SIDRA INTERSECTION 11
SIDRA INTERSECTION 11
NETWORK CONVERGENCE
Convergenceyou can trust
Stable results foroversaturated networks
The end of unsettlednetwork results
Deterministic precisionat the lane level
Where analytical rigourmeets network complexity

Enhanced Network Convergence Method — new in SIDRA INTERSECTION 11

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Network Convergence

Why convergence
mattersstability, reliability, auditability

When network model iterations fail to settle, results become unreliable — and unreliable results cannot be used for professional audits, infrastructure planning, or government submissions.

In any network model, the iterative process must resolve complex interdependencies between sites — lane-by-lane capacity with shared and opposed turns, signal timing, queue interactions, and downstream queue blockage effects on upstream lanes. Under congested and oversaturated conditions, these iterations can become unstable, producing results that oscillate from iteration to iteration without settling.

Queue-capacity feedback loops
A downstream queue blocks an upstream lane, reducing its capacity. The reduced capacity changes the queue pattern, which resets the blockage — creating oscillations that traditional single-loop methods struggle to resolve.
The lane blockage challenge
Lane blockage is a structural constraint — the physical reality of a queue from one intersection preventing flow at another. It behaves differently from performance variables like capacity and signal timing, and needs a more deliberate resolution process.
The cost of non-convergence
When the stopping condition is not satisfied, the maximum number of iterations is reached and results are unsettled. Large values of the Network Model Variability Index indicate high variability during iterations, and that final results may not be reliable.
Two-Loop Method

A new architecture
for difficult networksInner Loop, Outer Loop, stable equilibrium

Traditional single-loop models attempt to resolve all network variables simultaneously — SIDRA INTERSECTION 11 separates the problem, solving performance variables and structural constraints in dedicated loops for superior numerical stability.

The Enhanced Network Convergence Method in SIDRA INTERSECTION 11 introduces a Two-Loop Convergence architecture alongside the existing One-Loop method. By decoupling lane blockage constraints from capacity and timing calculations, the Two-Loop method achieves convergence in cases where single-loop approaches produce unsettled results — particularly in networks with high levels of lane blockage causing oversaturation.

Inner Loop — performance processor
Holds Lane Blockage Adjustment Factors constant (as passed from the Outer Loop) and iterates to resolve all other network variables: lane-by-lane capacity with shared and opposed turns, signal timing, and queue dynamics. By holding blockage factors fixed, the Inner Loop settles into a local equilibrium without the noise of fluctuating blockage values. Default: 10 iterations (range 5–60).
Outer Loop — structural validator
Receives updated lane blockage data, degree of saturation, and queue storage ratio values from the converged Inner Loop. Recalculates weighted Lane Blockage Adjustment Factors and checks overall convergence. If factors have changed significantly, a new Inner Loop cycle is initiated. Default: 30 iterations (range 5–100).
Stopping condition
Iterations stop when lane degree of saturation and queue storage ratio values do not change by more than the Adjusted Percentage Stopping Condition across three consecutive iterations, or when the maximum iteration count is reached. The default stopping condition is 1% (range 0.1%–10%), with programme-calculated adjusted values that are more tolerant at lower degrees of saturation.
Final Run step removed
The Final Run step used in earlier versions after network model iterations has been removed, streamlining the convergence process.
Convergence Diagnostics

Know when to trust
your resultsvariability index, iteration reporting, convergence metrics

Most tools provide a binary “converged” or “not converged” status — SIDRA INTERSECTION 11 provides granular metrics so you can diagnose exactly what is happening during network model iterations.

Reliable network analysis requires more than just a final answer — it requires confidence that the answer has stabilised. SIDRA INTERSECTION 11 reports detailed convergence diagnostics in the Network Summary, Route Summary, and Diagnostics reports, giving engineers the transparency they need to assess result quality and identify sources of instability.

