Vehicle dynamics, braking and stopping distances, traffic flow, highway geometry, railway operations, route planning and transit capacity.
Transportation (transportation-ai999x) is an offline Python package for transportation. It covers vehicle dynamics, braking and stopping distances, traffic flow, highway geometry, railway operations, route planning and transit capacity.
It has 77 capabilities — 77 computational procedures — in 13 topics, the largest being Traffic flow, Highway geometry, Vehicle dynamics, Vehicle performance, Braking and stopping and Mode choice. Ask a question in words with ask(), or call a capability by name with typed inputs with solve(). Every answer carries its value and unit, the steps that produced it and the formula in LaTeX.
When a question is not determined — a value is missing, an input is out of range, or the request is outside the package — it says so and names what it needs, instead of guessing. It runs on an ordinary CPU without a network connection (Python >=3.10), and the same question always gets the same answer.
pip install transportation-ai999x hf download AI999X/transportation-ai999x --local-dir transportation-ai999x
Each question below was put to transportation-ai999x and the answer shown is the one it returned, with the steps it took.
Stopping sight distance with speed = 100 km/h, reaction time = 2.5 s and deceleration = 3.4 m/s^2.
v = 27.77777778 m/s, t_r = 2.5 s, a = 3.4 m/s^2SSD = 182.9157589 m, d_r = 69.44444444 m, d_b = 113.4713145 mSignal queue and uniform delay with arrival flow = 600 veh/h, saturation flow = 1800 veh/h, red = 40 s and green = 30 s.
lam = 600 1/h, s = 1800 1/h, r = 40 s, g = 30 sQ_max = 6.666666667, t_clear = 20 s, D_total = 200 s, d_uniform = 17.14285714 s, P_stopped = 0.8571428571Fastest route with roads = [A-B 4, A-C 2.5, B-C 1.2, B-D 5, C-D 8, C-E 10, D-E 2], speeds = [60, 50, 40, 80, 100, 90, 50], origin = A and destination = E.
roads = A-B (4), A-C (2.5), B-C (1.2), B-D (5), C-D (8), C-E (10), D-E (2), speeds = [60, 50, 40, 80, 100, 90, 50], origin = A, destination = Eroute = A-C-E, time = 9.666666667 min, distance = 12.5 kmMaximum safe speed on a curve with radius = 300 m, superelevation = 6 % and side friction = 0.12.
R = 300 m, e = 0.06 1, f = 0.12 1v = 23.09938936 m/s, v_kmh = 83.1578017 km/hm.solve("transport_understeer_gradient", m="1500 kg", L="2.7 m", l_f="1.2 m", C_f="90000 N/rad", C_r="85000 N/rad") m = 1500 kg, L = 2.7 m, l_f = 1.2 m, C_f = 90000 N/rad, C_r = 85000 N/radK = 0.001416122004 rad*s^2/m, K_deg_per_g = 0.7959619566 deg, behaviour = understeer rad*s^2/m, v_c = 43.66480716 m/s, v_c_kmh = 157.1933058 km/hLogit elasticities with utilities = [-1.2, -0.8, -2.1], attribute = [30, 45, 20] and beta = -0.04.
V = [-1.2, -0.8, -2.1], x = [30, 45, 20], beta = -0.04P = [0.3450186126, 0.5147072874, 0.1402740999], direct = [-0.7859776649, -0.8735268826, -0.6877807201], cross = [0.4140223351, 0.9264731174, 0.1122192799]Erlang b blocking with arrival rate = 60 veh/h, service rate = 0.5 veh/h and spaces = 120.
lam = 60 1/h, mu = 0.5 1/h, c = 120P_block = 0.06941876906, carried = 111.6697477, lost_per_h = 4.165126144 1/hStation headway with line speed = 80 km/h, acceleration = 1 m/s^2, braking rate = 1.1 m/s^2, train length = 150 m, dwell time = 30 s and safety margin = 50 m.
v = 22.22222222 m/s, a = 1 m/s^2, b = 1.1 m/s^2, L_t = 150 m, t_d = 30 s, s_m = 50 mh = 70.2020202 s, trains_per_h = 51.28057554 1/hEvery snippet was run as shown; the output under it is what it printed.
import transportation_ai999x as m
a = m.ask("Stopping sight distance with speed = 100 km/h, reaction time = 2.5 s and deceleration = 3.4 m/s^2.")
print(a.outcome)
print(a.values)
for step in a.steps:
print(step["name"])SOLVED
{'SSD': 182.915758896, 'd_r': 69.4444444444, 'd_b': 113.471314452}
Stopping sight distance (reaction plus braking, with grade)
import transportation_ai999x as m
a = m.solve("transport_understeer_gradient", m="1500 kg", L="2.7 m", l_f="1.2 m", C_f="90000 N/rad", C_r="85000 N/rad")
print(a.outcome)
print(a.values)SOLVED
{'K': 0.00141612200436, 'K_deg_per_g': 0.795961956569, 'behaviour': 'understeer', 'v_c': 43.6648071634, 'v_c_kmh': 157.193305788}
import transportation_ai999x as m
# an input is missing: the answer says what it needs instead of guessing
a = m.solve("transport_understeer_gradient")
print(a.outcome)
print(a.message)NEEDS_INPUT
transport_understeer_gradient needs m, L, l_f, C_f, C_r (vehicle mass; wheelbase; distance from the front axle to the centre of gravity; cornering stiffness of the front axle; cornering stiffness of the rear axle). Example: solve('transport_understeer_gradient', m='1500 kg', L='2.7 m', l_f='1.2 m', C_f='90000 N/rad', C_r='85000 N/rad').
transportation-ai999x "Stopping sight distance with speed = 100 km/h, reaction time = 2.5 s and deceleration = 3.4 m/s^2."
