Distributed Systems on Johannes Karl Arnold

Consensus Algorithms

Sun, 22 Oct 2023 00:00:00 +0000

Multiple independent processes need to agree on an outcome.

A correct consensus protocol fulfills the following criteria:

Termination: every correct process decides some value
Integrity: if all processes proposed the same value (v), then any correct process must decide (v)
Agreement: Every correct process must agree on the same value

Faults and Failures

Sun, 22 Oct 2023 00:00:00 +0000

Types of Faults #

Transient: Occurs only once and then goes away
Intermittent: Irregular, comes and goes
Permanent: Occurs only once and then goes away. Continues to exist (until repair)

Propagation #

Fault: the cause of an error
Error: part of a system’s state that may lead to a failure
Failure: a system does not operate according to its specifications

Faults lead to errors, errors lead to failures.

Types of Failures #

Crash failure: A server halts, but is working correctly until it halts
Omission failure: A server fails to respond to incoming requests, fails to receive incoming messages or fails to send messages
Timing failure: A server’s response lies outside the specified time interval
Response failure: The server’s response is incorrect, value of the response is wrong, or server deviates from the correct flow of control
Arbitrary (Byzantine) Failure: A server may produce arbitrary responses at arbitrary times

(k)-Fault-Tolerance #

Fail-Silent #

[ n=k+1 ] Replica produces either correct responses or no response at all.

Logical Time

Sun, 22 Oct 2023 00:00:00 +0000

Time is a canonical way of establishing ordering between events

In distributed systems, time is not a global variable because machines have independently running clocks

Lamport Timestamps #

Propose we have two events, (A) and (B). Lamport timestamps allow for a “happens before” relationship, (A \to B.)

Each node (p) maintains a counter (LT(p)), which gets incremented when (p) performs an action. When (p) sends a message, it includes (LT(p)). A recieving node (q) then updates its own counter to (\max{LT(p),~LT(q)})