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History of Urban Development • Early cities supported by links to water (harbors & rivers) and later rail & highways • City core + moderate density residential; radial highway and transit links (streetcars, rail, & later bus) • Add low-density suburbs; urban & suburban freeways (1960s & 70s) • Add suburban and exurban centers; arterial & freeway expansion, decline of transit Trans-based Services & Costs • Many transportation-related services in urban areas + public transit + private auto use • Costs of the services tend to increase with city size, but opportunities for jobs, etc. also increase: Optimal city size? • Externalities – pollution and congestion Urban Transportation Modes • Private auto – “driver only”, carpool • Van-pool; bus-pool • Taxi • Buses • Light Rail – at-grade/some grade separation • Rail Rapid Transit • Other: Commuter Rail, Ferry Urban Transportation Issues • Traffic congestion • Peaking (inefficient use of facilities) • Infrastructure financing • Specialized transit (elderly & disabled) • Environment • Safety • Technological Innovation Transportation Problem Solutions • Pricing – roadway tolls, parking costs, transit fares, fuel taxes, regional road pricing • Management & policy – ramp-metering, land use controls, flexible work hours, bus/ped malls, parking/delivery controls, improved public transit, high-occupancy veh incentives • Advanced technology Advanced Technology • Informatics (Intelligent Transportation Systems – Driver Information Services) – Variable Message Signs (VMS), route guidance, in-vehicle navigation • Safety – collision warning/avoidance, night vision • Capacity – headway control (liability issues), bus rapid transit Advanced Technology – con’t • Pricing – Electronic Toll Collection (ETC), congestion pricing (using ETC) – equity issue, but large system benefits • Environment – emissions controls, alternative fuels (fuel cells), hybrid vehicles • Telecommunications – Telecommuting, teleshopping, teleconferencing ITS – User Services Groups • Travel and Transportation Management • Public Transit Operations • Electronic Payment • Commercial Vehicle Operations (CVO) • Emergency Management • Vehicle Control and Safety Systems Urban Trans Planning Process • Base Data: trans sys, activity sys, demand • Problem Definition UTP Models • Goals & Objectives • Alternative Solutions • Evaluate Solutions UTP Models • Select Best Plan • Implement • Monitor Urban Trans Planning Models • Activity System (land use) – Population and Employment by zone • Trip Generation: How many trips? • Trip Distribution: Which destination? • Modal Choice: Which mode? • Assignment: Which route? • Output: Level of Service by mode TRANSPORTATION PLANNING i j Trip Generation Pi Aj k Qik Qij i j Trip Distribution TRANSPORTATION PLANNING Qijm CAR i BUS j SUBWAY Modal Choice Qijmp i j Network Assignment (Trip Assignment) Trip Generation Models • Objective: forecast number of person trips that begin or end in a travel analysis zone for a typical day in a target year Future Land Calibrated Trip Ends Use & Socio- Trip QI and QJ Econ Activity Generation or by Zone Model PI and AJ • Prior to application, model must be calibrated using travel data for base year • Model output - trip ends by zone • Trip ends are estimated by trip purpose: – 1) work – 2) school – 3) shopping – 4) social/recreation – 5) personal business/medical Time-of-day distribution of trips by purpose 1) “purpose to” definition - going to work, to school, to home 2) peaking AM with work and school trip PM with “to home” and all other trips 3) peak spreading in PM Zonal vs household-based models 1) zonal: direct estimate of total trips in travel analysis year based on zonal attributes 2) household: combine contributions of groups of similar households to obtain total trips for a zone Productions and Attractions 1) trips are assumed to be produced at the “home” zone and attracted to the “non-home” zone, e.g. Home-based Work 2) trip origin & destination is based on the direction of a trip (from “origin” to “dest.”) Home Work Home Work 2 Productions 2 Attractions Productions and Attractions 3) generally will have some productions, PI, and attractions, AJ, in