PTOE cheat sheet

Spot speed studies: 85th percentile speed approximates the upper limit of a reasonable speed limit; pace is the 10-mph band containing the most observations.

Traffic crash rate per million entering vehicles (MEV) = (crashes × 1,000,000) / (AADT × 365 × years).

Poisson distribution models random arrivals: P(x) = e^(−m) m^x / x!, where m is the mean arrival rate per interval.

Queueing at a signal: uniform delay d1 = 0.5 C (1 − g/C)^2 / (1 − min(1, X) g/C), where X is degree of saturation.

Saturation flow rate in passenger cars per hour green = 3600 / headway (s); a 2.0 s headway yields 1800 pc/h.

Time-mean speed vs. space-mean speed: space mean speed = total distance / total travel time across all vehicles.

Capacity of a single lane under ideal conditions is roughly 1900–2000 pc/h; practical capacity is lower once LOS constraints are applied.

MUTCD requires that a traffic control device fulfill a need, command respect, convey a clear simple message, allow adequate response time, and be uniform.

Roundabout entry capacity decreases as circulating flow increases; the critical gap and follow-up headway drive the entry flow model.

Flow-speed-density fundamental relation: q = k * u, where q is flow (veh/h), k is density (veh/km or veh/mi), and u is space mean speed.

Space mean speed (harmonic mean of spot speeds) is the correct speed for flow-density relations; time mean speed (arithmetic mean) always exceeds it.

Level of Service for basic freeway segments is defined by density (pc/km/ln or pc/mi/ln); LOS A ≤7 pc/km/ln (≈11 pc/mi/ln) and LOS F exceeds capacity.

Signalized intersection LOS is based on control delay per vehicle; LOS D spans 35–55 s/veh and LOS E spans 55–80 s/veh under HCM methodology.

Webster's optimal cycle length: C = (1.5L + 5) / (1 − Y), where L is total lost time and Y is the sum of critical flow ratios.

Highway Capacity Manual saturation flow base is 1900 pc/h/ln; adjust for lane width, heavy vehicles, grade, parking, bus stops, and turning movements.

Passenger car equivalent for heavy vehicles on upgrades rises with grade length; a 3% grade of 1 km can push PCE above 3 for trucks.

Traffic signal warrants include eight conditions (e.g., eight-hour vehicular volume, four-hour volume, peak hour delay, crash experience); satisfying any one warrant justifies a signal.

Gap acceptance at unsignalized intersections uses critical gap (typically 4.5–7 s for major-road through traffic) and follow-up time (typically 2–3 s).