Clock Fundamentals

Real-time clock (RTC)

Battery-powered CMOS chip with quartz oscillator that keeps time when computer is powered off, providing approximate time on boot.

System clock

Software clock maintained by the operating system using interval timers, more accurate than RTC during system operation.

Epoch

The fixed reference point from which elapsed time is measured; Unix uses January 1, 1970, 00:00:00 UTC, while Windows uses January 1, 1601, 00:00:00 UTC.

Unix epoch

The reference point for Unix timestamps, defined as January 1, 1970, 00:00:00 UTC.

Coordinated Universal Time (UTC)

The primary time standard based on International Atomic Time with occasional leap seconds added to account for Earth’s irregular rotation.

Leap second

An occasional one-second adjustment to UTC to keep it aligned with Earth’s rotation, announced months in advance.

Wall clock

The system clock representing current date and time that clock synchronization protocols adjust; can jump forward or backward due to NTP corrections, manual adjustments, or DST transitions.

Monotonic clock

A clock that always moves forward, unaffected by wall clock adjustments, used for measuring durations and timeouts.

Elapsed seconds representation

Representing time as the number of seconds (and fractions) since a fixed epoch, avoiding timezone, DST, and leap second complications.

Clock Properties and Measurements

Clock model

Mathematical representation \(C(t) = \alpha t + \beta\) where \(C(t)\) is clock reading at true time \(t\), \(\alpha\) is clock rate (rate error from drift), and \(\beta\) is offset from true time.

Clock rate (\(\alpha\))

The multiplicative factor in the clock model representing how fast or slow a clock runs; ideally 1.0, but drift causes deviation (rate error).

Clock offset (\(\beta\))

The additive factor in the clock model representing how far ahead or behind a clock is from true time (the instantaneous time difference).

Accuracy

How close a clock measurement is to the true value; if a clock shows 12:00:00.005 and true UTC is 12:00:00.000, the clock has 5ms of error.

Precision

The consistency of repeated measurements; a clock consistently 5ms fast is precise but not accurate.

Resolution

The shortest time increment a clock can represent; a nanosecond-resolution clock can distinguish events 1 nanosecond apart, independent of accuracy.

Clock drift

The rate at which a clock’s frequency deviates from its nominal frequency, typically measured in parts per million (ppm).

Clock offset

The instantaneous difference in time between two clocks or between a clock and true time.

Parts per million (ppm)

A measure of clock drift representing the fractional frequency error; 100 ppm means 100 microseconds error per second.

Quartz oscillator

A piezoelectric crystal that vibrates at a precise frequency when voltage is applied, used as the timekeeping element in computer clocks.

Temperature-Compensated Crystal Oscillator (TCXO)

A quartz oscillator with circuitry to compensate for temperature-induced frequency variations, achieving 1-5 ppm drift.

Oven-Controlled Crystal Oscillator (OCXO)

A quartz oscillator maintained at constant temperature in a miniature oven, achieving drift below 0.01 ppm.

Clock Adjustment Mechanisms

Slewing

Gradually adjusting a clock by changing its rate, making each tick slightly longer or shorter to correct offset while maintaining monotonic behavior.

Stepping

Instantly jumping a clock to the correct time, used for large offsets but can break applications measuring durations.

Periodic resynchronization

Regular synchronization measurements needed because drift rate changes with temperature and aging.

Synchronization Algorithms

Cristian’s algorithm

A client-server clock synchronization algorithm that estimates network delay using round-trip time and adjusts the client clock based on the server’s timestamp plus estimated one-way delay.

Round-trip time (RTT)

The total time for a message to travel from sender to receiver and back, used in synchronization algorithms to estimate network delay.

Network Time Protocol (NTP)

A hierarchical protocol for synchronizing clocks over networks using stratified time servers and sophisticated filtering algorithms.

Stratum

In NTP, the hierarchical level of a time server representing its distance from authoritative time sources (stratum 0 is direct reference, stratum 1 synchronizes from stratum 0, etc.).

Clock discipline

The algorithm used to gradually adjust a system clock toward a reference time by modifying tick frequency rather than making discontinuous jumps.

Simple Network Time Protocol (SNTP)

A simplified subset of NTP suitable for client devices that synchronize time but do not serve time to other systems.

Precision Time Protocol (PTP)

IEEE 1588 standard for sub-microsecond clock synchronization in LANs using hardware timestamping in network interface cards.

Hardware timestamping

Capturing packet transmission and receipt timestamps at the network physical layer in specialized hardware, bypassing software stack delays to achieve nanosecond-level timing accuracy.

Grandmaster clock

The authoritative time source in a PTP domain from which all other clocks synchronize.

Best Master Clock Algorithm (BMCA)

The PTP algorithm that selects the most suitable grandmaster based on priority, clock quality, accuracy, and stability.

Network and Error Concepts

Symmetric delay assumption

The assumption that network transmission time is equal in both directions, which simplifies synchronization but may not hold in real networks.

Error bounds

Mathematical limits on synchronization error computed from minimum network transmission time and measured RTT.

Additive errors

The accumulation of synchronization errors in chains where machine A synchronizes from B which synchronized from C, requiring hierarchy depth limits.

Fault-tolerant averaging

Technique of querying multiple time sources, discarding outliers, and averaging the remaining values to reduce impact of faulty clocks.

Jitter

Variation in network latency that makes message transmission times unpredictable, affecting the accuracy of clock synchronization.

Asymmetric delay

Network condition where transmission times differ significantly in forward and reverse directions, introducing error in clock synchronization algorithms.

Clock synchronization uncertainty

The maximum possible error in synchronized time, determined by network jitter, asymmetric delays, and algorithm limitations.

Outlier rejection

Statistical filtering technique used in NTP and fault-tolerant averaging to discard time samples from faulty or unreliable sources before computing adjustments.

Logical Clocks

Happened-before relationship

Lamport’s partial ordering (\(\rightarrow\)) on events where \(a \rightarrow b\) if they occur on the same process in sequence, if a sends a message received at b, or transitively through these relationships.

Concurrent events

Events where neither happened-before nor happened-after relationship exists, meaning neither could have causally influenced the other through system communication.

Causality

The potential for one event to influence another through the system’s communication channels, captured by the happened-before relationship.

Lamport timestamp

A logical clock that assigns integer timestamps to events such that if event a happened-before event b, then timestamp(a) < timestamp(b).

Logical clock

A mechanism for ordering events in a distributed system based on causality rather than physical time, using counters that increment with events and message exchanges.

Total ordering

An ordering that provides a definite sequence for all events, achieved by combining Lamport timestamps with process IDs to break ties.

Vector clock

A logical clock where each process maintains a vector of counters (one per process) that fully captures causal relationships and enables detection of concurrent events.

Causal ordering

An ordering of events that respects the happened-before relationship, ensuring causally related events are ordered correctly.

Version vector

A variant of vector clocks that tracks versions of data objects rather than process events, used in systems like Dynamo and Riak.

Matrix clock

A logical clock using a two-dimensional array where each process tracks its knowledge of all other processes’ logical times, enabling garbage collection through knowledge of global progress.

Hybrid Logical Clock (HLC)

A timestamp combining physical time and logical components that preserves causal ordering while maintaining closeness to wall-clock time for time-based queries.

Partial ordering

An ordering relation (like happened-before) that does not necessarily order all pairs of elements, only those with a causal relationship.