SSD = 182.916 m, d_r = 69.4444 m, d_b = 113.471 m 1. Stopping sight distance (reaction plus braking, with grade): SSD = v t_r + v^2 / (2 g (f + G)), or with a deceleration rate v t_r + v^2 / (2 (a + g G)) with v = 27.7778 m/s, t_r = 2.5 s, a = 3.4 m/s^2 -> SSD = 182.916 m, d_r = 69.4444 m, d_b = 113.471 m Assumptions: v > 0; t_r >= 0; exactly one of f, a; f + G > 0 (or a + g G > 0) …
Every value in these figures was computed by the package, each point a run of solve(); in a notebook, plot() and plot_relation() draw a capability's curves the same way.
12 of its 77 formulas; every one is in the capability browser below.
Search by name, formula, input or topic. Each capability opens to show what it takes, what it returns, when it applies, and a question it answered.
transport_braking_distanceDistance and time for a vehicle to stop from speed v at a constant deceleration a (no reaction time).
v initial speed [m/s]a deceleration (magnitude) [m/s^2]d braking distance (m) [m]t braking time (s) [s]transport_speed_reduction_distanceBraking distance and time to slow from v1 to v2 with friction coefficient f on a grade G (deceleration g (f + G)).
v1 initial speed [m/s]v2 final speed [m/s]f friction coefficientG grade, decimal (positive uphill) optionald braking distance (m) [m]t braking time (s) [s]transport_impact_speedA driver at speed v sees an obstacle at distance D, reacts after t_r and brakes with friction f on grade G: the speed at the obstacle (0 if the vehicle stops in time) and the full stopping distance.
v initial speed [m/s]D distance to the obstacle [m]t_r perception-reaction time [s]f friction coefficientG grade, decimal (positive uphill) optionalv_impact speed at the obstacle (m/s), 0 if the vehicle stops before it [m/s]v_impact_kmh speed at the obstacle (km/h) [km/h]d_stop stopping distance from the moment the obstacle is seen (m) [m]transport_skid_speedInitial speed of a vehicle that skidded to rest over a length d with friction coefficient f on a grade G.
d skid-mark length [m]f friction coefficientG grade, decimal (positive uphill) optionalv initial speed (m/s) [m/s]v_kmh initial speed (km/h) [km/h]transport_stopping_sight_distanceStopping sight distance = perception-reaction distance + braking distance on a grade, with either the longitudinal friction coefficient f (braking deceleration g (f + G)) or a deceleration rate a (AASHTO: a + g G, design value 3.4 m/s^2).
v design speed [m/s]t_r perception-reaction time [s]f longitudinal friction coefficient optionala deceleration rate [m/s^2] optionalG grade, decimal (positive uphill) optionalSSD stopping sight distance (m) [m]d_r perception-reaction distance (m) [m]d_b braking distance (m) [m]transport_braking_with_air_resistanceStopping (or slowing) distance and time of a road vehicle braking with tyre-road friction mu and braking efficiency eta, helped by aerodynamic drag (rho C_D A v^2 / 2), rolling resistance f_r and the grade; gamma is the mass factor for rotating parts (1.04 for braking).
m vehicle mass [kg]v1 initial speed [m/s]mu tyre-road friction coefficientC_D drag coefficientA frontal area [m^2]rho air density (default 1.2 kg/m^3) [kg/m^3] optionalf_r rolling resistance coefficient (default 0.01) optionalG grade, decimal (positive uphill) optionaleta braking efficiency (default 1) optionalgamma mass factor for braking (default 1.04) optionalv2 final speed (default 0) [m/s] optionalS braking distance (m) [m]t braking time (s) [s]transport_clothoid_coordinatesCoordinates along the tangent (x) and offset from it (y), and the tangent deflection angle, at distance s along a clothoid transition of length L_s that ends at a circular curve of radius R (A^2 = R L_s).
R radius of the circular curve [m]L_s spiral length [m]s distance along the spiral (default L_s) [m] optionalx distance along the initial tangent (m) [m]y offset from the tangent (m) [m]theta tangent deflection angle (degrees) [deg]transport_simplified_curve_formulaThe minimum radius R = v^2/(g (e + f)) for a speed, or the maximum speed sqrt(g R (e + f)) on a radius, by the simplified (small-angle) point-mass formula of horizontal curves (the exact form is minimum curve radius).
e superelevation rate, decimalf side friction factorv design speed (give v or R) [m/s] optionalR curve radius (give v or R) [m] optionalR curve radius (m) [m]v speed (m/s) [m/s]v_kmh speed (km/h)transport_horizontal_sight_offsetThe clearance M needed from the centre of the inside lane to an obstruction (middle ordinate) so that a driver on a curve of radius R sees the sight distance S, both driver and object on the curve.
R radius of the inside lane centreline [m]S sight distance [m]M horizontal sightline offset (m) [m]transport_curve_safe_speedThe highest speed at which a vehicle (point mass) can hold a curve of radius R with superelevation e and side friction factor f.
