Examples
Examples
Try the starting example
- Poisson arrival rate per hour
- 30
- Mean exponential service duration (minutes)
- 2
- Identical continuously available agents
- 2
- Wait-time service threshold (minutes)
- 1
- Offered load (Erlangs)
- 1
- Agent occupancy (%)
- 50
- Probability an arrival waits (%)
- 33.333333
- Mean queue wait (minutes)
- 0.666667
- Model share starting service within threshold (%)
- 79.782311
- Mean queued customers
- 0.333333
Try another scenario
- Poisson arrival rate per hour
- 30
- Mean exponential service duration (minutes)
- 2
- Identical continuously available agents
- 3
- Wait-time service threshold (minutes)
- 1
- Offered load (Erlangs)
- 1
- Agent occupancy (%)
- 33.333333
- Probability an arrival waits (%)
- 9.090909
- Mean queue wait (minutes)
- 0.090909
- Model share starting service within threshold (%)
- 96.655641
- Mean queued customers
- 0.045455
Calculation method
Calculation method
Offered load (Erlangs)
Arrival rate×mean service hours.
Agent occupancy (%)
Offered load/agent count×100.
Probability an arrival waits (%)
Stationary M/M/n Erlang C probability, computed through a stable Erlang-B recurrence.
Mean queue wait (minutes)
C×mean service minutes/(agents−offered load).
Model share starting service within threshold (%)
100×[1−C exp(−(agents−load)×threshold/service minutes)].
Mean queued customers
Arrival rate per minute×mean wait minutes, by Little’s law under this stationary model.
Symbols and units
- a
- Poisson arrival rate per hour
- b
- Mean exponential service duration (minutes)
- c
- Identical continuously available agents
- d
- Wait-time service threshold (minutes)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Stationary M/M/n: independent Poisson arrivals, exponential independent service, identical agents, infinite waiting space and no abandonment. Requires offered load below agent count; it is not a real-system service guarantee.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
MIT: multiserver queues and Erlang C ↗
Background reading; this does not imply endorsement or independent review of SumFizz.