Dynamic Probabilistic Approach for Long-Term Pavement Restoration Program with Added User Cost

Abstract

A dynamic probabilistic-based approach has been developed for generating a long-term pavement restoration program for a given pavement system. The probabilistic approach applies the basic principles of stochastic processes to predict pavement conditions. Initial state probabilities and transition probabilities are the two main parameters required to develop the future state probability functions used in formulating an effective optimum decision policy. The future state probabilities are only functions of the restoration variables representing potential restoration actions. An optimum decision policy is deployed to yield a pavement restoration program comprising ( n) restoration plans corresponding to ( n) transitions. The derived pavement restoration program takes into consideration the long-term transitional performance and budget requirements. The applied decision policy is based on either maximizing the expected system condition ratings subjected to budget constraints or minimizing the net system costs subjected to desired expected system condition ratings. The net system cost may include restoration cost, deteriorated pavement added user cost, and work-zone added user cost. The two decision policy options are subjected to other constraints placing limits on the state probability functions and restoration variables. The restoration variables as applied to state probability functions result in optimum models that are sequentially solved to maintain their linearity. Sample results from a case study have indicated the usefulness of the developed dynamic probabilistic approach in yielding potential long-term pavement restoration programs.

Back-calculation of transition probabilities for Markovian-based pavement performance prediction models

“…The initial state probabilities and state probabilities after one transition are required to be able to backwardly solve the Markov model for the corresponding transition probabilities. It is typically assumed that any row in the transition matrix (P) only contains the two transition probabilities (Pi,i) and (Pi,i þ 1) in the absence of any M&R works (Butt et al 1987, Abaza and Ashur 1999, Abaza and Murad 2007. It is to be noted that the sum of any row in the transition matrix must equal to one.…”

“…The elements of the transition matrix (P) are the transition probabilities which are assumed to be equal for each transition, thus, indicating a homogenous Markovian chain. The transition matrix can be different for each transition if a nonhomogenous chain is to be used (Butt et al 1987, Abaza and Ashur 1999, Abaza and Murad 2007.…”

“…An effective pavement performance prediction model is considered to be an essential component of any modern pavement management system. Several advanced pavement management systems have incorporated a stochastic-based model to develop an optimum long-term pavement maintenance and rehabilitation (M&R) plan at the network level (Ferreira et al 2002, Reigle and Zaniewski 2002, Abaza and Murad 2007.…”

Effectiveness and Service Lives/Survival Curves of Various Pavement Rehabilitation Treatments

“…Similar to priority ranking, mathematical optimization requires current-condition data on pavement sections at the network level, treatment alternatives and their effect on pavement condition, associated costs, and so on. Approaches typically used to solve problems for true and exact optimal solutions include linear and nonlinear programming, integer programming, and dynamic programming (FHWA, 1990;Zimmerman, 1995;Abaza and Murad, 2007). In the 1980s,…”

Predicting Remaining Strength of Flexible Pavement and Overlay Design Thickness with Stochastic Modeling

“…The probabilistic model predicts the future pavement condition with some degree of uncertainty, whereas the deterministic model predicts it with certainty (7). The probabilistic model that was extensively used by several researchers to predict pavement performance is the discrete time Markov model (8)(9)(10)(11)(12). The Markov model can be used with homogenous or nonhomogenous transition chains.…”