R curve radius [m]e superelevation rate, decimalf side friction factorv maximum safe speed (m/s) [m/s]v_kmh maximum safe speed (km/h) [km/h]transport_crest_curve_lengthThe shortest crest vertical curve between grades g1 and g2 that provides the sight distance S (AASHTO: eye height 1.08 m, object height 0.60 m unless stated), choosing the S < L or S > L form.
g1 grade before the curve, decimal (positive uphill)g2 grade after the curve, decimalS required sight distance [m]h1 driver eye height (default 1.08 m) [m] optionalh2 object height (default 0.60 m) [m] optionalL minimum curve length (m) [m]case S < L, S > L or no curve neededtransport_minimum_curve_radiusThe smallest curve radius for a design speed v, maximum superelevation e and side friction factor f.
v design speed [m/s]e superelevation rate, decimalf side friction factorR_min minimum curve radius (m) [m]transport_passing_sight_distanceThe passing sight distance on a two-lane road as d1 + d2 + d3 + d4: the initial manoeuvre d1 = t1 (v - m + a t1/2), the time in the left lane d2 = v t2, the clearance d3 and the opposing vehicle's travel d4 = 2 d2/3 (AASHTO 2001).
v average speed of the passing vehicle [m/s]m_diff speed difference between passing and passed vehicles [m/s]a average acceleration during the initial manoeuvre [m/s^2]t1 time of the initial manoeuvre [s]t2 time in the left lane [s]d3 clearance between the passing and opposing vehicles [m]PSD passing sight distance (m) [m]d1 initial manoeuvre distance (m) [m]d2 distance in the left lane (m) [m]d3 clearance (m) [m]d4 opposing vehicle distance (m) [m]transport_sag_curve_headlightThe minimum length of a sag vertical curve for the headlight sight distance S by the AASHTO formulas (headlight 0.6 m high, beam rising 1 degree): L = A S^2/(120 + 3.5 S) when S < L, L = 2S - (120 + 3.5 S)/A when S > L, A = g2 - g1 in percent.
g1 entering grade, decimalg2 leaving grade, decimalS headlight sight distance [m]L minimum curve length (m) [m]A algebraic grade difference (%)K rate of vertical curvature L/A (m per %)case S < L or S > Ltransport_side_friction_demandThe side friction factor a vehicle needs at speed v on a curve of radius R with superelevation e (negative: the superelevation alone exceeds the demand and friction acts up the slope).
v design speed [m/s]R curve radius [m]e superelevation rate, decimalf side friction factor demandedtransport_sight_distance_from_offsetThe sight distance available on a curve of radius R (inside lane centreline) when an obstruction stands at the offset M from that centreline.
R radius of the inside lane centreline [m]M offset to the obstruction [m]S available sight distance (m) [m]transport_crest_curve_sight_distanceThe sight distance a crest vertical curve of length L between grades g1 and g2 provides (eye height 1.08 m, object height 0.60 m unless stated).
g1 grade before the curve, decimal (positive uphill)g2 grade after the curve, decimalL curve length [m]h1 driver eye height (default 1.08 m) [m] optionalh2 object height (default 0.60 m) [m] optionalS available sight distance (m) [m]case S < L or S > Ltransport_superelevation_requiredThe superelevation rate needed at speed v on a curve of radius R when the side friction factor f is used.
v design speed [m/s]R curve radius [m]f side friction factore superelevation rate (decimal)e_percent superelevation rate (%)transport_logit_elasticitiesPoint elasticities of logit probabilities with respect to an attribute x (such as cost or time) that enters the utility linearly with coefficient beta: direct E_ii = beta x_i (1 - P_i) and cross E_ji = -beta x_i P_i (the same for every other alternative j, the IIA property).
V utility of each alternative vectorx value of the attribute for each alternative vectorbeta coefficient of the attributeP probability of each alternativedirect direct elasticity of each alternativecross cross elasticity of the other alternatives with respect to each alternative's attributetransport_logit_from_attributesUtilities V_i = ASC_i + sum_k beta_k x_ik of each mode from its attributes (rows of X: modes; columns: attributes such as time in min and cost) and the coefficients, and the resulting logit choice probabilities.
X attributes: one row per mode, one column per attribute matrixbeta coefficient of each attribute vectorasc alternative-specific constant of each mode (default 0) vector optionalV utility of each modeP probability of each modetransport_nested_logitChoice probabilities of a two-level nested logit model (for example car / public transport nests holding bus and rail): alternatives grouped into nests 1..K with dissimilarity (logsum) parameters lam_k in (0, 1]; also the probability of each nest.
V utility of each alternative vectornest nest number (1, 2, ...) of each alternative vectorlam dissimilarity parameter of each nest, in (0, 1] vectorP probability of each alternativeP_nest probability of each nesttransport_logsum_user_benefitChange in consumer surplus per trip (in money units) when the utilities of the alternatives change from V0 to V1, from the difference of the logsums divided by the (negative) cost coefficient.
V0 utilities before the change vectorV1 utilities after the change vectorbeta_cost cost coefficient (utility per money unit, negative)dCS change in consumer surplus per trip (money units)logsum0 logsum beforelogsum1 logsum aftertransport_erlang_b_blockingArrivals at lam (veh/h) to c spaces or servers held for a mean time 1/mu with no waiting room (a car park, loading bays, taxi ranks): the probability an arrival is turned away (Erlang B), the mean number of occupied spaces and the vehicles lost per hour. Rates in veh/h.
lam arrival rate (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]mu service rate per server (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]c number of spaces or servers (whole number) integerP_block probability an arrival is turned awaycarried mean number of occupied spaceslost_per_h vehicles turned away (veh/h) [1/h]transport_fifo_queue_simulationWaiting time of every vehicle (or passenger) at c identical servers in first-come-first-served order from given arrival times and service times (a toll plaza, a bus stop with c berths): mean and longest wait, mean time in the system, when the last one leaves and the longest waiting line. Times in s.
