"Distributed Computing" Chapter 2 Study Notes

2.1 Distributed program

Distributed system: a system in which components are distributed on different computer nodes, and different nodes communicate through message passing, and coordinate with each other to complete tasks.

$C_{ij}$: process $i$ to processjjmessage channel between$j$

$m_{ij}$: process $i$ is sent to process$j$ 's news

Global state: The global state of a distributed system consists of the state of all processes and the state of all communication channels.

2.2 Distributed operation model

$e_i^x$: process $i$ 's$x$ events.

$send\left(m\right)$ : send event of message m.

$rec\left(m\right)$ : Receive event for message m.

Distributed space-time graph:

Figure 1 Distributed space-time diagram

$H$ : collection of events in the process of distributed computing

$a\to b$ : event$a$ precedes event$b$ happens.

$$\forall e_i^x,e_j^y\in H，e_i^x\to e_j^y\iff \{\begin{array}{c}{e}_i^x\to e_j^y,(i=j)and(x<y)(events\; in\; the\; same\; process)\\ \\ e_i^x{\to }_{msg}{e}_j^y(messaging)\\ \\ e_i^x\to e_j^{y}ande{}_i^x\to e_j^y(transitive\end{array}$$

This is an anti-reflexive partial ordering relationship.

$e_i||e_j$：$e_i\nrightarrow e_{j}ande{}_j\nrightarrow e_i$(concurrent)

2.4 Global State of Distributed Systems

$L{S}_i^x$: Processor at event $e_i^x$After that happens, and event $e_i^{x+1}$state before

$S{C}_{ij}^{x,y}$: channel $C_{ij}$In process $p_i$until event $e_i^x$The message sent and the process $p_j$until event $e_j^y$unreceived message

Figure 2 Channel status

2.5 Segmentation of distributed computing

        ~~~~~~~        Drawing a zigzag line intersecting a certain point of each process line can divide the entire calculation process into two parts, and this zigzag line is called a splitting line.
        ~~~~~~~       This line divides the space-time graph into two parts, and also divides all distributed computing events into two sets, called the past (PAST) set and the future (FUTURE) set. The PAST collection contains all events to the left of the dividing line, and the FUTURE collection contains all events to the right of the dividing line.

Figure 3 Dividing line

Figure 4 Global state of the dividing line

2.6 The past and future of events

P a s t ( e j ) = { e i   ∣   ∀ e i ∈ H , e i → e j } Past(e_j)=\{e_i~|~\forall e_i\in H,e_i\rightarrow e_j\} Past(ej​)={ ei​ ∣ ∀ei​∈H,ei​→ej​}

F u t u r e ( e j ) = { e i   ∣   ∀ e i ∈ H , e j → e i } Future(e_j)=\{e_i~|~\forall e_i\in H,e_j\rightarrow e_i\} Future(ej​)={ ei​ ∣ ∀ei​∈H,ej​→ei​}