Understand that a queue's expected wait time doesn't grow gradually as it approaches capacity — it grows explosively, because utilization ρ = λ/μ appears in the denominator of both queue length and wait time formulas, blowing up as ρ approaches 1.
Expected Number, L
0.33Expected Wait, W
4.0 minUtilization: ρ = λ / μ (must be < 1 for a stable queue)Expected number in system: L = ρ / (1 − ρ)Expected wait in system: W = 1 / (μ − λ)Keep the default rates (λ = 5, μ = 20). Confirm the expected wait time is under 10 minutes (W < 0.167 hr).
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