arrivals arrival times in s, increasing vectorservice service times in s (one per arrival, or one for all) vectorc number of servers (default 1) integer optionalwaits waiting time of each arrival (s)mean_wait mean waiting time (s) [s]max_wait longest wait (s) [s]mean_time_in_system mean time in the system (s) [s]last_departure time the last one leaves (s) [s]max_queue longest waiting linetransport_mmc_queuePoisson arrivals at lam served by c parallel exponential servers at mu each (toll lanes, loading bays, ticket windows): probability of waiting (Erlang C), mean queue, mean wait, mean time in the system and mean number in the system. Rates in veh/h.
lam arrival rate (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]mu service rate per server (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]c number of servers (whole number) integerP_wait probability an arrival waits (Erlang C)Lq mean number waiting (veh)Wq mean waiting time (s) [s]W mean time in the system (s) [s]L mean number in the system (veh)transport_md1_queuePoisson arrivals at lam and a constant service time 1/mu (an automated toll gate, a ramp meter): mean queue, mean wait, mean time in the system and mean number in the system. Rates in veh/h.
lam arrival rate (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]mu service rate per server (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]Lq mean number waiting (veh)Wq mean waiting time (s) [s]W mean time in the system (s) [s]L mean number in the system (veh)transport_mm1_queuePoisson arrivals at lam and exponential service at mu at one server (a toll booth, a ramp meter): utilisation, mean number in the system and in the queue, mean time in the system and waiting, and the probability that the server is idle. Rates in veh/h.
lam arrival rate (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]mu service rate per server (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]rho utilisation lam / muL mean number in the system (veh)Lq mean number waiting (veh)W mean time in the system (s) [s]Wq mean waiting time (s) [s]P0 probability the system is emptytransport_rail_station_headwayShortest headway between trains serving a station under a brick-wall (moving-block) separation: the leader dwells t_d, accelerates at a until its rear clears the platform plus the safety margin s_m, while the follower approaches at the line speed v and brakes at b to stop at the platform; and the corresponding line capacity in trains per hour.
v line (approach) speed [m/s]a acceleration [m/s^2]b braking rate [m/s^2]L_t train length [m]t_d dwell time [s]s_m safety margin (default 0) [m] optionalh minimum headway (s) [s]trains_per_h line capacity (trains/h) [1/h]transport_train_running_timeMinimum running time of a train (or bus) between two stops a distance D apart with acceleration a, braking rate b and line speed v_max; when the stops are too close to reach v_max the profile is accelerate-brake.
D distance between stops [m]v_max maximum (line) speed [m/s]a acceleration [m/s^2]b braking rate [m/s^2]T running time stop to stop (s) [s]v_peak highest speed reached (m/s) [m/s]profile accelerate-cruise-brake or accelerate-braketransport_train_accelerationTime and distance for a train to accelerate from v1 to v2 with a tractive effort F_max up to the speed P / F_max and constant power P above it, against the Davis resistance A + B v + C v^2 and the gradient, with a rotating-mass factor gamma.
m train mass [kg]v1 initial speed [m/s]v2 final speed [m/s]F_max maximum (starting) tractive effort [N]P power at the wheel rim [W]A Davis coefficient A (constant resistance) [N]B Davis coefficient B (per speed) [N*s/m]C Davis coefficient C (per speed squared) [N*s^2/m^2]G grade, decimal (positive uphill) optionalgamma rotating-mass factor (default 1.08) optionalt acceleration time (s) [s]d distance travelled (m) [m]transport_train_braking_distanceBraking distance and time of a train of mass m braking with a constant brake force F_b from v1 to v2, helped by the Davis train resistance R = A + B v + C v^2 and the gradient (positive uphill), with a rotating-mass factor gamma.
m train mass [kg]v1 initial speed [m/s]F_b brake force [N]A Davis coefficient A (constant resistance) [N]B Davis coefficient B (per speed) [N*s/m]C Davis coefficient C (per speed squared) [N*s^2/m^2]G grade, decimal (positive uphill) optionalgamma rotating-mass factor (default 1.06) optionalv2 final speed (default 0) [m/s] optionalS braking distance (m) [m]t braking time (s) [s]transport_fastest_routeThe quickest route between two places on a road network whose links are given by length (km) and speed (km/h): the route, its travel time in minutes and its length in km. Roads are two-way unless directed = yes.
roads roads as 'A-B length' with lengths in km edgesspeeds speed on each road in km/h, in the same order vectororigin starting place textdestination destination textdirected one-way links as written (default no) boolean optionalroute fastest route (places joined by '-')time travel time (min) [min]distance route length (km) [km]transport_travel_time_skimThe fastest travel time in minutes between every pair of places of a road network given by link lengths (km) and speeds (km/h), as a matrix in alphabetical order of the places (the skim used for trip distribution).
roads roads as 'A-B length' with lengths in km edgesspeeds speed on each road in km/h, in the same order vectordirected one-way links as written (default no) boolean optionalplaces places in the order of the matrixtimes travel time matrix (min)transport_greenberg_fitLeast-squares fit of Greenberg's model v = v0 ln(kj / k) (v against ln k) to observed speeds (km/h) and densities (veh/km): the optimum speed v0, jam density, capacity v0 kj / e and the coefficient of determination.
speeds observed space-mean speeds in km/h vectordensities observed densities in veh/km, in the same order vectorv0 optimum speed v0 (km/h) [km/h]kj jam density (veh/km) [1/km]q_max capacity (veh/h) [1/h]r2 coefficient of determination (v on ln k)transport_greenshields_fitLeast-squares fit of Greenshields' line v = vf - (vf/kj) k to observed speeds (km/h) and densities (veh/km): the free-flow speed, jam density, capacity and the coefficient of determination of the line.
