Abstract
We demonstrate how behaviour of car sharing system can be modelled by continuous time Markov chains using Phase-type distributions. A straight forward approach is to keep a track of each car. However, the state space of such a model increases very rapidly by increasing number of cars. Assuming that cars are of the same type, it suffices to model how the number of cars changes, which results in a significantly smaller state space. We assume that distributions of travel time are not Markovian. We approximate behaviour of non-Markovian system by a Markovian model in which distributions of travel time are approximated by Phase-type distributions. Our results showed that probability of non-empty zone does depend on travel time mean and not on the actual form of travel time distribution.
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Bražėnas, M., Valakevičius, E. (2023). Approximation of Non-Markovian Car Sharing Systems Models by Markovian One. In: Arai, K. (eds) Intelligent Systems and Applications. IntelliSys 2022. Lecture Notes in Networks and Systems, vol 543. Springer, Cham. https://doi.org/10.1007/978-3-031-16078-3_31
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DOI: https://doi.org/10.1007/978-3-031-16078-3_31
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