When the UTC time is $t$, the value of the clock on machine $p$ is $C_p(t)$. If $C_p(t) = t$ for all $t$, the clock is perfectly synchronized.

• $\frac{dC}{dt} > 1$ means fast clock
• $\frac{dC}{dt} < 1$ means slow clock

How to synchronize time between two entities? Assuming the following scenario:

• A sends a request to B at T1
• B receives at T2
• B returns a response at T3
• A receives at T4

The offset of A relative to B is $\theta = T_3 + \frac{(T_2-T_1) + (T_4-T_3)}{2} - T_4=\frac{(T_2-T_1) + (T_3-T_4)}{2}$.

The delay is $\delta=\frac{(T_4-T_1)-(T_3 - T_2)}{2}$.

Here is a real example:

• T1: 231
• T2: 135
• T3: 137
• T4: 298
• Offset is -128.5
• Delay is 32.5

That means when A sends the request at T1 (A local time), B local time is 231 - 128.5 = 102.5.