speeds observed space-mean speeds in km/h vectordensities observed densities in veh/km, in the same order vectorvf free-flow speed (km/h) [km/h]kj jam density (veh/km) [1/km]q_max capacity (veh/h) [1/h]r2 coefficient of determination of the fittransport_underwood_fitLeast-squares fit of Underwood's model v = vf exp(-k / k0) (ln v against k) to observed speeds (km/h) and densities (veh/km): the free-flow speed, the optimum density k0, capacity vf k0 / e and the coefficient of determination.
speeds observed space-mean speeds in km/h vectordensities observed densities in veh/km, in the same order vectorvf free-flow speed (km/h) [km/h]k0 optimum density (veh/km) [1/km]q_max capacity (veh/h) [1/h]r2 coefficient of determination (ln v on k)transport_greenberg_capacityCapacity of a traffic stream following Greenberg's model v = v0 ln(kj / k) and the density at which it occurs (the speed there is v0).
v0 optimum speed v0 [m/s]kj jam density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]q_max capacity (veh/h) [1/h]k_m density at capacity (veh/km) [1/km]transport_greenshields_capacityCapacity (maximum flow) of a traffic stream following Greenshields' linear speed-density model v = vf (1 - k/kj), with the density and speed at which it occurs.
vf free-flow speed [m/s]kj jam density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]q_max capacity (veh/h) [1/h]k_m density at capacity (veh/km) [1/km]v_m speed at capacity (km/h) [km/h]transport_greenshields_speed_at_flowThe two traffic states (uncongested and congested) of a Greenshields stream that carry the flow q: their densities and speeds.
vf free-flow speed [m/s]kj jam density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]q traffic flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]k_1 uncongested density (veh/km) [1/km]v_1 uncongested speed (km/h) [km/h]k_2 congested density (veh/km) [1/km]v_2 congested speed (km/h) [km/h]transport_headway_probabilityProbability that the time headway between random vehicles at flow q is at least h (and shorter than h), for the negative exponential distribution or the shifted one with a minimum headway tau.
q traffic flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]h headway [s]tau minimum headway (default 0) [s] optionalP_ge P(headway >= h)P_lt P(headway < h)transport_poisson_arrivalsProbability that exactly n, at most n and at least n vehicles arrive in an interval t when arrivals are random (Poisson) at the flow q.
q traffic flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]t interval length [s]n number of arrivals (whole number) integerP_n P(exactly n arrivals)P_le P(at most n arrivals)P_ge P(at least n arrivals)transport_bottleneck_queueDeterministic queue when the capacity of a road falls from mu to mu_r for a time t_r (an incident or a work zone) while vehicles arrive at lam: the longest queue, how long the queue lasts and the total delay.
lam arrival flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]mu normal capacity (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]mu_r reduced capacity (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]t_r duration of the reduction [s]Q_max longest queue (veh)T duration of the queue from the start of the reduction (s) [s]T_min duration of the queue (min) [min]D_total total delay (veh h) [h]transport_interval_queueVehicles queued at the end of each counting interval when the arrivals per interval are served up to the capacity per interval (deterministic queue, first in first out), the longest queue and the vehicles served per interval.
arrivals arrivals in each interval (veh) vectorcapacity capacity of each interval (veh), or one value for all vectorqueue queue at the end of each interval (veh)Q_max longest queue (veh)served vehicles served in each interval (veh)transport_shockwave_speedSpeed of the boundary (shockwave) between an upstream traffic state (q1, k1) and a downstream state (q2, k2): u = (q2 - q1) / (k2 - k1), negative when it moves upstream (for example the back of a queue).
q1 upstream flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]k1 upstream density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]q2 downstream flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]k2 downstream density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]u shockwave speed (km/h), positive downstream [km/h]u_ms shockwave speed (m/s) [m/s]direction upstream, downstream or stationarytransport_greenshields_shockwaveSpeed of the shockwave between two states of a Greenshields stream with densities k1 (upstream) < k2 (downstream): u = vf (1 - (k1 + k2) / kj).
vf free-flow speed [m/s]kj jam density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]k1 upstream density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]k2 downstream density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]u shockwave speed (km/h), positive downstream [km/h]u_ms shockwave speed (m/s) [m/s]transport_travel_time_reliabilityThe buffer index (T95 - mean)/mean, the planning time index T95/T_free and the travel time index mean/T_free of observed travel times on a route (T95 the 95th percentile by linear interpolation). Times in minutes.
times observed travel times in min vectort_free free-flow travel time in minmean mean travel time (min)t95 95th-percentile travel time (min)buffer_index buffer index (T95 - mean)/meanplanning_time_index planning time index T95/T_freetravel_time_index travel time index mean/T_freetransport_underwood_capacityCapacity of a traffic stream following Underwood's model v = vf exp(-k / k0), with the speed and density at capacity.
vf free-flow speed [m/s]k0 optimum density k0 (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]q_max capacity (veh/h) [1/h]v_m speed at capacity (km/h) [km/h]k_m density at capacity (veh/km) [1/km]transport_signal_green_splitsEffective green time of each critical phase for a given cycle C and total lost time L, shared in proportion to the critical flow ratios y_i = v_i / s_i (equal degree of saturation), and the critical degree of saturation X_c. Greens in s.
C cycle length [s]L total lost time per cycle [s]y critical flow ratio v/s of each phase vectorg effective green of each phase (s)X_c critical degree of saturationtransport_webster_optimum_cycleWebster's optimum cycle length C0 = (1.5 L + 5)/(1 - Y) of a fixed-time signal from the total lost time L (s) and the critical flow ratios y_i = v_i/s_i (Y = sum y_i), with the minimum cycle L/(1 - Y) and the total effective green. Times in s.