each zone 4) Trip with neither “end” at “home” is a Non-Home Based (Non-HB) trip Home Work Shop Home Zone 1 Zone 2 Zone 3 Zone 1 HB-Work Non-HB HB-Shop Regression Models • Yi = a0 + a1*X1i + a2*X2i + … + aN*XNi where: Yi - trip ends for the ith household or zone XNi - Nth attribute of the ith household or zone 1) Model calibrated using travel survey data for the base year. 2) Apply model to estimate future “trip ends” based on projections of the values of the independent variables, XNi. • Must be linearly related to the dependent variable • Must be highly correlated with the dependent variable • Must not be highly correlated between themselves • Must lend themselves to relatively easy projection Typical Independent Variables 1) Income 2) Auto ownership 3) Household size 4) Land use density 5) Number of employees (attractions) 6) Sq. feet of floor area (attractions) The correlation matrix contains the simple correlation coefficients between pairs of variables computed by Eq C.3.4 using base-year data. Which explanatory variables X should be included in a linear multiple regression? Y X1 X2 X3 X4 Y 1.00 0.32 0.92 0.95 0.62 X1 1.00 0.25 0.19 0.03 X2 1.00 0.99 0.29 X3 1.00 0.33 X4 1.00 Trip Rate Analysis • Trip rates are expressed with respect to the intensity of use at specific traffic generators • PI = Σ Rk * Xk where: • PI - total trip productions in zone I • Rk - trip prod. per unit of the kth land use type • Xk - number of units of the kth land use type - ITE TG Manual example - Office Park Cross-classification Models • Represent extension of simple trip rate models • generally developed at household level • stratify the “trip ends” by the independent variables (typically two) and estimate the mean trip rate within each cell • See Table 8.2.4 - Total HB-NonWork Trip Rates Cross-classification Models-con’t • Estimate total hsld trip productions in zone I as: PI = ∑ nqr * Rqr where: nqr - no. households of category qr Rqr - daily trip rate for category qr Cross-classification Models-con’t Estimate the trip rate in the qr th cell of the cross- classification matrix by: Rqr = [∑ Pqrk ]/nk where: Pqrk - no. trip productions by kth household in the qr th category nk - no. households in the category qr Trip Distribution • Objective: estimate future trip volumes, QIJ, between zones I and J • Assumptions: – All attraction zones, J, in competition w/others – Trips to J are proportional to “attractions” AJ – Trips I to J are inversely proportional to WIJ, the impedance (time, distance, cost) from I to J Gravity Model QIJ = k * PI*AJ/WIJc where: PI – number of trip productions in zone I AJ – number of trip attractions in zone J or relative attractiveness index WIJ – impedance (time, distance, or cost) between zones I and J k, c – calibration parameters Gravity Model Derivation • Trip production balance equation is: PI = ∑X QIX Thus, all trip productions in zone I are “distributed” to attraction zones • Substitute the trip interchange expression into the trip-production balance equation so: PI = k * PI * [∑X AX / WIXc ] Gravity Model Derivation-con’t • Solving for k: k = 1/ [∑X AX / WIXc ] so QIJ = PI {(AJ / WIJc )/ [∑X AX / WIXc ]} Note: the term in brackets is not affected by multiplying all the A by a constant. So “zonal attractiveness” can be measured by employment or GFA where appropriate. Also QIJ = PI {AJ FIJ/ [∑X AX FIX]} with FIJ =1 / WIJc where FIJ is the friction factor or travel time factor Gravity Model Derivation-con’t • Trip attractions to zone J from GM output: AJ* = ∑X QXJ In general AJ* ≠ AJ , thus, must “balance attr.” • Add inter-zonal “soc-economic”factors, KIJ as selective adjustments to the Gravity Model QIJ = PI {AJ FIJ KIJ /[∑X AX FIX KIX]} QIJ = PI * pIJ where: pIJ - proportion of trips attracted to zone J GM Application – Example 8.4 Zone Productions Attractiveness 1 1500 0 2 0 3 3 2600 2 4 0 5 Inter-zonal Impedances (minutes) J Z1 Z2 Z3 Z4 I Z1 5 10 15 20 Z2 10 5 10 15 Z3 15 10 5 10 Z4 20 15 10 5 GM Calculations- I=1;P1=1500 J AJ F1J AJ F1J p1J Q1J 1 0 .0400 0 0 0 2 3 .0100 .0300 .584 875 3 2 .0044 .0089 .173 260 4 5 .0025 .0125 .243 365 Sum .0514 1.00 1500 GM Calculations- I=3;P1=2600 J A w3J F3J AJ F3J p3J Q3J 1 0 15 2 3 10 3 2 5 4 5 10 