hse-2026/materials/08-scaling/seminar/load-balancing-lab/src/metrics.rs

use std::cmp::Ordering;
use std::collections::BTreeSet;

pub const WINDOW: f64 = 60.0;

#[derive(Copy, Clone, PartialEq)]
struct RequestTime {
    time: f64,
    id: usize,
}

impl Eq for RequestTime {}

impl Ord for RequestTime {
    fn cmp(&self, other: &Self) -> Ordering {
        self.time
            .total_cmp(&other.time)
            .then(self.id.cmp(&other.id))
    }
}

impl PartialOrd for RequestTime {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

/// Nearest-rank p99 of response times for requests arriving in [t, t + WINDOW).
/// Emit one point per distinct arrival time t <= time_limit.
pub fn windowed_p99(mut requests: Vec<(f64, f64)>, time_limit: f64) -> Vec<(f64, f64)> {
    requests.sort_by(|a, b| a.0.total_cmp(&b.0));
    let mut result = Vec::new();
    let mut items = BTreeSet::new();
    let mut end = 0;
    let mut start = 0;
    while start < requests.len() && requests[start].0 <= time_limit {
        let time = requests[start].0;
        while end < requests.len() && requests[end].0 < time + WINDOW {
            items.insert(RequestTime {
                time: requests[end].1,
                id: end,
            });
            end += 1;
        }
        // ceil(0.99 * n), computed exactly, without floating-point rounding.
        let rank = items.len() - items.len() / 100;
        let p99 = items.iter().rev().nth(items.len() - rank).unwrap().time;
        result.push((time, p99));
        // Equal response times remain distinct observations thanks to id.
        // Remove the entire arrival-time group before advancing the window.
        while start < requests.len() && requests[start].0 == time {
            items.remove(&RequestTime {
                time: requests[start].1,
                id: start,
            });
            start += 1;
        }
    }
    result
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn expires_old_requests_and_excludes_right_boundary() {
        let requests = vec![
            (0.0, 100.0),
            (1.0, 10.0),
            (61.0, 1.0),
            (62.0, 1.0),
            (123.0, 3.0),
        ];
        assert_eq!(
            windowed_p99(requests, 123.0),
            vec![
                (0.0, 100.0),
                (1.0, 10.0),
                (61.0, 1.0),
                (62.0, 1.0),
                (123.0, 3.0)
            ]
        );
    }

    #[test]
    fn uses_nearest_rank_and_counts_equal_response_times() {
        let mut requests = vec![(0.0, 1.0); 99];
        requests.push((0.0, 100.0));
        assert_eq!(windowed_p99(requests, 0.0), vec![(0.0, 1.0)]);
        let requests = (1..=100).map(|n| (0.0, n as f64)).collect();
        assert_eq!(windowed_p99(requests, 0.0), vec![(0.0, 99.0)]);
    }

    #[test]
    fn sorts_arrivals_and_limits_reported_times() {
        assert_eq!(
            windowed_p99(vec![(120.0, 8.0), (60.0, 2.0), (0.0, 4.0)], 60.0),
            vec![(0.0, 4.0), (60.0, 2.0)]
        );
        assert!(windowed_p99(Vec::new(), 60.0).is_empty());
    }

    #[test]
    fn matches_independent_sort_per_window_reference() {
        let requests: Vec<_> = (0..400)
            .map(|i| (((i * 37) % 241) as f64, ((i * 17) % 31 + 1) as f64))
            .collect();
        let mut times: Vec<_> = requests
            .iter()
            .map(|r| r.0)
            .filter(|t| *t <= 180.0)
            .collect();
        times.sort_by(f64::total_cmp);
        times.dedup();
        let expected: Vec<_> = times
            .into_iter()
            .map(|t| {
                let mut values: Vec<_> = requests
                    .iter()
                    .filter(|r| r.0 >= t && r.0 < t + WINDOW)
                    .map(|r| r.1)
                    .collect();
                values.sort_by(f64::total_cmp);
                let rank = (0.99 * values.len() as f64).ceil() as usize;
                (t, values[rank - 1])
            })
            .collect();
        assert_eq!(windowed_p99(requests, 180.0), expected);
    }
}