A Probabilistic Traffic-Theoretic Network Loading Model Suitable for Large-Scale Network Analysis

Abstract

This paper formulates an analytical stochastic network loading model. It is a stochastic formulation of the link transmission model (LTM), which itself is an operational formulation of Newell's simplified theory of kinematic waves. The proposed model builds on an existing initial model. It proposes a formulation with enhanced scalability. In particular, compared with the initial model, it has a complexity that is linear rather than cubic in the link's space capacity. This makes it suitable for large-scale network analysis. The model is validated versus a simulation-based implementation of the stochastic LTM. The proposed model yields significant gains in computational efficiency while preserving accuracy. The validation experiments illustrate how computational run times of the proposed model increase linearly with the link's space capacity, while the initial model has an exponential increase in run times. The proposed model yields accurate distributional approximations of the link's boundary conditions. It is used to address a probabilistic formulation of a citywide signal control problem. The model is shown to be robust to the quality of the initial signal plans. It yields signal plans that systematically outperform both initial plans, as well as a plan derived by widely used commercial signal control software. The model is suitable for large-scale network optimization.

Analytical model assessing the effect of increased traffic flow intensities on the road administration, maintenance and lifetime

“…Last but not least, the financial equivalent for the replacement of the upper roadway layer or the whole roadway construction is based on approved cost databases, but it can´t be generalized to all roads of the same class (each road administrator of the given road uses apart from these cost databases its own pricelists). In spite of all these deficiencies, the analytical model also brings into the calculation of total costs I 2 other factors in accordance with [5,[18][19][20][21], which have a major effect on the negative impacts of the diverted traffic flow. These externalities are subsequently expressed by the financial equivalent, of which is the road administrator in case of higher intensities (proportion) of heavy freight vehicles more loaded compared to the road management in normal operation.…”

On the approximation of queue-length distributions in transportation networks

“…Probabilistic link model formulations with traffic-theoretic foundations include Boel and Mihaylova (2006); Sumalee et al (2011); Liu (2012, 2013); Osorio et al (2011); Deng et al (2013); Laval and Chilukuri (2014); Laval and Castrillón (2015); Osorio and Flötteröd (2015); Lu and Osorio (2018); Lu (2020). The main approaches have been the introduction of randomness in the cell transmission model, extensions of the variational theory of Daganzo (2005) and the use of probabilistic queueing theory (Olszewski, 1994;Heidemann, 2001;Viti and Van Zuylen, 2010;Osorio et al, 2011;Osorio and Flötteröd, 2015;Lu and Osorio, 2018). Another stream of research in the estimation of queue length distribution is based on observed data collected from probe vehicles Cetin, 2009, 2011;Comert, 2013Comert, , 2016.…”

“…For a link with space capacity , the model complexity is in the order of O( 3 ). Lu and Osorio (2018) have extended the formulation of Osorio and Flötteröd (2015), leading to a model with complexity in the order of O( ). This is a formulation that scales linearly with the link's space capacity, making it efficient and appropriate for large-scale network analysis.…”

“…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 traffictheoretic link transmission model. The proposed network model is scalable and computationally efficient, making it suitable for urban network optimization.…”

“…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.…”