Stationary and Transient

Jupiter provides two stochastic simulation regimes. The choice is not a visual preference: each regime answers fundamentally different questions.

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Core Difference

Definition

• Stationary Analysis: Answers "how does the system behave once it reaches long-term equilibrium?"
• Transient Analysis: Answers "what happens instant by instant over time from cold start to stabilization?"

Attribute	Stationary Simulation	Transient Simulation
Primary Goal	Steady-state equilibrium averages	Trajectory and time evolution
Output Format	Scalar summary per metric ($\mu \pm \text{error}$)	Time series curve $f(t)$ per metric
Typical Questions	"What is the average throughput?", "Where is the bottleneck?"	"How long to recover from a spike?", "When does queue exceed limit?"
Computational Cost	Lower (single long integrated run)	Higher (parallel independent replications)

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Direct Comparison on the Same Model

Consider an M/M/1 queue with 1 attendant starting completely empty at $t = 0$:

Stationary Regime

Summarizes the entire steady-state operation into single scalars:

• total_in_system: 1.00
• server_busy_pct: 50.0%

Transient Regime

Traces the path taken to reach that steady state:

Simulation Time ($t$)	Total in system	Server busy %
10 min	0.48	35.6%
20 min	0.76	43.2%
30 min	0.74	44.4%
40 min	0.89	49.2%
60 min	0.88	45.2%
100 min	0.89	45.2%

The system requires approximately 40 minutes to climb out of its cold start and approach steady-state equilibrium.

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When to Choose Each Mode

Choose Stationary Analysis when:

• Sizing steady production capacity (number of workers, buffer limits, server instances).
• Verifying contractual SLA targets.
• Running rapid parameter sensitivity sweeps across dozens of configurations.

Choose Transient Analysis when:

• The time dimension is central to the investigation.
• Studying system warm-up times and cold-start dynamics.
• Evaluating resilience and recovery times following sudden burst traffic.
• The modeled process is inherently time-bounded (e.g., a 4-hour work shift).

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Mode-Specific Caveats

Stationary: Cold-Start Distortion

Because models begin empty, the initial filling phase skews overall averages downward.

• Solution: Configure a warm-up period or extend the total simulation horizon to dilute early startup states.

Transient: Fluctuation in Ratio Metrics

In transient mode, each curve point is the cross-sectional mean across independent replications at a specific instant.

• If a metric divides by a fast transit place (where tokens linger for microseconds), that place is empty in most replications at any sampled instant.
• Symptom: The metric reports 0 or exhibits severe erratic spikes.
• Solution: Use the robust formulation explained in Response Time, multiplying by the arrival delay rather than dividing by instantaneous throughput.

Next steps

Learn how to launch and supervise simulations in Running the Model.