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Wait time estimator

Get a rough sense of counter utilization and customer wait from arrivals per hour, average service minutes, and how many counters are open. This is an educational estimate—not a guarantee of real-world wait times.

Interactive estimator loads with JavaScript. Results are planning estimates, not guarantees.

How the estimate works

Service rate per counter μ = 60 ÷ average service minutes (customers that one counter can finish per hour).

Utilization ρ = arrivals per hour ÷ (counters × μ). If ρ ≥ 100%, demand meets or exceeds capacity and the simple model says the queue never clears.

When ρ < 100%, a common rule of thumb is: wait ≈ service minutes × (ρ ÷ (1 − ρ)). That grows sharply as you approach full utilization—same intuition as M/M/c-style models, simplified for planning.

Formulas

  • μ = 60 / serviceMinutes
  • ρ = λ / (counters × μ)
  • if ρ ≥ 1 → overloaded (add capacity)
  • else waitMinutes ≈ serviceMinutes × (ρ / (1 − ρ))

What drives wait time

  • Arrival rate (λ)

    More arrivals per hour push utilization up. Peaks matter more than daily averages—model the busy hour you care about.

  • Service time

    Longer average service minutes cut capacity at every counter. Intake forms, lookups, and handoffs all show up here.

  • Open counters

    Adding a counter increases capacity linearly in this model. When ρ is already high (e.g. above ~80%), one more counter often cuts waits more than a small process tweak.

When to add a counter

  • Utilization stays above ~80–85% in your busy hour for more than a short spike.
  • Estimated wait climbs into a range customers (or your SLA) will notice.
  • Staff are constantly busy with no recovery gaps between tickets.

Honest caveats

  • Real queues have variability, batches, no-shows, priority rules, and lunch breaks—this model ignores most of that.
  • The wait formula is a planning rule of thumb, not a full M/M/c solver. Treat results as directional.
  • If arrivals are bursty, use your peak-hour λ, not a smoothed daily average.
  • Display wait is capped at 180 minutes so extreme ρ values near 1 do not produce misleading huge numbers—still treat “near capacity” as a red flag.

See Esperaly in a real queue

Browser-based counters, QR join, and TV displays help you run the line you just modeled. Try free, or read how clinics and desks keep waits visible.