METHODS / VERSION 1.0
Compare assumptions before comparing designs.
This is an exploratory, reproducible point-queue model. It compares eight explicit control and geometry variants on the same four-arm network. It is not a calibrated capacity, emissions or safety forecast. A real design comparison needs turning counts, lane geometry, signal plans, pedestrians, heavy vehicles and a validated spatial traffic model.
What each design actually does
| Design | Routing and service | Important scope |
|---|---|---|
| Permissive / shared | Opposing approaches get green together. Lefts accept gaps in opposing through/right traffic. A left at the queue head blocks followers. | One lane per approach. No yellow left-clearance exception in this module. |
| Permissive / pocket | Same two-phase control, separate left-turn queue. | Adds a lane; does not hold the roadway footprint constant. Approximate pocket storage: 20 vehicles, diagnostic only. |
| Protected-only | EW left, EW through/right, NS left, NS through/right. Separate left queues. Lefts depart only on their protected phase. | Four clearance periods; user chooses left share. No permissive arrow interval or actuation. |
| Split-phase | EB, WB, NB, SB approaches receive green separately; all movements in one shared lane per approach. | Symmetric four-approach interpretation of split phasing, not a site signal plan. |
| Full median U-turn (MUT) | Major left: through → U-turn → right. Minor left: right → U-turn → through. Minor through remains direct. | Two crossovers on the EW arterial. Choose yield or signal control. |
| Signalized RCUT | Major left remains direct. Minor left: right → U-turn → through. Minor through: right → U-turn → right. First main phase serves major through/right; second serves major lefts and minor rights. | The two arterial halves use a tied common schedule here. Real RCUT halves can operate independently. Always signalized crossovers in this model. |
| Single-lane roundabout | Yield at entry; counterclockwise circulation. Right/through/left travels 1/2/3 quarter arcs. Circulating traffic has priority. | 25 m centerline radius, 7 m/s ring speed, 4.5 s entry gap, 2 s minimum passage spacing. Reservations at each entry point permit concurrent circulation; no whole-circle lock. |
| All-way stop | Every car stops at least 1 s. Earlier arrivals precede later conflicting arrivals; close ties yield right, with rotating resolution of a four-way tie. | Assumed 3 s occupancy. Compatible opposing non-lefts, opposing lefts and some right pairs can run together. Other perpendicular movements are conservatively treated as conflicting. |
These routing and control families follow FHWA signal phasing descriptions, MUT guidance, RCUT guidance, roundabout principles, and all-way-stop guidance. Numerical gap, occupancy, speed and storage values here are model assumptions, not values fitted from those pages.
How a Michigan-left signal relates to the center light
A crossover can have no signal, or it can have its own signal coordinated with the main junction. In the two-phase arrangement described by FHWA, the arterial through movements run in one phase, while the minor road at the main junction and U-turns at the crossovers run in the other. “Coordinated” does not mean every light changes at the same instant.
FHWA's 2010 Alternative Intersections/Interchanges report, chapter 3, section 3.4, describes an MDOT example in which crossover arterial green starts and ends approximately 7 seconds earlier than the center arterial green. It says the offset depends on crossover distance, arterial speed and the expected queue at the center stop line. It also discusses common cycle lengths/splits and actuated operation. This is a historical reported practice, not a universal current Michigan timing requirement.
The 2007 FHWA synthesis also describes delaying the crossover U-turn phase relative to the minor-road phase to help cross-street left-turn trips reach the crossover. The 2014 Median U-Turn Informational Guide, chapter 8 discusses both signalized and unsignalized crossovers. A specific intersection's actual timing requires its controller plan or field observations.
Model convention: crossover phase(t) = two-phase clock(t − offset) offset = −7 s: crossover arterial green begins 7 s before center green offset = 0 s: matching phase boundaries offset = +7 s: crossover arterial green begins 7 s after center green
The model uses the same cycle and usable-green split at the center and both crossovers. The experiment workbench can search offsets over explicit values. The traffic engine does not actuate phases, model independent RCUT arterial halves, use corridor progression from adjacent junctions, or simulate a separate near/far minor-road clearance. The applied timing display makes these assumptions inspectable.
With signal control, all major-road entrants encounter the upstream crossover through signal before the center. A rerouted driver later encounters the U-turn signal and then the return center signal. Every wait, speed recovery and extra meter is charged. Moving the offset can change all these arrivals; it does not guarantee catching the return green.
Right on red and crossover left on red
Both settings default off. Right-on-red applies at the main signal in each signalized design, including the initial right and returning right of a Michigan-left route. It is available only to a right-turning vehicle at the head of its lane; a through vehicle ahead cannot be passed. Roundabout and all-way-stop control are unaffected.
Left-on-red applies only to eligible signalized median crossovers, not to a direct left at the center light. It is inactive for yield-controlled MUT crossovers. The checkbox assumes the site permits the maneuver and has adequate visibility; it must be off where a sign or other device prohibits it. Michigan State Police's traffic-law FAQ and Michigan's court benchbook on MCL 257.612 describe a left on red from a one- or two-way street onto a one-way roadway after stopping and yielding, unless prohibited. FHWA chapter 3, section 3.11 specifically discusses permitted left-on-red maneuvers at many Michigan crossovers. This model does not interpret red-arrow displays; the setting represents a permitted movement.
Red turns wait at least 1 s, use a future gap (right: 5.5 s; U-turn: 7 s), require 2 s since conflicting service and reserve the merge before releasing following traffic. The crossover red-turn approximation only operates while the opposing arterial signal is green; it conservatively excludes its yellow and intergreen intervals. This restriction is a modeling choice, not a statement of law. Crosswalk, bicycle, visibility and driver-compliance effects are absent. A red-turn benefit in this model is not a finding about safety.
