is a liveness property if executions, from some point on, contain a

conﬁguration in which the assertion holds. A liveness property typically expresses

that something good will eventually happen. Examples of liveness properties are:

– What goes up, must come down.

– The program always eventually terminates.

– If an interrupt occurs, a message will be printed.

A liveness property sometimes holds only with respect to the so-called fair ex-

ecutions of an algorithm. For example, consider a simple algorithm that consists of

ﬂipping a coin until the result is tails. Since there is an inﬁnite execution in which the

outcome of every coin ﬂip is heads, the liveness property that eventually the outcome

will be tails does not hold. However, if the coin is fair, this inﬁnite execution has zero

chance of happening; inﬁnitely often we ﬂip the coin with the possible outcome tails,

but never is the outcome tails. We say that an execution is fair if every event that can

happen in inﬁnitely many conﬁgurations in the execution is performed inﬁnitely of-

ten during the execution. The inﬁnite execution in which the outcome of every coin

ﬂip is heads is not fair. Note that any ﬁnite execution is by default fair.

Causal order

In each conﬁguration of an asynchronous distributed system, events that can occur

at different processes are independent, meaning that they can happen in any order.

The causal order ≺ is a binary relation on events in an execution such that a ≺ b

if and only if a must happen before b. That is, the events in the execution cannot be

reordered in such a way that a happens after b. The causal order for an execution is

the smallest relation such that:

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