Comparison of Markov Chain and Semi-Markov Models for Crack Deterioration on Flexible Pavements

Abstract

There is a growing demand to preserve transportation infrastructure utilizing limited funds, and the modeling of flexible pavement deterioration has become an integral component of any pavement preservation model. Markov chains have been used to model the performance of pavements in various pavement management systems (PMSs). The Markov property may be considered restrictive when modeling the deterioration of transportation assets, primarily because of the “memoryless” property and assumption of exponential distribution for sojourn times in the condition states. This paper outlines a semi-Markov model for modeling pavement deterioration in which the sojourn time in each condition state is assumed to follow a Weibull distribution and, thus, is more flexible than the traditional Markov chain model. The semi-Markov model does not possess the memoryless property if the sojourn time distribution is not exponential. Monte Carlo simulations are generated for the deterioration of flexible pavements over time based on both the traditional Markov chain model and the proposed semi-Markov model. The results of the work show that in some cases the semi-Markov model appears to be superior to the Markov chain model in modeling the actual deterioration patterns of the flexible pavements.