Controlled timing experiment in the two-layout engine
These are simulated results, not field observations: 400 vehicles/hour per approach, 20% intended lefts, 10% rights, 90 s cycle, 50/50 usable green, 660 ft crossovers, 35 mph, signalized crossovers, 20 matched seeds, crashes off. The table shows intended left-turn trips only. Each setting follows every observation entrant to completion; no unfinished trips occurred.
| Right on red | Crossover left on red | Mean wait (s) | Fuel / 1,000 left trips (gal) | Stopped at U + return (%) |
|---|---|---|---|---|
| Off | Off | 59.2 | 56.99 | 66.2 |
| Off | On | 55.5 | 56.29 | 57.2 |
| On | Off | 56.5 | 56.81 | 67.8 |
| On | On | 52.5 | 56.12 | 59.0 |
Above: offset −7 s. Below: both red-turn settings on, varying the offset. This is a small sensitivity grid, not an optimized signal plan. Changes in queues and arrival timing can increase some stop measures even when average wait falls.
| Offset (s) | Mean left-trip wait (s) | Fuel / 1,000 left trips (gal) | Stopped at U + return (%) |
|---|---|---|---|
| -15 | 52.9 | 56.39 | 56.4 |
| -7 | 52.5 | 56.12 | 59.0 |
| 0 | 52.9 | 56.20 | 59.6 |
| 7 | 59.4 | 57.25 | 61.7 |
| 15 | 76.1 | 59.84 | 63.2 |
Download the 20-scenario timing study with seed intervals (JSON). Reproduce with run-timing-study.cjs in the full-suite download.
Expanded workbench · version 2.0
All numerical examples below describe defaults. The replay page and experiment workbench expose the remaining model inputs, including observation windows, vehicle physics and queue-storage assumptions. The workbench separates controllable settings from sensitivity cases, freezes screening choices, and uses disjoint seeds for validation. Research protocol and preliminary findings.
Matched experiment and measurement
Each replication generates one set of vehicle IDs, entry times, approaches and intended destinations. Every selected design reuses it. The arrival process is shifted-exponential with a 2 s minimum entry headway, not pure Poisson. Default demand is 300 vehicles/hour on each approach; default intended turns are 20% left, 10% right. Seeds are separated by 7,919, modulo 2³².
Common endpoints are 600 m from the center on each arm, outside both crossovers. The observation cohort enters after 600 s warmup and during the next 3,600 s. Another 600 s of background arrivals follows; then queues drain for up to 7,200 s. Completed-cohort means exclude unfinished trips and explicitly flag this censoring. Empty cohorts display unavailable values. Exit flow counts all vehicles whose exit time falls within the observation hour. It is distinct from the fraction of the entry cohort already finished.
Full-trip time equals route distance at cruise speed + queue wait + speed-change loss + turn-speed penalties. Each rerouted MUT/RCUT trip adds twice the center-to-crossover distance plus a 30 m U-turn arc. Conventional route length is idealized as 1,200 m for all movements. Roundabout length is 2 × (600 − radius) + the applicable ring arc. Curvature is schematic; signal turn speed penalties do not add extra meters.
Fuel (US gal) = distance(m) / 1609.344 / cruise_mpg
+ wait(s) × idle_gal_per_hour / 3600
+ Σ [0.5 × mass × (cruise_speed² − minimum_speed²)
/ (drivetrain_efficiency × joules_per_gallon)]
Speed-change time loss = (v − v_min)² / (2v) × (1/accel + 1/decel)Defaults: 1,600 kg gasoline vehicle, 25% drivetrain efficiency, 121 MJ/US gallon, 1.5 m/s² acceleration, 2 m/s² deceleration, 35 mph, 30 steady-cruise mpg, 0.25 gal/h idle, 8 m/s center turns and 5 m/s U-turns. A wait of at least 1 s counts as a stop; mandatory stop and red-turn service always stop. Slowing losses are lumped into downstream travel. There is no regenerative braking, automatic stop/start, cold-start penalty, gradient or vehicle mix. Cruise mpg should not be substituted with a combined-cycle rating without calibration.
Means and paired differences are averaged across independent run means. A 95% Student-t interval uses n − 1 degrees of freedom; one run has no interval. These intervals measure Monte Carlo seed variation, not uncertainty in demand, fuel model, crash rates or geometry. Different phases, lane allocations and route lengths are intentional design differences. A common cycle is not evidence that each design is optimized or equally provisioned.
Queues, animations and safety limits
Queues are point queues with assumed service headways. They do not physically block upstream junctions or lanes. Sampled queues exceeding approximate storage are flagged: default 7.5 m per car, 10-car U-turn storage, 20-car left pockets, all now editable. These are diagnostics, not simulated spillback. Drawings compress distances and show queues schematically; they are not physical vehicle trajectories for crash analysis. Roundabout entry-point reservations are not calibrated car-following dynamics.
This module does not infer crash rates from stop counts, conflicts or a winning operational rank. Optional user-entered rates produce expected events = rate × unique observation entrants / 1,000,000, pooled over replications. No crash events are injected here. The original two-layout lab retains its separately documented stochastic closure experiments and historical evidence. Site boundaries and crash definitions must match before comparing rates. Blank crash assumptions mean unavailable, not zero crashes.
Run and reproduce
Unzip and open index.html in a browser. No installation or internet needed.
Tests / reference study (Node.js):
node tests.cjs
node run-study.cjs
Import the independent engine:
const M = require('./engine.js');
const run = M.simulate({seeds:20}, 'mut', 271828, true);
// true retains the first-run trajectories for inspection.The downloadable archive includes the UI, model engine, tests, a reference study and these notes. Exported JSON preserves parameters and run-level summaries; CSV exports one row per design per replication. The first replication alone supplies the synchronized animation.