The 6 th Conference on Applied I nfrastructure Research ( I nfraday) The 6 th Conference on Applied I nfrastructure Research ( I nfraday) Berlin - - October 2 0 0 7 October 2 0 0 7 Berlin Revisiting the Estim ation of the Revisiting the Estim ation of the Marginal Cost of Highw ay Marginal Cost of Highw ay Maintenance Maintenance Shadi B. Anani and Sam er M. Madanat University of California, Berkeley
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat I ntroduction I ntroduction � Obtaining accurate estimates of highway costs caused by each class of vehicles is an important component of: � Evaluation of current user charges � Design of new pricing strategies � Existing studies that estimate these costs have shortcomings. October 2007 2
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Outline of presentation Outline of presentation � Background information � Engineering � Economics � State-of-the-art in the estimation of marginal cost � Methodology � Results October 2007 3
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Background – – pavem ent deterioration pavem ent deterioration Background � Highway pavement deterioration is the loss of pavement performance. � Pavement performance can be expressed in terms of: � Distresses (cracking, rutting, etc.) � Roughness � Serviceability (a combination of roughness and some distresses) Cracking Rutting Roughness-measuring van October 2007 4 Photos: http: / / training.ce.washington.edu/ WSDOT/
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Background – – pavem ent deterioration m odels pavem ent deterioration m odels Background � A pavement deterioration model predict roughness, serviceability or a distress. Explanatory variables describe: Traffic loading Pavement structure Current condition Maintenance Environment Age � Traffic loading is the total number of deterioration equivalence factors (DEF) passing during a time period. The number of DEFs for a vehicle expresses the relative pavement deterioration level that it causes. � The axle loads of a vehicle determine its contribution to pavement deterioration. Number of DEFs per axle = (axle load/ constant) power October 2007 5
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Background – – equivalent single axle load equivalent single axle load Background � A commonly used DEF is the equivalent single axle load (ESAL), which assumes a power of four. � For a single axle, ESAL = (axle load in kips/ 18 kips) 4 October 2007 6
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Background – – pavem ent MR&R pavem ent MR&R Background � Pavement deterioration necessitates Photo: maintenance, rehabilitation and http: / / traini ng.ce.washi reconstruction (MR&R) activities. ngton.edu/ WSDOT/ Pothole repair � MR&R strategies can be non- condition- responsive or condition- responsive. A condition-responsive MR&R strategy October 2007 7
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Background – – m arginal cost m arginal cost Background � The cost caused to society by an additional unit of axle load � Classification of highway pavement marginal costs: Highway agency MR&R marginal cost Marginal private cost (vehicle operating cost) Other users marginal cost (other vehicles) Marginal social cost October 2007 8
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Background – – highw ay pricing highw ay pricing Background � Marginal cost pricing sets price equal to social marginal cost. � Advantages of marginal cost pricing: � Economic efficiency � Equity � Problems with highway pavement marginal cost pricing: � Difficulty in quantifying pavement marginal costs � Potential lack of cost recovery October 2007 9
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Approaches for estim ation of pavem ent m arginal cost Approaches for estim ation of pavem ent m arginal cost � Approaches used in the literature 1 : 1. The pavement management system direct approach 2. The simple roughness approach 3. The econometric approach 4. The cost allocation approach 5 . The perpetual overlay indirect approach ( POI A) � In the POIA, marginal costs are estimated by linking MR&R activities to pavement deterioration, and thus to traffic loading: Traffic Pavement MR&R MR&R a b c loading deterioration activities Cost 1. Based on Bruzelius (2004) October 2007 10
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat The perpetual overlay indirect approach ( POI A) The perpetual overlay indirect approach ( POI A) � Assumes a condition-responsive MR&R strategy that uses only overlays. � Uses an infinite planning horizon. � Uses ESAL as DEF. An additional ESAL is defined either as a one-time event or a recurring annual event . � Assumes pavement deterioration and overlay effectiveness are deterministic. p p p . . . time 0 T 2T 3T Perpetual overlay costs October 2007 11
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Com m on assum ptions Com m on assum ptions � POIA studies make three unrealistic assumptions: The first common assumption is that the increase in pavement deterioration is proportional to the fourth power of the axle load. � The fourth power was obtained from the AASHO Road Test by defining deterioration as loss in serviceability . However, other definitions of deterioration are often used in practice. Photo: FHWA website Measuring axle load October 2007 12
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Com m on assum ptions Com m on assum ptions � The power used for DEF should depend on the type of deterioration, as the table shows: Type of Deterioration Pow er used for DEF Relevant study Prozzi & Madanat Loss of serviceability 4.15 (2004) Prozzi & Madanat Increase in roughness 3.85 (2004) 2 .9 8 (for single axle) Archilla & Madanat Increase in rutting 3.89 (for tandem axle) (2000) October 2007 13
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Com m on assum ptions Com m on assum ptions The second common assumption is that the only MR&R activity used by a highway agency is an overlay of constant intensity. � In reality, highway agencies often use strategies with multiple MR&R activities. � Different MR&R activities are triggered by different indicators of pavement overlay performance (cracking, rutting, Photo: roughness, etc.) http: / / training.ce.washington.edu/ WSDOT/ October 2007 14
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Com m on assum ptions Com m on assum ptions The third common assumption is that pavement deterioration is deterministic. � However, pavement deterioration is inherently stochastic. Thus, the time intervals between MR&R activities are random variables. � Because the marginal cost is not a linear function of the time interval between MR&R activities, the expected marginal cost is not equal to the marginal cost estimated at the mean value of the time intervals. � This third assumption is relaxed in this paper 2 . 2. The authors are also working on relaxing the other two assumptions. October 2007 15
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Methodology Methodology � Assume highway agency uses a simple condition- responsive MR&R policy based on serviceability. � Use stochastic duration model to predict deterioration, where the hazard rate follows a Weibull distribution. Figure from Prozzi & Madanat (2000) � The number of ESALs to “failure” (trigger value) for the i th overlay cycle is a random variable X i October 2007 16
Estimation of the Marginal Cost of Highw ay Maintenance under Stochastic Pavement Deterioration – Anani and Madanat Methodology Methodology � Let positive constant L be the annual traffic loading (ESAL/ year). Then, the duration of the i th overlay cycle is defined as random variable T i (year): T i = X i / L p p p . . . . 0 time T 1 T 2 T 3 � Assume that { T i } i ≥ 1 are independent, and identically distributed. � Find expected MR&R marginal cost taken over the distributions of { T i } i ≥ 1 . Compare with deterministic case. October 2007 17
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