Transportation Revenue Forecasting: Theory and Models. Moshe Ben-Akiva / / ESD.210 Transportation Systems Analysis: Demand & Economics

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1 Transportation Revenue Forecastg: Theory and Models Moshe Ben-Aiva / / ESD.210 Transportation Systems Analysis: Demand & Economics Fall 2008 Overview Increasg reliance on private sector fancg of transportation projects (particularly toll roads) has emphasized the importance of accurate revenue forecastg Ma factors of revenue forecastg: Pricg/tollg strategy Travel demand forecastg Traffic assignment 2

2 Outle Review Basic Pricg Concepts Public Sector Pricg Private Sector Pricg Revenue Forecastg Forecastg Accuracy Sources of Uncertaty Enhanced Methods Conclusion 3 Review of Public Sector Pricg Maximize welfare Margal cost pricg Under constrats Cost recovery: Ramsey pricg Distortions: second-best pricg 4

3 Review of Private Sector Pricg Maximize profit or revenue Perfectly competitive maret Price close to margal cost Less competitive maret Price discrimation 5 Outle Review Basic Pricg Concepts Revenue Forecastg Forecastg Accuracy Sources of Uncertaty Enhanced Methods Conclusion 6

4 Revenue Forecastg Revenue forecastg is essential for assessg fancial feasibility and project approval Here we focus on toll roads and toll bridges 7 Forecastg Accuracy Few examples where actual revenue exceeded the forecast Many examples where actual traffic demand and revenue have significantly lagged the forecasts Dulles Greenway Virgia went to default 1996, when toll revenues were less than the forecast (20% of the forecast its first year of operation; and only 35% its fifth year) 8

5 Forecastg Accuracy (cont.) 68 case studies durg 2003 of traffic forecastg for ternational toll roads Ratio of actual/forecast traffic volumes follows a normal distribution with average 0.74 and standard deviation 0.26 Image removed due to copyright issues. Source: Ba, R. and Plantagie, T.W. (2003), Traffic Forecastg Ris: Study Update 2003, Standard & Poor s RatgsDirect, the McGraw-Hill Companies, New Yor, [Onle], May 2008, Available at: 9 Forecastg Accuracy (cont.) Examples: Actual revenue as percentage of forecast Facility Year of openg Year 1 Year 2 Year 3 Year 4 Year 5 Florida's Turnpie Enterprise/ Sawgrass Expressway Orlando-Orange Expressway Authority/Central Florida Greenway North Segment State Road and Tollway Authority (Georgia)/GA 400 Transportation Corridor Agencies (California)/San Joaqu Hills Santa Rosa Bay Bridge Authority (Florida)/Garcon Pot Bridge Pocahontas Parway Association (Virgia)/Pocahontas Parway % 23.4% 32.0% 37.1% 38.4% % 85.7% 81.4% 69.6% 77.1% % 133.1% 139.8% 145.8% 141.8% % 47.5% 51.5% 52.9% 54.1% % 54.8% 50.5% 47.1% 48.7% % 40.4% 50.8% NA NA Figure by MIT OpenCourseWare. Source: Kriger, D., Shiu, S. and Naylor, S. (2006), Estimatg Toll Road Demand and Revenue, National Cooperative Highway Research Program Synthesis 364, Transportation Research Board, [Onle], May 2008, Availble at: 10

6 Sources of Uncertaty Revenue forecastg is based on: Travel forecasts: models and assumptions on which the travel forecasts were based, such as economic growth, land use, and changes traffic patterns The tollg schedule and structure, e.g., by vehicle type The enforcement of toll collection Revenue is estimated by multiplyg the forecasted traffic volumes by the toll amount, tag to account different toll rates by vehicle type, potential toll evasion, and discounts 11 Sources of Uncertaty: Modelg The four-step modelg process is widely used for traffic demand forecastg Travel demand models tended for regional planng purpose may not be appropriate for toll roads Steady-state forecast does not corporate the lielihood of traffic fluctuations durg economic cycles Pea-hour travel characteristics do not represent annual traffic demand, typically required for toll road revenue forecasts Limited data on weeend/truc traffic patterns Value of time is heterogeneous and difficult to estimate 12

7 Sources of Uncertaty: Input Data Demographic, socioeconomic and land-use variables, e.g., population, economic growth, employment, and zone defition Transportation networ Travel characteristics, e.g. orig-destation demand, travel cost, traffic counts and speeds, stated preferences data Individual value of time or willgness to pay Tollg amount and structure 13 Other Sources of Uncertaty Traffic ramp-up period High fancial ris durg the itial years of operation Traffic volumes may be lower than forecasted as drivers slowly become aware of the toll facility and time savg, or if population or economic growth is less than forecasted Event and political effects, e.g. competg roads 14