L total lost time per cycle [s]y critical flow ratio v/s of each phase vectorC0 Webster optimum cycle length (s) [s]Y sum of the critical flow ratiosC_min minimum cycle length L/(1 - Y) (s) [s]green_total total effective green C0 - L (s) [s]transport_signal_queue_uniform_delayUniform arrivals at a fixed-time signal with saturation flow s, effective red r and effective green g (undersaturated): the largest queue, the time after the start of green until it clears, the total delay per cycle, the average (uniform) delay per vehicle and the share of vehicles that stop.
lam arrival flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]s saturation flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]r effective red [s]g effective green [s]Q_max largest queue (veh)t_clear time after the start of green to clear the queue (s) [s]D_total total delay per cycle (veh s) [s]d_uniform average delay per vehicle (s) [s]P_stopped share of vehicles that stoptransport_signal_queue_shockwaveKinematic-wave analysis of a signal: the queue grows upstream during the red at the shock speed between the arrival state (q_a, k_a) and jam density k_j, and from the start of green the discharge wave (saturation state q_s, k_s) chases it. The longest queue, the time it is reached (from the start of red) and both wave speeds.
q_a arrival flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]k_a arrival density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]k_j jam density (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]q_s saturation (discharge) flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]k_s density of the discharging stream (veh/km in questions; veh/m in solve(), or '25 1/km') [1/m]r red time [s]L_max longest queue (m) [m]t_max time from the start of red to the longest queue (s) [s]w_queue speed of the back of the queue (km/h) [km/h]w_discharge speed of the discharge wave (km/h) [km/h]transport_yellow_change_intervalMinimum yellow change interval Y = t_r + v / (2a + 2gG) so that a driver who is just too close to stop can clear at the approach speed, and the critical stopping distance from the stop line.
v approach speed [m/s]t_r perception-reaction time [s]a comfortable deceleration rate [m/s^2]G grade, decimal (positive uphill) optionalY yellow change interval (s) [s]x_c critical stopping distance (m) [m]transport_spot_speed_percentilesPercentile speeds of a spot-speed sample (85th percentile for speed limits and design, median, 15th) by linear interpolation between ranks (position (n - 1) p / 100, as Excel PERCENTILE.INC). Speeds in km/h.
speeds spot speeds in km/h vectorp85 85th percentile speed (km/h) [km/h]p50 median speed (km/h) [km/h]p15 15th percentile speed (km/h) [km/h]transport_time_and_space_mean_speedFrom spot speeds measured at a point: the time-mean speed (arithmetic mean), the space-mean speed (harmonic mean, the speed that matches travel times over a fixed length) and the sample standard deviation. Speeds in km/h.
speeds spot speeds in km/h vectorTMS time-mean speed (km/h) [km/h]SMS space-mean speed (km/h) [km/h]s sample standard deviation (km/h) [km/h]transport_all_or_nothing_assignmentLoads every origin-destination demand onto its fastest path through a network of one-way links with travel times (min): the flow on each link (in the order given) and the total vehicle-hours travelled.
network one-way links as 'A-B time' with travel times in min edgesod trip demands as 'origin-destination trips' (veh) edgesflows flow on each link in the order given (veh)VHT vehicle-hours travelled (veh h) [h]transport_gravity_modelTrips between zones T_ij = A_i O_i B_j D_j f(c_ij) that match both the productions O_i and the attractions D_j, with deterrence f(c) = exp(-beta c) or c^-beta, balanced by Furness iterations until every total matches to 1e-13.
O trip productions of the origin zones vectorD trip attractions of the destination zones vectorcosts travel cost (time) matrix, rows origins, in min matrixbeta deterrence parameterdeterrence exponential (default) or power choice optionaltrips trip matrix (rows origins, columns destinations)transport_furness_balancingScales a base-year trip matrix to future row totals (productions) and column totals (attractions) by the Furness (biproportional) method, iterated until every total matches to 1e-13.
base base-year trip matrix (rows origins) matrixO target row totals (productions) vectorD target column totals (attractions) vectortrips balanced trip matrixtransport_trip_generation_regressionLeast-squares trip-generation model trips = b0 + b1 x1 + ... fitted to zonal data (rows of X: zones; columns: households, employment, cars, ...), its coefficient of determination, and optionally the trips predicted for a new zone.
X zonal predictors: one row per zone matrixy observed trips of each zone vectorx_new predictors of a zone to forecast (optional) vector optionalcoef coefficients b0 (intercept), b1, ...r2 coefficient of determinationy_new forecast trips of the new zonetransport_gap_acceptance_capacityCapacity of a minor (stop- or yield-controlled) movement crossing a random major stream of flow q, with critical gap t_c and follow-up time t_f: Harders' formula (as in the HCM) or Siegloch's.
q major-stream flow (veh/h in questions; veh/s in solve(), or a string such as '600 1/h') [1/s]t_c critical gap [s]t_f follow-up time [s]model harders (HCM, default) or siegloch choice optionalc capacity of the minor movement (veh/h) [1/h]transport_lateral_load_transferOuter and inner wheel loads of a rigid vehicle (no suspension roll) cornering at lateral acceleration a_y, and the load transferred to the outer wheels.
m vehicle mass [kg]a_y lateral acceleration [m/s^2]h height of the centre of gravity [m]t_w track width [m]W_out load on the outer wheels (N) [N]W_in load on the inner wheels (N) [N]dW load transferred to the outer wheels (N) [N]transport_braking_weight_transferDynamic front and rear axle loads of a vehicle decelerating at a, the load transferred to the front axle, and the ideal front share of the braking force (both axles at the same friction use).
