Industry: Transportation
Product: ModelRisk
Application: TMC Incident-Response Strategy on a 38-Mile Urban Freeway

When the Mean Incident Costs $57,000 but One in a Hundred Costs $660,000

A US Traffic Management Center (TMC) overseeing a 38-mile, 4-lane urban freeway segment was scoring well on its operational dashboard — mean incident-clearance time 28 minutes — and getting hammered every quarter by board complaints about specific catastrophic-incident days. The reason: incident-cost is massively right-skewed. The simulation rebuilt in ModelRisk produced a per-incident delay-cost distribution with a mean of $57,000 but a median of only $16,500 — the mean is dragged by a P99 of roughly $664,000 and a worst case near $4M. The dashboard centre was structurally hiding what the public actually experiences: a small share of multi-lane crashes accounts for the majority of the corridor's annual delay cost.

The distribution makes the problem unmissable: incidents costing more than $100,000 are only 13% of events but account for 67% of total delay cost. The TMC rebuilt the response model around three random variables — incident arrivals (Poisson), severity (categorical 1–4 lane blockage), and clearance time (LogNormal) — and a deterministic queueing engine that converts those three into vehicle-hours of delay and dollars. The decision the simulation supports is not "how do we average down the mean," it is "what response posture clips the tail?"

Why incidents need three distributions, not one travel-time SD

Incidents on the corridor arrive at a Poisson rate of 0.42 per peak-hour (one every 2h 24m on average across the 4 peak hours per day, 250 days/year — roughly 420 incidents/year). The Poisson rate is stable across years because exposure is stable; what varies wildly is severity and clearance time.

• Severity (lanes blocked): categorical with probabilities 0.62 / 0.25 / 0.10 / 0.03 for 1, 2, 3, and all-4 lanes — fitted from three years of TMC dispatch logs.
• Clearance time T (minutes): LogNormal with mean 28 min, σ_log 0.55. The right-skew is real — debris and fender-benders clear in 8–15 minutes, multi-vehicle crashes with secondary fires sit in the 90–180 minute tail.

With peak demand D = 7,400 vph and per-lane capacity 2,000 vph, the queueing dynamics are deterministic given the inputs: deficit D − cap_during builds queue at the deficit rate for the duration T, then dissipates at slack 4×2000 − D = 600 vph. A single 3-lane blockage for the mean 28-minute clearance generates 2,520 queued vehicles, which then take 252 minutes (over 4 hours) to dissipate — long after the peak window closes. The vehicle-hours-of-delay (VHD) triangle gives the cost.

Deterministic said clearance time is fine. Monte Carlo said the tail is the entire problem.

The simulation reports per-incident:

• Mean cost ~$57,000
• Median cost ~$16,500
• P90 cost ~$130,000
• P99 cost ~$664,000
• Worst observed ~$4M

A flat operational mean masks the fact that incidents above $100k — roughly 13% of incidents — drive 67% of the corridor's annual incident-delay cost. Any improvement program must be evaluated on the tail, not the average.

Three response postures, three tail shapes

The TMC evaluated three operational postures: thin coverage (rural-style camera grid, mean clearance 35 min), current (existing camera coverage, 28 min), and full posture (Automated Incident Detection (AID) + a Freeway Service Patrol every 6 miles, mean clearance 15 min, σ_log 0.40). The simulation produces:

• Thin coverage: mean per-incident cost ~$92k, P90 ~$204k, P99 ~$1.1M.
• Current: mean ~$57k, P90 ~$130k, P99 ~$664k.
• Full posture (AID + FSP): mean ~$14k, P90 ~$34k, P99 ~$116k.

The full posture cuts mean cost by 76% and compresses the P99 by more than 80% — the tail collapses faster than the mean because clearance time enters the VHD calculation through both the queue-build duration and the dissipation triangle. The annual savings from full posture relative to current: ($57k − $14k) × 420 incidents ≈ $18M/yr in operational benefit, against a $1.8M capex and $450k/yr opex — a payback of well under a year.

Before / after: what AID alone (no FSP) buys

AID alone — cameras with machine-vision incident classification — drops the mean clearance from 28 min to 19 min and σ_log from 0.55 to 0.45. The per-incident cost distribution shifts left and compresses: mean drops from $57k to $23k (about 60%) and P90 from $130k to $56k. The probability that an incident exceeds $100k falls from 13% to 4% — that is the metric that ended up on the public-facing dashboard, because "P(major-incident) cut by two-thirds" reads in a board meeting where "mean clearance down 9 minutes" does not.

Which incident types matter most

The Pareto, weighted by frequency × per-event cost, ranks single-vehicle crashes (1–2 lane blockage, P = 22% per peak-day on the corridor) and multi-vehicle crashes (≥3 lanes, P = 4.5%) at the top of the expected-cost list, with weather-related crashes (P = 9.5%) third. Vehicle fires carry the heaviest per-event cost (mean $24k) but sit lower on the list because they are rare. The Pareto top three account for 69% of the corridor's annual incident-delay cost — and informed the placement of the four highest-impact AID camera clusters along the 38-mile alignment.

What the model changed

• AID procurement justified at $1.8M capex. The simulated mean shift (28 → 19 min) and the substantial P99 compression anchored the benefit-cost calculation at a BCR well above 5 for AID alone and above 10 for the full AID + FSP package.
• FSP coverage spaced at 6 miles, not the originally proposed 9 miles — the simulation showed the 6-mile spacing cuts the P90 incident-response time by 8 minutes, worth meaningful annual delay-cost reduction per mile-position shift.
• Public dashboard metric changed from "mean clearance time" to "probability of a major-incident day this week" — a metric that moves with the right tail, not just the centre.
• Annual incident-delay cost estimate for the corridor recalibrated from a deterministic placeholder to a simulated ~$24M/year (mean per-incident cost × roughly 420 incidents/year) — used to size the operational-contingency line in the next budget cycle.

ModelRisk Functionality Used

• Poisson incident arrivals at λ = 0.42 per peak-hour, fitted from three years of TMC dispatch records, producing the 420 incidents/year rate that anchored every downstream calculation.
• Categorical severity distribution (1L 62%, 2L 25%, 3L 10%, 4L 3%) for lane-blockage count — the input that drives the queueing-deficit calculation.
• LogNormal clearance time (mean 28 min, σ_log 0.55), capturing the multi-vehicle-crash tail that a Normal fit truncated; the alternative AID posture shifts both the mean (28 → 19 min) and σ (0.55 → 0.45), and the simulation tracks both effects.
• Deterministic queueing-and-dissipation engine inside the simulation loop, converting (severity, T, demand) into VHD and dollars at $19/hr SOV VOT and $58/hr truck VOT (10% truck share).
• Pareto across eight incident types, identifying the three event categories that produce 69% of the corridor's annual delay cost and steering AID camera-cluster placement.
• Three-posture scenario CDF that produced the multi-million-dollar annual operational benefit estimate and the sub-year payback on the full AID + FSP package.

The deterministic dashboard said 28 minutes. The simulation said the public is reacting to the 99th percentile, not the mean — and an incident-response program that does not move the tail does not move the public's experience of the corridor.