8 Outle Review Basic Pricg Concepts Revenue Forecastg Enhanced Methods Activity-based models Travel choice models (eg time, mode, path) Traffic Assignment (simulation & dynamic models) Models with heterogeneous value of time Travel time reliability Uncertaty of forecast results Conclusion 15 Preference Heterogeneity: An Example SR-91 California, USA Source: Tian, X., Kularni, A. and Jha, M. (2008), Modelg Congestion Pricg, presented at Worshop on Traffic Modelg: Traffic Behavior and Simulation, University of Technology, Graz, Austria Google map image of California highway SR-91 removed due to copyright restrictions. 16

9 Toll Rates SR-91 Express Express Lanes Lanes Toll Toll Schedule Toll Toll Rate $9.00 $8.00 $7.00 $6.00 $5.00 $4.00 $3.00 $2.00 $1.00 $ 0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 0:00 Time EB WB 17 Travel Time Difference between HOT and General Purpose Lanes: AM Total Traffic (Tolled & Untolled) :00 6:30 7:00 7:30 8:00 8:30 Time Travel TimeDifference 15 Mute Count Travel Time Difference (HOT-G.P.Ln) 18

10 Travel Time Difference between HOT and General Purpose Lanes: PM 1200 All EB Traffic Tolled 4PM 6PM 0.00 Total Traffic (Tolled & Untolled) :00 15:30 16:00 16:30 17:00 17:30 18:00 18:30 Time Travel Time Difference 15-Mute Count Travel Time Difference (HOT-G.P.Ln) 19 Heterogeneous Value of Time Value of time (VOT) or willgness to pay (WTP) varies by Trip purpose Time-of-travel Travel mode Vehicle occupancy Congestion levels Trip length Socio-economic variables, e.g. come, gender, occupation and education level 20

11 Heterogeneous Value of Time: Explicit Segmentation An explicit segmentation of the correspondg assignment, mode choice and time-of-travel choice models, while assumg a sgle average VOT with each segment Limitations: Requires multi-class assignment with a large number of segments Problematic when different choice dimensions use different segmentation Does not account for with-segment variability 21 Heterogeneous Value of Time: Explicit Segmentation (cont.) Example: VOT estimates for toll road users Montreal model Source: Vovsha, P., Davidson, W. and Donnelly, R. (2005), Mag the state of the art the state of the practice: advanced modelg techniques for road pricg, Expert Forum on Road Pricg and Travel Demand Modelg, Volpe National Transportation Systems Center, [Onle], May 2008, Available at: 22

12 Distributed Value of Time Probabilistic distribution of VOT stead of determistic values, with a correspondg adjustment of the structure of the assignment, mode choice, and time-of-travel choice models Latent Class Choice Model Discrete distribution of VOT Gopath, D.A. and Ben-Aiva, M. (1997), Estimation of randomly distributed value of time, Worg paper, Department of Civil and Environmental Engeerg, Massachusetts Institute of Technology. Random Coefficient Logit Model Contuous distribution of VOT Coefficients for travel time and travel cost, or their ratio (VOT), is assumed to be randomly distributed 23 Distributed Value of Time (cont.) Ben-Aiva, M., Bolduc, D. and Bradley, M. (1993), Estimation of travel choice models with randomly distributed value of time, Transportation Research Record, vol. 1413, pp Value of time U i = µ c i + β 'Y i + ν ( t i + γ ' Z i ) + ε i c i t i Y i = travel cost of alternative = travel time of alternative = vector of additional variables for alternative i (may clude teractions with ) Z i = vector of additional variables for alternative i, whose coefficients vary proportionally to the time coefficient (may clude teractions with ) ε i c i = additive error terms µ = scale parameter β,γ = unnown parameters i i t i 24

13 Distributed Value of Time (cont.) Choice probability for a lognormal distribution of VOT lnν : N ( ω,σ 2 ) 2 1 exp{ µ [ ci + β ' Yi + ν ( ti + γ ' Zi )]} 1 1 ln ν ω P ( i) = d ν J σ π exp 2 ν σ 0 µ c j + β Y j + ν t j + γ Z 2 exp{ [ ' ( ' j )]} j = 1 where µ, β,γ,ω,σ are the parameters to be estimated simultaneously usg maximum lielihood 25 Distributed Value of Time (cont.) 1988 stated preferences survey Netherlands Asymmetric distribution sewed to the left of the mean, with a mimum value 0 and a tail to the right 1.00 Other:F(v) Cumulative probability Other:f(v) Comm:f(v) Comm:F(v) Bus:F(v) Bus: Busess Comm: Commutg Bus:f(v) Value of time: v (1988 fl/hour) Figure by MIT OpenCourseWare. 26

