POLARIS Convergence Strategy#
What is Convergence?#
Convergence in POLARIS refers to the state where the transportation simulation reaches stability across iterations. Rather than a single definition, convergence encompasses multiple interrelated criteria that indicate the model has reached a reliable steady state suitable for analysis.
Convergence occurs when there is minimal difference between successive iterations, indicating that the system has reached a stable equilibrium where further iterations do not significantly change the results.
Key Components#
Network Stability
Vehicle Miles Traveled (VMT) and Vehicle Hours Traveled (VHT) stabilize between iterations
Network performance metrics show consistent patterns
Travel time distributions become stable across the network
Network Clearing
The transportation network successfully processes all travelers by the end of the simulation day
Minimal artificial congestion removal events occur
This is necessary but not sufficient for true convergence
Convergence Challenges and Considerations#
Overcapacity Scenarios#
When travel demand exceeds network capacity:
Traditional convergence may not be achievable in the mathematical sense
The model may reach a stable state of gridlock that represents the physical limitations of the network
An operational stopping point must be defined where further iterations provide no additional insight
Such scenarios require careful interpretation and are generally not suitable for comparative analysis
Distinguishing Gridlock from Non-Convergence#
Gridlocked but converged: Demand consistently exceeds capacity, but the system reaches a stable (albeit congested) state
Non-converged: Results continue to fluctuate significantly between iterations, indicating the model has not stabilized
Recommended Convergence Strategy#
Step 1 Monitor Key Metrics
Track the following indicators across iterations:
VMT and VHT totals and distributions
Network clearing rates
Artificial congestion removal events
Travel time consistency
In-network curve stability
Step 2 Establish Stability Thresholds
Define acceptable variation levels between iterations:
VMT/VHT changes of less than 1-2% between iterations
Consistent network clearing (>95% of vehicles processed)
Minimal artificial interventions
Step 3 Iteration Management
Minimum iterations: Allow sufficient iterations for system dynamics to stabilize
Maximum iterations: Set practical limits to prevent infinite iteration in problem scenarios
Assessment intervals: Evaluate convergence criteria every 3-5 iterations
Step 4 Scenario-Specific Considerations
Well-designed scenarios: Expect traditional convergence with network clearing
Stress-test scenarios: May require modified convergence criteria focused on stability rather than clearing
Comparative analysis: Only use converged scenarios for meaningful comparisons
When to Stop Iterating#
Ideal case: Network clears consistently AND metrics stabilize
Acceptable case: Metrics stabilize even if some capacity constraints exist
Problem case: Define operational stopping point for over-capacity scenarios, but flag results as unsuitable for comparative analysis
Quality Assurance#
Document convergence criteria used for each analysis
Report both convergence status and any capacity limitations
Provide iteration-by-iteration convergence metrics in technical documentation
Limitations and Caveats#
POLARIS and similar detailed simulation models may not represent highly congested networks in a perfectly stable manner
Convergence does not guarantee that the model accurately represents real-world conditions
Over-capacity scenarios require careful interpretation and may not be suitable for policy analysis
The definition of “acceptable” convergence may vary depending on the specific analysis objectives