By introducing the concepts of logical clocks and the "happened-before" relation, Leslie Lamport provided a framework for understanding and managing the ordering of events in distributed systems.
The Concept of Event Ordering
In a distributed system, events occur in different processes that are spatially separated and communicate by exchanging messages. Lamport introduces the "happened-before" relation (denoted as ( → )) to define a partial ordering of events. This relation is based on three conditions:
- Within a Process: If event ( a ) occurs before event ( b ) in the same process, then ( a → b ).
- Message Passing: If event ( a ) is the sending of a message and event ( b ) is the receipt of that message, then ( a → b ).
- Transitivity: If ( a → b ) and ( b → c ), then ( a → c ).
This partial ordering helps in understanding the causal relationships between events in a distributed system.
Logical Clocks
To implement the "happened-before" relation, Lamport introduces the concept of logical clocks. Each process in the system maintains a logical clock, which is a counter that increments with each event. The logical clocks must satisfy the following conditions to ensure the correct ordering of events:
- Incrementing Clock: The clock value is incremented between any two successive events in a process.
- Message Timestamps: When a message is sent, it carries a timestamp equal to the sender's clock value. Upon receiving a message, the recipient process sets its clock to be greater than or equal to its current value and the message's timestamp.
These rules ensure that if event ( a ) happens before event ( b ), then the logical clock value of ( a ) is less than that of ( b ).
Total Ordering of Events
While the "happened-before" relation provides a partial ordering, Lamport also describes how to achieve a total ordering of events. This is done by combining the logical clock values with a unique identifier for each process. If two events have the same logical clock value, the process identifiers are used to break the tie, ensuring a consistent total ordering across the system.
Synchronization and Mutual Exclusion
One of the practical applications of these concepts is in solving synchronization problems, such as mutual exclusion. Lamport presents an algorithm that uses logical clocks to ensure that requests for a shared resource are granted in the order they were made, thus preventing conflicts and ensuring fairness.
Physical Clocks and Synchronization
Lamport also discusses the use of physical clocks to avoid anomalous behavior that can arise from the arbitrary nature of logical clocks. He introduces methods for synchronizing physical clocks across processes, ensuring that the clocks run at approximately the correct rate and remain within a bounded difference from each other. This synchronization is crucial for maintaining a consistent view of time across the distributed system.
Key Terms
Distributed System
A collection of independent processes that communicate with each other by exchanging messages. These processes are spatially separated and can be located on different computers connected by a network.
Event
An occurrence within a process, such as the execution of a subprogram or the sending/receiving of a message. Events are the fundamental units of action in a distributed system.
Happened-Before Relation (→)
A partial ordering of events in a distributed system. It is defined by:
- If event ( a ) occurs before event ( b ) in the same process, then ( a → b ).
- If event ( a ) is the sending of a message and event ( b ) is the receipt of that message, then ( a → b ).
- If ( a → b ) and ( b → c ), then ( a → c ).
Logical Clock
A mechanism for assigning a numerical value to an event, representing the time at which the event occurred. Logical clocks help in maintaining the order of events in a distributed system.
Clock Condition
A condition that ensures the correctness of logical clocks. It states that if event ( a ) happens before event ( b ), then the logical clock value of ( a ) is less than that of ( b ).
Total Ordering
An extension of the partial ordering provided by the happened-before relation to a complete ordering of all events in the system. This is achieved by combining logical clock values with unique process identifiers.
Synchronization
The process of coordinating the actions of processes in a distributed system to ensure correct sequencing and timing of events. Synchronization is crucial for tasks like mutual exclusion and resource sharing.
Mutual Exclusion
A synchronization problem where multiple processes must not access a shared resource simultaneously. Lamport's algorithm uses logical clocks to ensure that requests for the resource are granted in the order they were made.
Physical Clock
A real-world clock that measures physical time. Physical clocks are used to avoid anomalous behavior in distributed systems by ensuring that the clocks of different processes remain synchronized.
Anomalous Behavior
Unexpected or incorrect behavior in a distributed system due to discrepancies in the perceived order of events. This can occur if the logical clocks do not accurately reflect the actual sequence of events.
Strong Clock Condition
A stricter version of the clock condition that ensures the logical clock values respect the actual physical ordering of events. This condition helps in preventing anomalous behavior.
Message Timestamp
A value assigned to a message indicating the logical clock value of the sending process at the time the message was sent. Timestamps are used to maintain the order of events across different processes.
Partial Ordering
An ordering of events where some events are ordered relative to each other, but not all events are comparable. The happened-before relation defines a partial ordering of events in a distributed system.
Total Delay
The time taken for a message to travel from the sending process to the receiving process. It includes both predictable and unpredictable delays.
Unpredictable Delay
The portion of the total delay that cannot be precisely determined in advance. It is the difference between the total delay and the minimum possible delay for a message.
State Machine
A model used to specify the synchronization of processes in a distributed system. It consists of a set of possible commands, states, and a function that defines the state transitions based on the commands.
Directed Graph
A representation of the communication structure in a distributed system, where nodes represent processes and directed edges represent communication paths between processes.
Diameter of a Graph
The longest shortest path between any two nodes in a directed graph. It is used to determine the maximum time required for synchronization messages to propagate through the system.
@incollection{lamport2019time,
title={Time, clocks, and the ordering of events in a distributed system},
author={Lamport, Leslie},
booktitle={Concurrency: the Works of Leslie Lamport},
pages={179--196},
year={2019}
}