14 Travel Time Reliability Motivation Unreliability is one of the primary costs of road congestion There is evidence that people choose toll roads for reliability, even when there are no obvious travel time savgs Examples of reliability measures The standard deviation The difference between the 90 th percentile and the median Value of reliability (VOR) Willgness to pay for reduction the day-to-day variability of travel time 27 Modelg Route Choice with Travel Time Reliability Lam, T.C. and Small, K. (2001), The value of time and reliability: measurement from a value pricg experiment, Transportation Research Part E, vol. 37, pp Revealed preferences survey (1998) of commuters on State Route 91 Orange County, California Travel time measured with loop detectors Bary Logit choice model of two parallel routes (either free or with variable toll) 28

15 Modelg Route Choice with Travel Time Reliability: Model Specification Variables cluded: Travel time median + teraction with a distance function Travel time unreliability (difference between the 90 th percentile and the median) + teraction with gender Travel cost Socio-economic variables 29 Modelg Route Choice with Travel Time Reliability: Estimatg VOR U VOR VOT = V n n = = ( t, υ,c,x ) ( V υ ) ( V c ) ( V t ) ( V c ) n n + ε n n where : U t = utility of alternative i for dividiual n = travel time υ = travel time variability c = travel cost x = other attributes or characteristics ε = error term 30

16 Modelg Route Choice with Travel Time Reliability: Estimation Results VOT Trip distance miles (%) 13 (5%) 27 (25%) 37 (50%) 40 (mean) 50 (75%) 74 (95%) 92 (99%) VOT ($/h) VOT/mean wage (%) 16% 59% 76% 79% 84% 51% -13% VOR Gender Male Female VOR ($/h) VOR/mean wage (%) 38% 94% 31 Estimation of Uncertaty Uncertaty of Revenue Forecastg is unavoidable Inherent uncertaty the assumptions about future events and errors the forecastg procedure Expected value may have large variance and bias Probability distribution of forecast results Monte-Carlo simulation Simplified methods 32

17 Simplified Method of Estimatg the Uncertaty Bowman, J.L., Gopath, D. and Ben-Aiva, M. (2002), Estimatg the probability distribution of a travel demand forecast, Worg paper, Department of Civil and Environmental Engeerg, Massachusetts Institute of Technology. Requires fewer model runs to estimate elasticities of forecast w.r.t. critical factors affectg uncertaty 33 Simplified Method of Estimatg the Uncertaty (cont.) Step 1: Identify dependent sources of uncertaty (e.g., economic growth, model error and value of time), and estimate a probability distribution of each source x = ( x 1,..., x,... x K ) x, n = 1,..., N n p ( x ), n = 1,..., N n s.t. ( ) N p x n = 1 n =1 x where is the vector of sources that duces errors the n forecast; x n is a discrete outcome of x, and p ( x ) is its correspondg probability 34

18 Simplified Method of Estimatg the Uncertaty (cont.) Step 2: Defe a set of scenarios S, and compute the probability of each scenario, p( s), under the assumption of dependence of error sources n 1 {(,..., n n K S = x1 x,..., xk ); n = 1,..., N ; = 1,..., K} n ( s) p ( s) = = p( x ); s S Step 3: Assume travel demand constant elasticity e r = a r depends on each source with a K =1 ( x ) e and perform model runs to estimate these elasticities K 1 35 Simplified Method of Estimatg the Uncertaty (cont.) Step 4: Calculate travel demand for each scenario the predicted value r ( p) r (s) = r p ( ) K n x ( s ) n ( p) =1 x e, s S ( ) r s based on ( ) All pairs of r ( s) and p s provide an estimated discrete approximation of r 's probability distribution function 36

19 Simplified Method of Estimatg the Uncertaty (cont.) Example: Estimated cumulative distribution function of 2001 revenue of a new transit system a major Asian city Total 16 sources of uncertaty, such as economic growth, model errors, transit captivity, VOT, measurement errors, operatg speeds and headways 37 Conclusion Knowledge of demand and price sensitivities is critical Traffic simulation, dynamic traffic assignment, activity-based models, time-of-travel choice models, distributed value of time, and travel time reliability are needed to improve forecastg accuracy Uncertaty revenue forecasts can be estimated 38

20 Additional Readgs Ben-Aiva, M., Bolduc, D. and Bradley, M. (1993), Estimation of travel choice models with randomly distributed value of time, Transportation Research Record, vol. 1413, pp Bowman, J.L., Gopath, D. and Ben-Aiva, M. (2002), Estimatg the probability distribution of a travel demand forecast, Worg paper, Department of Civil and Environmental Engeerg, Massachusetts Institute of Technology. Gopath, D.A. and Ben-Aiva, M. (1997), Estimation of randomly distributed value of time, Worg paper, Department of Civil and Environmental Engeerg, Massachusetts Institute of Technology. 39 Additional Readgs (cont.) Kriger, D., Shiu, S. and Naylor, S. (2006), Estimatg Toll Road Demand and Revenue, National Cooperative Highway Research Program Synthesis 364, Transportation Research Board, [Onle], May 2008, Availble at: Lam, T.C. and Small, K. (2001), The value of time and reliability: measurement from a value pricg experiment, Transportation Research Part E, vol. 37, pp

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