Large-scale simulation of traffic flow using Markov model.

Renátó Besenczi,Fanny Monori,Márton Ispány,Roland Major,Péter Jeszenszky,Norbert Bátfai

doi:10.1371/journal.pone.0246062

Abstract

Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps in 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 and superior to the frequency based maximum likelihood method. 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 which, when used together to analyze traffic on large road networks, has not previously been reported.

Highlights

In the past decade, research and development of smart city applications have become an active topic [1, 2]
To evaluate the performance of the proposed weighted least squares (WLS) estimation method by comparing it to the traditional maximum likelihood (ML) one discussed above, a simple simulation study was conducted at different sample sizes for small and medium road network
In order to mimic the real traffic, we tried to keep the length of trajectories low and the number of trajectories high compared to the size of the road network, to the Porto example

Summary

Introduction

Research and development of smart city applications have become an active topic [1, 2]. We propose a method for estimating the two-dimensional stationary distribution Q immediately instead of the pair (P, π) of a transition matrix and its stationary distribution using mobile sensor data which may be gathered by vehicles, passengers etc In this case, we have trajectories data which consists of the sequences of consecutive vertices, like in the TTP dataset. For the TTP dataset, the number of trajectories is above 80K with the mean length 40 and maximum length 2K, see Table 1 They are asymptotic estimators in the sense that, for finite sample size, the estimated stationary distribution does not satisfy the global balance equation given by the estimated transition probability matrix. One can see that, to the Google’s PageRank algorithm, see Chapter 15 in [73]), a linear recursion could be computationally more efficient in large-scale problems

Results

Conclusions

World Urbanization Prospects