Comparative Analysis of Markovian Methodologies for Modeling Infrastructure System Performance

Abstract

Various types of Markov chain methodologies have been used in past research to develop stochastic performance models for infrastructure systems—the staged-homogeneous, nonhomogeneous, homogeneous, semi-, and hidden Markov. The primary components of a Markov model are the transition probability matrix, condition states, and duty cycle. This paper hypothesizes that the number of condition states (NCS) and length of duty cycle (LDC) significantly influence the prediction accuracy of a Markov model and that the nature of such influence varies across the different Markov methodologies. In previous studies on Markovian performance modeling, not only did this hypothesis go unanswered, but also there is a lack of comparison across the different Markov methodologies. In an attempt to shed light on this issue, this paper describes the development and comparison of performance models using these Markov methodologies and empirical data. The paper also investigates the sensitivity of Markovian model prediction accuracy to NCS and LDC. The results indicate that the semi-Markov techniques yield performance models that are generally statistically superior to those of the homogeneous and staged-homogeneous Markov (except in a few cases of NCS and LDC combinations) and that the prediction accuracy of Markovian models is very sensitive to NCS and LDC: an increase in NCS improves the prediction accuracy up to a certain NCS threshold, after which the accuracy diminishes, likely due to data overfitting. In addition, an increase in LDC generally enhances prediction accuracy when the NCS is small. The results can help guide highway agencies and researchers not only in selecting the appropriate Markovian methodology for a given NCS and LDC but also in selecting the appropriate NCS and LDC for a given Markovian methodology.