Capturing Dependency Among Link Boundaries in a Stochastic Dynamic Network Loading Model

Abstract

This work adds realistic dependency structure to a previously developed analytical stochastic network loading model. The model is a stochastic formulation of the link-transmission model, which is an operational instance of Newell’s simplified theory of kinematic waves. Stochasticity is captured in the source terms, the flows, and, consequently, in the cumulative flows. The previous approach captured dependency between the upstream and downstream boundary conditions within a link (i.e., the respective cumulative flows) only in terms of time-dependent expectations without capturing higher-order dependency. The model proposed in this paper adds an approximation of full distributional stochastic dependency to the link model. The model is validated versus stochastic microsimulation in both stationary and transient regimes. The experiments reveal that the proposed model provides a very accurate approximation of the stochastic dependency between the link’s upstream and downstream boundary conditions. The model also yields detailed and accurate link state probability distributions.