Sum 1.00 2600 GM Output – “Trip Table” I J Z1 Z2 Z3 Z4 Z1 0 875 260 365 1500 Z2 0 0 0 0 0 Z3 0 488 1300 812 2600 Z4 0 0 0 0 0 Sum 0 1363 1560 1177 4100 0 33.2% 38.0% 28.7% 100% AJ 0 3 2 5 10 Trip Frequency Distribution wIJ 5 10 15 20 Total Avg. 1300 875 260 365 488 812 GMSum 1300 2175 260 365 4100 9.6 OD 870 2390 290 550 4100 10.6 Gravity Model Calibration 1) Compare average trip length – GM vs OD Survey trip frequency distributions 2) Reasonable fit? 1) Yes – model calibrated 2) No – Adjust “friction factor” curve F vs w Fnewk = Fpriork * [OD tripsk/GM tripsk] Where k – kth interval of the impedance w • Compute new trip table and go to 1) Trip Generation+GM Example 8.5 • Home-based Shopping Trips – 3 residential zones (1, 2, 3) & 2 commercial zones (4,5) • Trip Generation-Trip Production Model – HB Shop Productions – cross-classification – Matrix of trip rates (trip productions per person) for persons per household vs # of autos stratified by income level (level I or level II) – Apply household data for residential zones to estimate zonal trip productions • Trip Generation – Trip Attraction Model – “Attractiveness” model based on simple weighting of : – 1) shopping floor space (acres) – Xa – 2) parking area (acres) – Xb – For a zone the attractiveness, A, is: A = 5* Xa + 3* Xb • Gravity Model – Friction Factor & K values F = 1/wIJ Gravity Model Input Values I Z4 - CBD Z5 - Center PI J w F K w F K Z1 20 .05 1.0 5 .20 .09 670 Z2 10 .10 .09 10 .10 1.2 850 Z3 5 .20 1.0 20 .05 1.0 1640 AJ 22.5 19.0 GM Calculation – Zone 1 J AJ*F1J*K1J p1J Q1J 4 22.5*0.05*1.0 = 1.125 0.248 166 5 19.0*0.20*0.9 = 3.420 0.752 504 Sums 4.545 1.00 670 GM Results – Trip Table I J 4 (CBD) 5 (Center) PI 1 166 504 670 2 400 450 850 3 1354 286 1640 AJ* 1920 (61%) 1240 (39%) 3160 (100%) AJ 22.5 (54%) 19.0 (46%) 41.5 (100%) Discussion of TG/TD Model • Able to estimate future travel patterns given forecasts of population and land use • Trip Generation Limitations: – Are trip rates stable over time? – Precision of estimate of population & land use? • Gravity Model – Attractions do not balance – Includes primary factors, PI, AJ, wIJ – Models completely new development (synthetic) Trip Distribution - Summary • Estimate QIJ given PI, AJ, wIJ, FIJ, KIJ • Use Gravity Model – Distribute all productions (share model) – Attractions don’t balance [AJ* ≠ AJ ] – AJ and FIJ are scale independent – Calibrate by adjusting FIJ to match the GM trip length frequency distribution with the OD data – Synthetic model – apply to new development Mode Choice – Which mode? • Important for : • 1) Investment decisions – Madison – Milwaukee – Chicago • 2) Operational decisions – Route changes – Frequency of service (headway) Mode Choice Behavior • Depends on “attributes” of: 1) transportation system – time, cost, comfort, convenience 2) tripmaker – auto available, income, employed, family needs 3) trip – purpose, time-of-day Transit Ridership Groups • Transit Captives – Lack access to private auto – Who? – elderly, young, disabled – Estimate as percentage of trips in a zone • Choice Riders – Choose between public transit & private auto – Apply “mode choice” model Mode Choice Model Types • Pre-distribution (trip-end) – Household based – Focus on transit captives – Transportation system attributes – accessibility • Post-distribution (trip interchange) – Consider individual traveler – Trans. System attributes – transit vs auto – Consider alternative modes Post-Distr – Logit Model • Probability-based model • Describe alternative modes by a utility function • Probability of choosing an alternative involves an exponential function of utility Utility Function • Measures degree of satisfaction • Disutility measures generalized cost (analogous to impedance) • Value of utility depends on attributes of: – Mode – Trip-maker – Trip • Calibrate at individual trip level (disaggregate) to obtain choice behavior – “behavioral model” • Assume a linear utility function: • U = a0 + ∑ i ai * Xi where – Xi attributes of trip, trip-maker and mode – ai – model parameters • Model parameters can be “mode-specific” or “attribute specific” (mode abstract) • Consideration of new modes requires attribute specific model Multinomial Logit Model p(k) = exp(Uk)/ ∑ x exp(Ux) where p(k) – proportion of trips made by mode k Uk – utility function for mode k • For two alternative modes, have binomial logit model represented graphically as a sigmoidal (logistics) curve P(k=1) = 1/[1 + exp(U2-U1)] Example 8.9 – Logit Model • Utility equation: Uk = ak-0.025X1-0.032X2-0.015X3-0.002X4 • Where: – X1 – walk (at trip begin & end) time (minutes) – X2 –wait time (minutes) – X3 – line-haul (in-vehicle) time (minutes) – X4 – out-of-pocket costs (cents) – ak – mode specific constant (bias term) Mode Attribute Values Attribute Auto Bus RTransit Access time 5 10 10 Wait time 0 15 5 Line-haul time 20 40 30 Cost 100 50 75 Constant term -0.12 -0.56 -0.41 Estimated Market Share • For auto vs bus: – U(A) = -0.745 and U(B) = -1.990 so – p(A) = 0.78 and p(B) = 0.22 & for QIJ=5000 – QIJ(A) = 0.78*5000 = 3900 trips/day and – QIJ(B) = 0.22*5000 = 1100 trips/day • Transit revenue – 1100trips/day * $0.50/trip = $550 per day Market Share – Three Modes • For auto vs bus vs rapid transit (new mode) U(A)= -0.745 U(B)= -1.990 U(RT)=-1.420 p(A) = 0.56, p(B) = 0.16 and p(RT) = 0.28 – QIJ(A) = 0.56*5000 = 2800 trips/day and – QIJ(B) = 0.16*5000 = 800 trips/day – QIJ(RT) = 0.22*5000 = 1400 trips/day • Transit revenue – 800*$0.50 + 1400*$0.75 = $1450 per day Logit Model Properties • Relative use of auto vs bus is independent of other modes: p(B)/p(A) = exp(UB)/exp(UA) • Implied “value of travel time” (cents/min): Line-haul time – a3/a4 [(1/min)/(1/cents)] = 7.5 Wait time – a2/a4 [(1/min)/(1/cents)]=16 • Value of wait time = 2 * (line-haul time) Network Assignment • Concerned with choice of path • Solution represents equilibrium point between supply and demand curves • Supply curve represents reciprocal of speed- volume curve • Analyze equilibrium flows using capacity analysis to obtain LOS Input to Assignment Models • Person trips vs vehicle trips – Person trips needed for transit assignment – Vehicle trips needed for highway assignment • Peaking of trips – Trips usually estimated for “average day” – Need peak-hour volumes to estimate LOS – Solution: 1) factor “avg. day” or 2) model peak- hour volumes directly (e.g., HB Work trips) Input to Assignment Models • Trip direction – Account for directional flow – Use factors based on historical data Diversion Curve Models • Developed in 1950s and 60s (empirical) • Estimate diversion from arterial to freeway • Not used today • Unable to handle: – Multiple path choices – Alternative path with mix of freeway and arterial Network Assignment Methods • Require: 1) way of coding a network model 2) understanding of factors influencing trip- maker’s preferences (route choice) 3) computer algorithm able to generate preferred paths (route generation) Highway Network Model • Typical street map (all streets) • Coded traffic assignment network – Excludes local and minor streets – System of links and nodes – link attributes (capacity, volume, speed, travel time) – Travel analysis zones: 1) coded as zonal “centroids” 2) connected to network–“centroid connectors” Route-Choice Behavior • Trip-makers consider impedance of competing paths in selecting travel path • Alternative assignment methods: • 1) all-or-nothing (minimum time path) – Often not realistic – Expect equilibrium where travel times are equal for competing paths Route-Choice Behavior – con’t • Alternative Assignment methods: • 2) multipath – Allocates trips to “all reasonable paths” • 3) Capacity Restrained vs unrestrained – Link travel time is a function of the link volume to capacity ratio – Requires iterative solution Minimum Path Algorithms • Minimum tree = all interzonal minimum paths that begin with a given zone • Minimum time path only requires: – 1) time to node (from the origin node) – 2) prior node on the path (direction of approach) – 3) computer representation using a “tree table” • Example 5 node network & assignment Capacity Restrained Assignment • 1) All-or-nothing assignment (20% of trips) • 2) Adjust link travel times based on assigned link volume to link capacity ratio using: t = t0[1 + 0.15(q/cap)**4] • 3) Perform new assignment with revised travel times and next 20% of trips and go to step 2) (4 iterations) • 4) Add assigned volumes (five assignments)