m vehicle mass [kg]a deceleration [m/s^2]h height of the centre of gravity [m]L wheelbase [m]l_f distance from the front axle to the centre of gravity [m]W_f front axle load (N) [N]W_r rear axle load (N) [N]dW load transferred to the front axle (N) [N]front_share ideal front brake sharetransport_quarter_car_frequenciesUndamped natural frequencies of the two-degree-of-freedom quarter-car ride model: the body (bounce) mode and the wheel-hop mode, from the sprung and unsprung masses, suspension and tyre stiffnesses.
m_s sprung mass (a quarter of the body) [kg]m_u unsprung mass (wheel) [kg]k_s suspension spring stiffness [N/m]k_t tyre vertical stiffness [N/m]f_body body (bounce) natural frequency (Hz) [Hz]f_wheel wheel-hop natural frequency (Hz) [Hz]transport_quarter_car_transmissibilityAmplitude ratio between body (sprung-mass) motion and road displacement, and between wheel motion and road displacement, of the damped quarter-car model for a sinusoidal road input of frequency f.
m_s sprung mass (a quarter of the body) [kg]m_u unsprung mass (wheel) [kg]k_s suspension spring stiffness [N/m]c_s suspension damping coefficient [kg/s]k_t tyre vertical stiffness [N/m]f road input frequency [Hz]T_body body displacement / road displacementT_wheel wheel displacement / road displacementtransport_rollover_thresholdStatic stability factor SSF = t / (2h) of a rigid vehicle and the speed at which it would tip over on a curve of radius R with superelevation e (enough friction assumed for the tyres not to slide).
t_w track width [m]h height of the centre of gravity [m]R curve radius [m]e superelevation rate, decimal optionalSSF static stability factor t / (2h) (rollover threshold in g)v_roll rollover speed on the curve (m/s) [m/s]v_roll_kmh rollover speed (km/h) [km/h]transport_steady_state_corneringSteady turning response of the linear bicycle model at speed u to a front-wheel steer angle delta: yaw rate, lateral acceleration, turn radius and the sideslip angle at the centre of gravity (small angles).
m vehicle mass [kg]L wheelbase [m]l_f distance from the front axle to the centre of gravity [m]C_f cornering stiffness of the front axle [N/rad]C_r cornering stiffness of the rear axle [N/rad]u forward speed [m/s]delta front-wheel steer angle (degrees in questions; rad in solve(), or '2 deg') [rad]r yaw rate (rad/s) [rad/s]a_y lateral acceleration (m/s^2) [m/s^2]R turn radius (m) [m]beta sideslip angle at the centre of gravity (degrees) [deg]transport_steer_angle_for_radiusFront-wheel steer angle the linear bicycle model needs to hold a turn of radius R at speed u (Ackermann angle L/R plus the understeer term K u^2 / R).
m vehicle mass [kg]L wheelbase [m]l_f distance from the front axle to the centre of gravity [m]C_f cornering stiffness of the front axle [N/rad]C_r cornering stiffness of the rear axle [N/rad]u forward speed [m/s]R turn radius [m]delta front-wheel steer angle (degrees) [deg]transport_understeer_gradientUndersteer gradient K of the linear single-track model from axle cornering stiffnesses and the centre-of-gravity position, in rad/(m/s^2) and deg/g, whether the vehicle understeers or oversteers, and its characteristic speed (understeer: the steer angle is twice the Ackermann angle) or critical speed (oversteer: it becomes unstable).
m vehicle mass [kg]L wheelbase [m]l_f distance from the front axle to the centre of gravity [m]C_f cornering stiffness of the front axle [N/rad]C_r cornering stiffness of the rear axle [N/rad]K understeer gradient (rad s^2/m) [rad*s^2/m]K_deg_per_g understeer gradient (deg/g) [deg]behaviour understeer or oversteerv_c characteristic or critical speed (m/s) [m/s]v_c_kmh characteristic or critical speed (km/h) [km/h]transport_yaw_natural_frequencyUndamped natural frequency and damping ratio of the lateral-yaw motion of the linear bicycle model at speed u (from the characteristic equation of its two states), below the critical speed.
m vehicle mass [kg]Iz yaw moment of inertia [kg*m^2]L wheelbase [m]l_f distance from the front axle to the centre of gravity [m]C_f cornering stiffness of the front axle [N/rad]C_r cornering stiffness of the rear axle [N/rad]u forward speed [m/s]wn undamped natural frequency (rad/s) [rad/s]zeta damping ratiof_n undamped natural frequency (Hz) [Hz]transport_acceleration_under_powerTime and distance for a vehicle of mass m to change speed from v1 to v2 with constant power P at the wheels (tractive force eta P / v) against rolling, aerodynamic and grade resistance. A truck slowing on an upgrade towards its crawl speed is covered too (v2 < v1); both speeds must lie on the same side of the speed at which the power balances the resistance.
m vehicle mass [kg]P engine power [W]v1 initial speed [m/s]v2 final speed [m/s]C_D drag coefficientA frontal area [m^2]rho air density (default 1.2 kg/m^3) [kg/m^3] optionalf_r rolling resistance coefficient (default 0.015) optionalG grade, decimal (positive uphill) optionaleta drivetrain efficiency (default 1) optionalgamma mass factor for rotating parts (default 1) optionalt time to change speed (s) [s]d distance travelled (m) [m]transport_coast_downTime and distance for a vehicle coasting in neutral to slow from v1 to v2 under rolling resistance f_r, the grade and aerodynamic drag rho C_D A v^2 / 2.
