Calculation of the Expressway OD Matrix Based on Grey Markov Chain Model

Estimating and studying an expressway's Origin-Destination (OD) matrix is very important for its managements and project assessments. Based on a few historical data of Annual Average Daily Traffic (AADT), this paper develops Grey GM(1,1) model, determines the parametric vector to gain the time series of AADT and its short term sequences, then divides the series combined with Markov chain process. Next, the modified value is accquired by ascertaining the transition matrix to attain the state probability and Grey Markov chain forecasting model is derived. Finally, OD calculation and the formula of a single directional flow are discussed, then OD matrix is calculated.