Network Model Variability Index
The average value of the largest changes in lane degrees of saturation or queue storage ratios from the third to the last network iteration. High values indicate that results may be unsettled and should be interpreted with caution — an indicator of uncertainty in the analysis.
Iteration-by-iteration reporting
The largest change in lane degrees of saturation or queue storage ratios is reported for the last three iterations, along with the change in Network Control Delay (average) and Network Speed Efficiency. This allows engineers to see whether results are trending towards stability or oscillating.
Convergence method identification
Output reports clearly identify which convergence method was used (One-Loop or Two-Loop), the number of iterations completed versus the maximum specified, and the stopping condition applied — providing a complete audit trail.
Adjusted Percentage Stopping Condition
The programme calculates adjusted stopping condition values based on the degree of saturation and queue storage ratio, applying more tolerant thresholds at lower saturation levels. This relationship is documented so engineers understand exactly how convergence is assessed.
Analytical Precision

Deterministic results
without stochastic uncertaintyno seed runs, no averaging, no modeller noise

Microsimulation tools require multiple random seed runs to achieve statistical confidence — SIDRA INTERSECTION 11 delivers repeatable, auditable results from a single deterministic analysis.

Stochastic simulation tools model individual vehicle trajectories with random variation, requiring multiple simulation runs (typically 5–10 or more) to produce a statistically valid average. Two engineers modelling the same network with different seed counts or warm-up periods may arrive at different conclusions. SIDRA INTERSECTION 11's micro-analytical approach eliminates this uncertainty — given the same inputs, it produces the same output every time.

No seed run overhead
Deterministic analysis means a single run produces the definitive result. There is no need to run, average, and document multiple simulations — saving significant processing time and simplifying the audit trail.
Lane-level precision
SIDRA's unique lane-based network model resolves capacity, performance, and blockage at the individual lane level — capturing the effects of short turn bays, shared lanes, and merge points that link-based models aggregate away.
Transparent methodology
Every parameter, stopping condition, and convergence metric is documented and reported. Unlike simulation “black boxes”, engineers can trace exactly how results were derived and defend their findings in professional or legal audits.
Traffic Assignment

Route choice meets
lane-level performanceassignment convergence and network convergence in one platform

Most workflows require separate tools for traffic assignment and intersection analysis — SIDRA INTERSECTION 11 integrates both in a single environment where route choices are informed by detailed lane-by-lane performance.

The new SIDRA ASSIGN module brings micro-analytical traffic assignment to the network model, using Origin-Destination (O-D) trip demand data to estimate intersection movement volumes while accounting for network-wide traffic interactions and detailed intersection capacity and performance estimation at the lane level. SIDRA ASSIGN has its own convergence metrics, providing a comprehensive resolution of both route choice and intersection performance.

Five assignment methods
Stochastic User Equilibrium (default), User Equilibrium, Fixed Route Assignment, Incremental Assignment, and All-or-Nothing — each with method-specific convergence parameters including maximum iterations and Duality Gap convergence tolerance.
Duality Gap convergence
A proximity convergence metric measuring how close the current assignment is to a true equilibrium where no user can improve their travel time by unilaterally changing routes. Default tolerance: 1%.
Stability convergence metrics
Consistency Index, absolute total travel time change, maximum change in route flows, and maximum change in site movement flows — these metrics ensure that the traffic assignment solution is stabilising in the last few iterations, confirming that results are not just mathematically accurate but operationally stable.
Practical Guidance

Choosing the right
convergence methodOne-Loop for standard cases, Two-Loop for difficult networks

The Two-Loop method is recommended for cases that are unsettled after the maximum number of iterations is reached — even when the largest value of this parameter is specified using the One-Loop method.

The One-Loop Convergence Method remains the default and is suitable for most network analyses. The Two-Loop method is an additional option specifically designed for difficult cases where high levels of lane blockage under oversaturated conditions prevent the One-Loop method from settling. Engineers can switch between methods in the Network Data input dialog under Network Analysis Settings.

One-Loop method (default)
Resolves all network variable interactions simultaneously in a single iterative loop. Suitable for the majority of network analyses. Maximum iterations: 30 (range 5–100). Percentage Stopping Condition: 1% (range 0.1%–10%).
Two-Loop method (for difficult cases)
Recommended when the One-Loop method produces unsettled results with high Network Model Variability Index values. May take longer to process in some cases. Inner Loop: 10 iterations (range 5–60). Outer Loop: 30 iterations (range 5–100).
Balancing precision and processing time
When using demand and sensitivity analysis or optimum cycle time options for network signal timing calculations, the maximum number of iterations can be decreased and the stopping condition increased to reduce processing time. Default values should be reinstated once the network configuration stage is completed.
Explore further

Convergence is just one part of the network story.

Discover how SIDRA ASSIGN brings micro-analytical traffic assignment to the network model — or explore all the new capabilities in SIDRA INTERSECTION 11.

SIDRA ASSIGN →What's New in Version 11 →Request a Trial →