Large-scale Analysis and Simulation of Traffic Flow using Markov Models
- URL: http://arxiv.org/abs/2007.02681v1
- Date: Mon, 6 Jul 2020 12:31:27 GMT
- Title: Large-scale Analysis and Simulation of Traffic Flow using Markov Models
- Authors: Ren\'at\'o Besenczi, Norbert B\'atfai, P\'eter Jeszenszky, Roland
Major, Fanny Monori, M\'arton Isp\'any
- Abstract summary: A mathematically rigorous model that can be used for traffic analysis was proposed earlier by other researchers.
In this paper, a new parametrization is presented for this model by introducing the concept of two-dimensional stationary distribution.
We have run simulations in medium and large scales and both the model and estimation procedure, based on artificial and real datasets, have been proved satisfactory.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Modeling and simulating movement of vehicles in established transportation
infrastructures, especially in large urban road networks is an important task.
It helps with understanding and handling traffic problems, optimizing traffic
regulations and adapting the traffic management in real time for unexpected
disaster events. A mathematically rigorous stochastic model that can be used
for traffic analysis was proposed earlier by other researchers which is based
on an interplay between graph and Markov chain theories. This model provides a
transition probability matrix which describes the traffic's dynamic with its
unique stationary distribution of the vehicles on the road network. In this
paper, a new parametrization is presented for this model by introducing the
concept of two-dimensional stationary distribution which can handle the
traffic's dynamic together with the vehicles' distribution. In addition, the
weighted least squares estimation method is applied for estimating this new
parameter matrix using trajectory data. In a case study, we apply our method on
the Taxi Trajectory Prediction dataset and road network data from the
OpenStreetMap project, both available publicly. To test our approach, we have
implemented the proposed model in software. We have run simulations in medium
and large scales and both the model and estimation procedure, based on
artificial and real datasets, have been proved satisfactory. In a real
application, we have unfolded a stationary distribution on the map graph of
Porto, based on the dataset. The approach described here combines techniques
whose use together to analyze traffic on large road networks has not previously
been reported.
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