Use Little’s law and a capacity screen to relate arrival rate, service time, parallel servers, WIP, and utilization.
Parameters
Arrival rate lambda
1/h
Input Arrival rate lambda.
Service time
min
Input Service time.
Servers c
count
Input Servers c.
Target lead time
min
Input Target lead time.
Results
—
Average WIP L
—
Capacity
—
Utilization
—
Queue growth index
Flow, WIP, and lead time
Capacity and load breakdown
Arrival-service margin map
Model and equations
$$L=\lambda W,\quad \rho=\frac{\lambda}{c\mu}$$
This simplified model captures the main relationship only. Boundary conditions, losses, nonlinear effects, and code-specific corrections still need separate checks.
How to read it
Use the main plot to read the controlling trend, including break points that a single result card can hide.
Use the sensitivity view to find input combinations where margin collapses quickly.
For early design, focus on which input controls margin before trusting the absolute value.
Learn Capacity Planning Little Law by dialogue
🙋
When reading Capacity Planning Little Law, where should I look first? Moving Arrival rate lambda changes both the plots and the result cards.
🎓
Start with Average WIP L, but do not treat the number as the whole answer. Use Flow, WIP, and lead time to confirm the assumed state, then read Capacity and load breakdown for the distribution or trend. Use the main plot to read the controlling trend, including break points that a single result card can hide.
🙋
I can see why Arrival rate lambda changes Average WIP L. How should I judge the influence of Service time?
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Move Service time in small steps and watch Capacity. That reveals which term is controlling the result. This simplified model captures the main relationship only. Boundary conditions, losses, nonlinear effects, and code-specific corrections still need separate checks. A single operating point is not enough; sweep the realistic scatter range.
🙋
What is Arrival-service margin map for? It feels like the ordinary curve already tells the story.
🎓
Arrival-service margin map is for finding boundaries where the condition becomes risky or margin collapses quickly. Use the sensitivity view to find input combinations where margin collapses quickly. In First-pass comparison of design options before review, the important question is often what happens after a small change, not only the nominal value.
🙋
So if Average WIP L is within the target, can I accept the condition?
🎓
Treat this as a first-pass review. It helps with Narrowing controlling factors and worst-side conditions before detailed analysis and Teaching or explaining the equation, numbers, and visualization under the same inputs, but final decisions still need standards, measured data, detailed analysis, and vendor limits. For early design, focus on which input controls margin before trusting the absolute value.
Practical use
First-pass comparison of design options before review.
Narrowing controlling factors and worst-side conditions before detailed analysis.
Teaching or explaining the equation, numbers, and visualization under the same inputs.
FAQ
Start with Average WIP L and Capacity. Then use Flow, WIP, and lead time to confirm the assumed state and Capacity and load breakdown to read distribution or bias. Use the main plot to read the controlling trend, including break points that a single result card can hide
Move Arrival rate lambda alone, then move Service time by a comparable amount and compare the change in Average WIP L. Arrival-service margin map shows combinations where margin or performance changes quickly.
Use it for First-pass comparison of design options before review. Instead of trusting a single point, widen the input range and check whether Average WIP L keeps enough margin before moving to detailed analysis.
This simplified model captures the main relationship only. Boundary conditions, losses, nonlinear effects, and code-specific corrections still need separate checks. Final decisions still require standards, measured data, detailed analysis, and vendor limits.