m vehicle mass [kg]v1 initial speed [m/s]v2 final speed [m/s]C_D drag coefficientA frontal area [m^2]rho air density (default 1.2 kg/m^3) [kg/m^3] optionalf_r rolling resistance coefficient (default 0.012) optionalG grade, decimal (positive uphill) optionalgamma mass factor (default 1) optionalt coast-down time (s) [s]d coast-down distance (m) [m]transport_acceleration_distanceDistance and time for a vehicle to accelerate from v1 to v2 at a constant acceleration a (for example the length of an acceleration lane).
v1 initial speed [m/s]v2 final speed [m/s]a acceleration [m/s^2]d distance travelled while accelerating (m) [m]t time taken (s) [s]transport_traction_limited_accelerationThe largest tractive force the road can transmit (rear-, front- or all-wheel drive), the resulting maximum acceleration and the dynamic axle loads, with weight transfer from a centre of gravity at height h and rolling resistance f_r (aerodynamic drag neglected, level road).
m vehicle mass [kg]L wheelbase [m]l_f distance from the front axle to the centre of gravity [m]h height of the centre of gravity [m]mu tyre-road friction coefficientf_r rolling resistance coefficient (default 0) optionaldrive driven axles: rear, front or all choice optionalF_max maximum tractive force (N) [N]a_max maximum acceleration (m/s^2) [m/s^2]W_f front axle load (N) [N]W_r rear axle load (N) [N]transport_safe_following_gapSmallest initial gap that avoids a rear-end collision when a leader brakes at a_l and the follower, at the same initial speed, reacts after t_r and brakes at a_f (the closest approach can happen while both still move).
v initial speed of both vehicles [m/s]t_r follower reaction time [s]a_l deceleration of the leader [m/s^2]a_f deceleration of the follower [m/s^2]gap minimum safe initial gap (m) [m]transport_overtaking_manoeuvreA vehicle that starts at the speed v of the vehicle it passes accelerates at a until it has gained the relative distance s (initial gap + both lengths + final gap): the time, its distance travelled and its final speed.
v speed of the overtaken vehicle (and initial speed of the passing vehicle) [m/s]a acceleration of the passing vehicle [m/s^2]s relative distance to gain [m]t time to complete the overtaking (s) [s]d distance travelled by the passing vehicle (m) [m]v_f final speed of the passing vehicle (m/s) [m/s]transport_top_speedThe steady top speed at which the power at the wheels eta P equals the power absorbed by rolling, aerodynamic and grade resistance: rho C_D A v^3/2 + m g (f_r cos(theta) + sin(theta)) v = eta P.
m vehicle mass [kg]P engine power [W]C_D drag coefficientA frontal area [m^2]rho air density (default 1.2 kg/m^3) [kg/m^3] optionalf_r rolling resistance coefficient (default 0.015) optionalG grade, decimal (positive uphill) optionaleta drivetrain efficiency (default 1) optionalv_max top speed (m/s) [m/s]v_max_kmh top speed (km/h)transport_vehicle_resistanceRolling resistance f_r m g cos(theta), aerodynamic drag rho C_D A v^2/2 and grade resistance m g sin(theta) (tan theta = G) of a road vehicle at a speed, their sum and the power needed to overcome them.
m vehicle mass [kg]v speed [m/s]C_D drag coefficientA frontal area [m^2]rho air density (default 1.2 kg/m^3) [kg/m^3] optionalf_r rolling resistance coefficient (default 0.015) optionalG grade, decimal (positive uphill) optionalF_roll rolling resistance (N) [N]F_aero aerodynamic drag (N) [N]F_grade grade resistance (N) [N]F_total total resistance (N) [N]P power to overcome the resistance (W) [W]P_kW power (kW)15 files, 43 MB in total. The largest:
| File | Size |
|---|---|
| model.safetensors | 18.9 MB |
| dist/transportation_ai999x-1.0.1-py3-none-any.whl | 14.9 MB |
| onnx/search/encoder.int8.onnx | 4.9 MB |
| docs/transportation_ai999x_capabilities.pdf | 3.2 MB |
| onnx/search/index.json | 403.3 KB |
| docs/transportation_ai999x_capabilities.html | 292.1 KB |
| docs/transportation_ai999x_capabilities.md | 229.3 KB |
| onnx/search/tokenizer.json | 176.4 KB |
| README.md | 21 KB |
| LICENSE | 11.4 KB |
| evaluation/release_gate.md | 2.3 KB |
| evaluation/KNOWLEDGE_CARD.md | 1.4 KB |
Transportation answers questions in transportation: vehicle dynamics, braking and stopping distances, traffic flow, highway geometry, railway operations, route planning and transit capacity. Each answer gives the value with its unit, the steps and the formula in LaTeX.
With pip: pip install transportation-ai999x. The same files are on Hugging Face (hf download AI999X/transportation-ai999x --local-dir transportation-ai999x) and GitHub.
Yes. It is a Python package that runs on an ordinary CPU without a network connection (Python >=3.10); no GPU and no API key are needed.
77 capabilities in 13 topics, including Traffic flow, Highway geometry, Vehicle dynamics, Vehicle performance, Braking and stopping.
Field: Engineering. Tasks: Question Answering, Token Classification, Text Classification, Sentence Similarity, Feature Extraction.
Asked "Stopping sight distance with speed = 100 km/h, reaction time = 2.5 s and deceleration = 3.4 m/s^2.", it answers: SSD = 182.916 m, d_r = 69.4444 m, d_b = 113.471 m.
It says so and names what is missing or out of range, instead of guessing a number.