4. Definitions
A number of technical terms are defined in this section. A timescale is a frame of reference where time is expressed as the value of a monotonically increasing binary counter with an indefinite number of bits. It counts in seconds and fractions of a second, when a decimal point is employed. The Coordinated Universal Time (UTC) timescale is defined by ITU-R TF.460 [ITU-R_TF.460]. Under the auspices of the Metre Convention of 1865, in 1975 the CGPM [CGPM] strongly endorsed the use of UTC as the basis for civil time.
The Coordinated Universal Time (UTC) timescale represents mean solar time as disseminated by national standards laboratories. The system time is represented by the system clock maintained by the hardware and operating system. The goal of the NTP algorithms is to minimize both the time difference and frequency difference between UTC and the system clock. When these differences have been reduced below nominal tolerances, the system clock is said to be synchronized to UTC.
The date of an event is the UTC time at which the event takes place. Dates are ephemeral values designated with uppercase T. Running time is another timescale that is coincident to the synchronization function of the NTP program.
A timestamp T(t) represents either the UTC date or time offset from UTC at running time t. Which meaning is intended should be clear from the context. Let T(t) be the time offset, R(t) the frequency offset, and D(t) the aging rate (first derivative of R(t) with respect to t). Then, if T(t_0) is the UTC time offset determined at t = t_0, the UTC time offset at time t is
T(t) = T(t_0) + R(t_0)(t-t_0) + 1/2 * D(t_0)(t-t_0)^2 + e
where e is a stochastic error term discussed later in this document. While the D(t) term is important when characterizing precision oscillators, it is ordinarily neglected for computer oscillators. In this document, all time values are in seconds (s) and all frequency values are in seconds-per-second (s/s). It is sometimes convenient to express frequency offsets in parts-per-million (ppm), where 1 ppm is equal to 10^(-6) s/s.
It is important in computer timekeeping applications to assess the performance of the timekeeping function. The NTP performance model includes four statistics that are updated each time a client makes a measurement with a server. The offset (theta) represents the maximum-likelihood time offset of the server clock relative to the system clock. The delay (delta) represents the round-trip delay between the client and server. The dispersion (epsilon) represents the maximum error inherent in the measurement. It increases at a rate equal to the maximum disciplined system clock frequency tolerance (PHI), typically 15 ppm. The jitter (psi) is defined as the root-mean-square (RMS) average of the most recent offset differences, and it represents the nominal error in estimating the offset.
While the theta, delta, epsilon, and psi statistics represent measurements of the system clock relative to each server clock separately, the NTP protocol includes mechanisms to combine the statistics of several servers to more accurately discipline and calibrate the system clock. The system offset (THETA) represents the maximum-likelihood offset estimate for the server population. The system jitter (PSI) represents the nominal error in estimating the system offset. The delta and epsilon statistics are accumulated at each stratum level from the reference clock to produce the root delay (DELTA) and root dispersion (EPSILON) statistics. The synchronization distance (LAMBDA) equal to EPSILON + DELTA / 2 represents the maximum error due to all causes. The detailed formulations of these statistics are given in Section 11.2. They are available to the dependent applications in order to assess the performance of the synchronization function.