  This paper addresses the problem of estimating link flows in a road network
by combining limited traffic volume and vehicle trajectory data. While traffic
volume data from loop detectors have been the common data source for link flow
estimation, the detectors only cover a subset of links. Vehicle trajectory data
collected from vehicle tracking sensors are also incorporated these days.
However, trajectory data are often sparse in that the observed trajectories
only represent a small subset of the whole population, where the exact sampling
rate is unknown and may vary over space and time. This study proposes a novel
generative modelling framework, where we formulate the link-to-link movements
of a vehicle as a sequential decision-making problem using the Markov Decision
Process framework and train an agent to make sequential decisions to generate
realistic synthetic vehicle trajectories. We use Reinforcement Learning
(RL)-based methods to find the best behaviour of the agent, based on which
synthetic population vehicle trajectories can be generated to estimate link
flows across the whole network. To ensure the generated population vehicle
trajectories are consistent with the observed traffic volume and trajectory
data, two methods based on Inverse Reinforcement Learning and Constrained
Reinforcement Learning are proposed. The proposed generative modelling
framework solved by either of these RL-based methods is validated by solving
the link flow estimation problem in a real road network. Additionally, we
perform comprehensive experiments to compare the performance with two existing
methods. The results show that the proposed framework has higher estimation
accuracy and robustness under realistic scenarios where certain behavioural
assumptions about drivers are not met or the network coverage and penetration
rate of trajectory data are low.
