Iterative Linear Approach for Nonlinear Nonhomogenous Stochastic Pavement Management Models

Abstract

An iterative linear stochastic pavement management model is proposed that deploys a nonhomogenous discrete-time Markov chain for predicting the future pavement conditions for a given pavement network. A nonhomogenous transition matrix is constructed to incorporate both the pavement deterioration rates and improvement rates. The pavement deterioration rates are simply the transition probabilities associated with the deployed pavement states. The improvement rates are mainly the maintenance and rehabilitation variables representing the deployed maintenance and rehabilitation actions. A decision policy is formulated to identify the optimal set of maintenance and rehabilitation actions and their respective timings, and to provide the optimal level of maintenance and rehabilitation funding over an analysis period. The nonhomogenous Markov chain allows for a distinct maintenance and rehabilitation plan (matrix) for each time interval (transition). However, the total number of maintenance and rehabilitation variables will substantially increase depending on the length of the deployed analysis period. The resulting optimum model is associated with a nonlinearity order that is equal to the number of time intervals within the specified analysis period. Solving a nonlinear model with a large number of variables is a very complex task. Alternatively, instead of solving a single nonlinear problem, a series of linear problems are formulated and iteratively solved wherein the optimal solution for one problem becomes the input for the next one. The sample results obtained from the iterative linear approach indicate the effectiveness of the proposed stochastic management model in predicting future pavement conditions.