Finite Source Repair Queue Calculator
Calculate stationary down-machine counts for a finite population with exponential failure and repair times.
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Result
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Calculation steps
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How to calculate
Normalize birth–death weights using logarithms so finite-population state probabilities remain representable.
Birth rate in state n=(N−n)λ; death rate=min(n,c)μ; stationary weights follow adjacent rate ratios
Worked example
With one machine, failure rateλ and repair rateμ, down probability isλ/(λ+μ).
Assumptions and input details
Finite identical independent exponential machines/repairs, one failure mode and unlimited waiting space up to population size. Servers cannot exceed population. No repair logistics, scheduled maintenance or production-loss forecast.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
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The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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