Time Discretization and 15-Minute Buckets

Live air routing systems track thousands of flights simultaneously, so continuous time is discretized into uniform intervals called buckets. The industry-standard granularity for trajectory analysis is 15 minutes.

Each UTC day contains $24 \cdot 4 = 96$ buckets, indexed $0$ through $95$:

• Bucket $0$: $00{:}00$ – $00{:}15$
• Bucket $1$: $00{:}15$ – $00{:}30$
• $\;\vdots$
• Bucket $95$: $23{:}45$ – $24{:}00$

To convert a UTC timestamp $t$ (expressed in minutes since midnight) into its bucket index $k$, take the floor of $t/15$:

$$k = \left\lfloor \dfrac{t}{15} \right\rfloor.$$

For example, $09{:}37$ corresponds to $t = 9 \cdot 60 + 37 = 577$ minutes, so

$$k = \left\lfloor \dfrac{577}{15} \right\rfloor = \lfloor 38.466\ldots \rfloor = 38.$$

Bucket $38$ spans $38 \cdot 15 = 570$ min ($09{:}30$) through $39 \cdot 15 = 585$ min ($09{:}45$), which indeed contains $09{:}37$.