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Queue Servers Required Calculator

Work out queue servers required instantly with clear inputs, formula shown and shareable results.

About Queue Servers Required Calculator

Offered load in erlangs is arrival rate multiplied by service time, and the number of servers must exceed it for the queue to be stable. Servers are then added until the estimated wait meets the target, because waiting time explodes non-linearly as utilisation approaches 100%.

Formulas

Offered load

Load (erlangs) = Arrivals per hour x Service minutes / 60

Starting point

Servers = ceiling(Offered load / Target utilisation)

Wait approximation

Wait = Service time x Utilisation / (Servers x (1 - Utilisation)), with servers increased until the wait target is met

Worked example

With the default values below, Queue Servers Required Calculator returns Servers required of 7. Change any input above and every figure here is recalculated in your browser.

Inputs used

Customer arrivals per hour
90
Average service time
3.5
Target server utilisation
80
Target maximum wait
4

Results

Servers required
7
Offered load (erlangs)
5.250
Resulting utilisation
75.00%
Estimated average wait
1.50

Step by step

  1. 1Values used
  2. 2Offered load
  3. 3Starting point
  4. 4Wait approximation
  5. 5Servers required= 7
  6. 6Offered load (erlangs)= 5.250
  7. 7Resulting utilisation= 75.00
  8. 8Estimated average wait= 1.50

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does waiting time explode near full utilisation?

Because arrivals are random. With no slack, a short cluster of arrivals creates a queue that never fully clears before the next cluster.

Is one fast server better than two slow ones?

Usually the two servers, because they absorb variability better even at the same total capacity. Pooling queues has the same effect.

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