Probability of breakdown at freeway merges using Markov chains

The objective of this paper is to review our recent research completed on the determination of the probability distribution of the time of breakdown on a freeway. The methodology applied was unique, in that, it applied Markov chains to develop the probability distribution of the time of breakdown. To develop an improved methodology for the prediction of breakdown, the probability distribution of the time of breakdown was determined based on the zonal merging probabilities with respect to the vehicles traveling on the throughway. Freeway flow, available gaps, and drivers' actions as they approach the merge area were taken into consideration in developing the model. The analytical model was developed based on the information obtained from the literature and an initial field data sample. After determining the arrival distributions of the merging vehicles and the probability of transitioning from state to state, the probability distribution of the time of breakdown occurring was determined before any time, t, through a model analysis which applied Markov chains and implemented it in MATLAB® code. Finally, field data were reduced and applied in the model validation. With respect to the application of Markov chains, it was expected that higher arrival rates of the vehicles traveling on the throughway would lead to higher probabilities of breakdown. This is logical since one would expect a greater probability of breakdown occurring when there are a large number of vehicles entering the system. The model did produce results which predicted a higher probability of breakdown for higher arrival rates. The significance of the results is a better understanding of the prediction of breakdown and capacity estimation. With an improved concept of breakdown on freeways, better freeway analysis and simulation software may be developed.

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