Description
Multiply servers by positive serviceRatePerServer for capacity.
Queue identities compare flow, inventory, and service capacity under a defined system boundary. Compatible long-run averages and a mean-load inequality are narrower than a complete waiting-time model.
Multiply servers by positive serviceRatePerServer for capacity.
When to use this tool
Use Queue Utilization Service Rate Gap when you need one queue-load or flow-identity diagnostic.
How to use the tool and how it works
- Enter arrivalRate, serviceRatePerServer, servers. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read capacity, utilization, capacityGap, stableMeanRateCondition. Inspect stableMeanRateCondition before interpreting the associated values.
Multiply servers by positive serviceRatePerServer for capacity. Divide arrivalRate by capacity and require strict arrivalRate < capacity for stableMeanRateCondition.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| arrivalRate | Arrival Rate | Required. Finite number; minimum 0. |
| serviceRatePerServer | Service Rate Per Server | Required. Finite number; strictly above 0. |
| servers | Servers | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| capacity | Capacity | Required. Finite number. |
| utilization | Utilization | Required. Finite number. |
| capacityGap | Capacity Gap | Required. Finite number. |
| stableMeanRateCondition | Strict arrival-rate-below-capacity condition only; not a complete stability proof. | Required. Boolean. |
{
"input": {
"arrivalRate": 8,
"serviceRatePerServer": 5,
"servers": 2
},
"output": {
"capacity": 10,
"utilization": 0.8,
"capacityGap": 2,
"stableMeanRateCondition": true
}
}Limitations and assumptions
- This is only a mean-rate load condition; distributional assumptions, blocking, scheduling, and transient behavior are needed for a queue-stability or waiting-time analysis.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Validate arrival and service assumptions, stability, and system boundaries using an appropriate queueing analysis.
References
Similar or alternative tools
- Littlelaw Wip Throughput Time Identity
Divide nonnegative wip by positive throughputPerHour for impliedFlowHours.
- Takt Cycle Slack Per Unit
Divide nonnegative availableMinutes by positive demand for taktMinutes.