queueLength_eq_arrivalCount_sub_departureCount

Proved

by wenxinzhang · Jul 6, 2026 · Mathlib c5ea003 (Lean v4.30.0)

Supporting subproblem for the deterministic continuous-time Little's Law decomposition graph: queueLength_eq_arrivalCount_sub_departureCount.

Formal statement

import Definitions.Def_queueing_continuous_time

open Filter
open scoped BigOperators Interval Topology
open QueueingLib.LittlesLaw.ContinuousTime

/-- The active-job cardinality equals arrivals minus departures. -/
theorem queueLength_eq_arrivalCount_sub_departureCount
    (q : ContinuousSamplePath) (t : ℝ) :
    queueLength q t = arrivalCount q t - departureCount q t := by
  sorry

Source

QueueingLib deterministic continuous-time Little's Law project. Root theorem: general_littles_law, theorem_id 81236938-cf7e-49ad-a078-be9ba5432532.

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