Same traffic. Two ways to turn.
Follow identical drivers through both intersections. Compare the wait, the whole trip, and the fuel used.
Standard left
Michigan left
Queues include background traffic (faint vehicles). Live wait and fuel count drivers entering during the observation period.
Queues against the clock
Standard — silver · Michigan — gold · vehicles queued, including background traffic
Incidents against the clock
Run 1 only · cumulative starts, including cleared incidents · solid: Standard, dashed: Michigan
Beyond the stoplight
Means across the selected number of paired runs. Observation-period entrants are followed through a drain period; any unfinished trips are flagged.
| All drivers | Standard | Michigan | Difference ± 95% interval |
|---|
Left-turn drivers: extra driving, waits & restarts
| Left-turn drivers only | Standard | Michigan |
|---|
| Fuel / 1,000 left-turn trips (US gal) | Standard | Michigan |
|---|
Restart fuel is charged only when that vehicle stops. A rolling turn has a separate speed-recovery cost. All rows above are additive; idling and restarts are already included in total fuel. Repeated stop-and-go creeping within one queue is not modeled.
Fuel components across all drivers
| Fuel / 1,000 full trips (US gal) | Standard | Michigan |
|---|
What does the difference cost over a year?
Michigan minus standard: negative means savings. These are conditional scenarios using your statewide assumptions—not an official inventory or statewide forecast. Operational costs use the matched crash-free baseline, even when the replay is a crash demonstration.
| Annual exposure scenario | Δ vehicle-hours | Δ US gallons | Δ fuel cost (USD) | Δ time value (USD) | Operating subtotal (USD) |
|---|
Per-maneuver differences, arithmetic and both scopes
| Applied difference / intended left maneuver | Michigan − standard |
|---|
Expected annual crash costs · separate scenario
| Type group | Standard expected/year | Michigan expected/year | Standard annual cost | Michigan annual cost | Δ annual cost |
|---|
Expected costs use base rates and severity probabilities, not sampled replay counts. The 1,000× demo does not multiply these values. Cost data and limitations ↗
Annualization methods, assumptions and source audit ↗ · Excludes construction, land, maintenance, emissions, vehicle wear and other unpriced effects. A single demand/timing scenario does not represent every Michigan intersection or hour.
What happens when a conflict becomes a crash?
A seeded event-and-closure model. Frequency is an input, not a safety result derived from the moving cars. The reference is a legacy signalized-intersection comparison; it is not today's statewide crash mix.
Crashes by type
Solid bars = expected · white diamonds = drawn count · silver = Standard · gold = Michigan. Type groups are exhaustive and mutually exclusive.
Exact chart values & category mapping
| Type group | Standard expected | Standard drawn | Michigan expected | Michigan drawn |
|---|
Rear-end includes rear-end–left-turn and rear-end–right-turn. Opposing direct-left is the legacy head-on–left-turn category. Angle/turning combines straight and turning angle crashes. Sideswipe/merge combines same- and opposite-direction sideswipes. The final group combines head-on, fixed object and overturn. The Michigan opposing-direct-left category represents external access/violation scenarios, not a legal modeled left at the main light.
| Change from same seed without closures | Standard | Michigan |
|---|
Crash mix, type-specific rates & editable weights
Starting weights reproduce FHWA Table 4 percentages (all crashes). Editing makes a custom scenario. Weights normalize to 100% in each layout. Rate = total rate × normalized share; it is not the share itself. “Caught in the turn” is usually head-on–left-turn when approaches oppose one another.
| Legacy crash category | Standard weight | Michigan weight | Standard / million | Michigan / million |
|---|
How events affect traffic, and what remains unmodeled
Each layout draws a Poisson crash count from rate × unique observation entrants / 1,000,000. A separate random stream leaves demand unchanged. Events are assigned to locations using the crash-free run: rear-end placement favors time queued; turning events favor matching turns. This placement is an assumption, not a fitted crash hazard. The rate does not automatically respond to speed, gap, spacing, or congestion.
Closures obstruct the corresponding approach or U-turn queue. Crossing/heading conflicts at the main intersection close all main approaches. The model then reruns those same drivers: delayed service changes waits, fuel, and later signal arrivals. Closure duration is user-assumed and identical across types. Background-period crashes, secondary crashes, emergency response, injuries, vehicle removal, and physical impacts are not modeled.
Markers depict external incidents, not identified pairs of crashing simulated drivers. Placement remains fixed during the rerun. If a matching movement is absent, an external approach event is explicitly flagged. Michigan residual head-on–left-turn events represent unmodeled direct-left/access violations, never a permitted left at the main light. Sideswipe/merge incidents are also external: the one-lane traffic engine has no lateral vehicle dynamics.
The study boundary includes the main junction, both crossovers and connecting travel. Published legacy spatial boundaries are insufficiently specified to calibrate this full system. Modern crossover statistics are shown separately in the study notes and are not spliced into the main-junction comparison. Seed intervals omit uncertainty in the chosen crash rates and mechanisms.
Model, limitations & sources
This is a reproducible exploratory simulation, not a calibrated forecast for a real intersection. Each direction receives a shifted-exponential arrival stream, with a minimum two-second entry headway. The same vehicle IDs, arrival times and destinations are used for both layouts.
The default signal is 40 seconds green, 3 seconds yellow and 2 seconds all-red for each axis. Queues discharge at a two-second headway after a two-second startup allowance. Conventional lefts accept gaps in opposing traffic; one staged vehicle may clear late in yellow. Both opposing left turns can run together. Yield-controlled U-turns use a seven-second gap by default. Optional signalized crossovers alternate arterial and U-turn greens with the same cycle and split as the center light and an adjustable offset. Optional red turns stop for at least one second and accept a gap. The −7 s preset is an FHWA-reported Michigan example, not a site-specific recommendation.
East–west is the divided arterial. Its left-turn drivers go straight, U-turn, then turn right. North–south left-turn drivers turn right, U-turn, then return through the main intersection. Boundaries are 600 meters from the center. A Michigan left adds twice the crossover spacing plus a 30-meter U-turn arc. The drawing compresses distances and spreads point queues into visible vehicles; it is not a car-following or physical collision model. Optional exogenous crash events obstruct queue service; see Crash processes above.
Fuel = distance / cruise mpg + waiting hours × idle rate + positive kinetic-energy recovery / drivetrain efficiency. Defaults: 1,600 kg gasoline car, 25% efficiency, 121 MJ/US gallon, acceleration 1.5 m/s² and deceleration 2 m/s². Stop/turn time losses are added to travel time. Cruise mpg is a steady-speed assumption, not EPA combined mpg. No regenerative braking, stop-start, cold starts, trucks, pedestrians, lane changing, hills, or physical spillback are modeled.
Ten minutes of warmup precede the 60-minute entry window; ten minutes of additional traffic follow it. Remaining trips are drained. Counts near the observation cutoff are displayed separately so unfinished trips are not silently dropped. If queues exceed approximate physical storage, results are flagged: this model cannot predict blocked upstream traffic reliably. Confidence intervals describe seed variation only, not model or parameter uncertainty. Yellow clearance, gaps and fuel parameters are assumptions to calibrate.
- FHWA: Median U-Turn Intersection Treatment — routing and 660-foot crossover spacing.
- FHWA: Traffic Signal Timing Manual, Chapter 3 — two-second headway and startup approximations.
- ORNL: Transportation Energy Data Book supporting information — examples of passenger-car idle fuel rates.
- DOE Alternative Fuels Data Center — gasoline heating values.