departedSojournRate_le_timeAverageQueueLength_eventually

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

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

Formal statement

import Definitions.Def_queueing_continuous_time

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

/-- The normalized departed-sojourn total eventually bounds the time average below. -/
theorem departedSojournRate_le_timeAverageQueueLength_eventually
    (q : ContinuousSamplePath) :
    ∀ᶠ t in atTop,
      departedSojournRate q t ≤ timeAverageQueueLength q t := by
  -- Depends on `departedSojourn_le_queueArea`.
  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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