Abstract
We explore numerically and analytically how a fleet of vehicles moving through a stations network becomes unbalanced. Framing the system in terms of a mathematical simplex subjected to stochastic flows allows us to understand system’s failure rigorously. This allows to find the effect of self-journeys in system’s stability. With a birth-death process approach we find analytical upper bounds for random walk and we monitor how the system collapses by super-diffusing under different randomisation conditions.
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Notes
- 1.
Note that permutations among the s components produce the same energy.
- 2.
Also in the non-random case but in a much more complicated way.
- 3.
If the first state is not exactly the barycentre, there is only one correction as an additive constant.
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Acknowledgment
The authors acknowledge support from Project No. PGC2018-093854-B-I00 of the Spanish Ministerio de Ciencia Innovación y Universidades of Spain.
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Prieto-Castrillo, F., Benito, R.M., Borondo, J. (2022). Understanding Imbalance Mechanisms in Shared Mobility Systems. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications X. COMPLEX NETWORKS 2021. Studies in Computational Intelligence, vol 1073. Springer, Cham. https://doi.org/10.1007/978-3-030-93413-2_62
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