  This paper focuses on the analytical probabilistic modeling of vehicular
traffic. It formulates a stochastic node model. It then formulates a network
model by coupling the node model with the link model of Lu and Osorio (2018),
which is a stochastic formulation of the traffic-theoretic link transmission
model. The proposed network model is scalable and computationally efficient,
making it suitable for urban network optimization. For a network with $r$
links, each of space capacity $\ell$, the model has a complexity of
$\mathcal{O}(r\ell)$. The network model yields the marginal distribution of
link states. The model is validated versus a simulation-based network
implementation of the stochastic link transmission model. The validation
experiments consider a set of small network with intricate traffic dynamics.
For all scenarios, the proposed model accurately captures the traffic dynamics.
The network model is used to address a signal control problem. Compared to the
probabilistic link model of Lu and Osorio (2018) with an exogenous node model
and a benchmark deterministic network loading model, the proposed network model
derives signal plans with better performance. The case study highlights the
added value of using between-link (i.e., across-node) interaction information
for traffic management and accounting for stochasticity in the network.
