littleLawProduct_nonneg

Proved

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

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

Formal statement

import Definitions.Def_queueing_continuous_time

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

/--
The product `lam * Theta` is nonnegative because arrival counts and sojourn
times are nonnegative.
-/
theorem littleLawProduct_nonneg
    (q : ContinuousSamplePath) (lam Theta : ℝ)
    (hArrivalRate : Tendsto (empiricalArrivalRate q) atTop (𝓝 lam))
    (hSojournMean : Tendsto (averageSojourn q) atTop (𝓝 Theta)) :
    0 ≤ lam * Theta := by
  -- Depends on nonnegativity of empirical arrival rates and sojourn averages.
  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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