This paper presents an efficient solution method for the matrix estimation problem using a static capacity constrained traffic assignment (SCCTA) model with residual queues. The solution method allows for inclusion of route queuing delays and congestion patterns besides the traditional link flows and prior demand matrix whilst the tractability of the SCCTA model avoids the need for tedious tuning of application specific algorithmic parameters. The proposed solution method solves a series of simplified optimization problems, thereby avoiding costly additional assignment model runs. Link state constraints are used to prevent usage of approximations outside their valid range as well as to include observed congestion patterns. The proposed solution method is designed to be fast, scalable, robust, tractable and reliable because conditions under which a solution to the simplified optimization problem exist are known and because the problem is convex and has a smooth objective function. Four test case applications on the small Sioux Falls model are presented, each consisting of 100 runs with varied input for robustness. The applications demonstrate the added value of inclusion of observed congestion patterns and route queuing delays within the solution method. In addition, application on the large scale BBMB model demonstrates that the proposed solution method is indeed scalable to large scale applications and clearly outperforms the method mostly used in current practice. ... Read more

Strategic traffic assignment (TA) models assess long-term effects of policies on route choices of travelers. To meet stability requirements, current strategic TA models lack modelling of queues. This thesis develops two TA models that include queue modelling whilst satisfying stability requirements along with a method to fuse observed link flows, congestion patterns and -delays. All methods are shown to be applicable in the large-scale strategic application context. ... Read more

To improve the accuracy of large-scale strategic transport models in congested conditions, this paper presents a straightforward extension of a static capacity-constrained traffic assignment model into a semi-dynamic version. The semi-dynamic model is more accurate than its static counterpart as it relaxes the empty network assumption, but, unlike its dynamic counterpart, maintains the stability and scalability properties required for application in large-scale strategic transport model systems. Applications show that, contrary to static models, semi-dynamic queue sizes and delays are very similar to dynamic outcomes, whereas only the congestion patterns differ due to the omission of spillback. The static and semi-dynamic models are able to reach user equilibrium conditions, whereas the dynamic model cannot. On a real-world transport model, the static model omits up to 76% of collective losses. It is therefore very likely that the empty network assumption influences (policy) decisions based on static model outcomes. ... Read more

In strategic transport models, road travel demand matrices are usually estimated using estimation methods that fuse prior or synthetic travel demand matrices with flow data observed on individual roads (‘links’) in the network. On the one hand, ever more data on flows, speeds and/or densities on link level is available, driven by technological advances (e.g. PnD’s, smartphones, IoT), trends in transport policy towards smarter usage instead of expansion of the network and the smart mobility concepts arising from them. On the other hand, the urgency of robust and sound estimation procedures is triggered by rising congestion levels on these networks that are at an all-time high.

In this paper we address the known difficulties when estimating travel demand using link flows observed on a network with high levels of congestion. Such a network incorporates at least several active bottlenecks, which influence flow values both upstream (queues will form) and downstream (flow is metered). This implies that, on such a network, observed link flow values may represent either 1) the unconstrained travel demand for that link, 2) a proportion of the capacity of a set of upstream links, 3) the capacity of the normative (in terms of capacity deficit) downstream link or 4) a combination of these quantities. Which quantity each observed link flow represents depends on the specific traffic conditions in the network. Note that in practice a very large portion of observed flows is affected by flow metering (2) whereas only a small portion is unaffected (1) or affected by queues (3 or 4).

Demand matrix estimation methods use a traffic assignment model to assess the relationship between travel demand and link flow in intercept information. If the assignment model that provides the intercept information does not strictly adhere to link capacity constraints, as with static traffic assignment models, flow metering effects of bottlenecks (2) are not taken into account and all traffic is considered unaffected (1), thereby forcing incorrect assumptions upon the estimation. Therefore, matrix estimation methods using these models should only be applied on observed flows values that are unaffected (1), rendering them mostly useless on networks with high congestion levels. Note that by nature these assignment models should actually not be applied on study areas with congestion altogether.

Current practice to use observed flows affected by congestion (2, 3 or 4) is to derive unconstrained link demand values from the observed flow values, for example using the ‘Tonenmethodiek’ (used in the Dutch LMS/NRM models), or similar techniques that shift observed flows to upstream unconstrained links. Then, instead of the actual observed flows, these post-processed link demand values are used during matrix estimation. As such, these methods exhibit poor tractability and robustness and do not integrate any information from the assignment model about the composition of routes on the observed links.

This paper describes and compares three novel demand matrix estimation methods for large scale strategic congested transport models that use assignment models that strictly adhere to link capacity constraints, allowing them to explicitly consider the conditions under which link flows are observed. It compares these methods to the current practice and gives practical insights from applications, thereby demonstrating that these methods allow for usage of (big) data sources such as floating car data, congestion patterns and (route) travel time observations. Using these novel approaches, the need to post-process synthetic link demands is taken away, thereby increasing tractability and robustness of the matrix estimation methods and allowing for use of observed congestion patterns as additional input. Furthermore, these methods more efficiently reveal inconsistencies between model link capacities and observed congestion patterns and inconsistencies between count values, allowing the modeler to correct the model network and other matrix estimation input.

Authors continue research on the topic, the next goal being to extent the methods to support estimation of OD demand covering multiple time period(s), which should eventually lead to a method that supports 24 hour estimation.
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This paper describes the road traffic assignment model Static Traffic Assignment with Queuing (STAQ) that was developed for situations where both static (STA) and dynamic (DTA) traffic assignment models are insufficient: strategic applications on large-scale congested networks. The paper demonstrates how the model overcomes shortcomings in STA and DTA modelling approaches in the strategic context by describing its concept, methodology and solution algorithm as well as by presenting model applications on (small) theoretical and (large) real-life networks. The STAQ model captures flow metering and spillback effects of bottlenecks like in DTA models, while its input and computational requirements are only slightly higher than those of STA models. It does so in a very tractable fashion, and acquires high-precision user equilibria (relative gap < 1E-04) on large-scale networks. In light of its accuracy, robustness and accountability, the STAQ model is discussed as a viable alternative to STA and DTA modelling approaches. ... Read more

To prepare the Dutch regional and national strategic transport models (LMS/NRM) for policy questions of the future, Rijkswaterstaat – WVL wants to improve the correspondence between link speeds and route travel times estimated by these models in the base year and observed link flows and route travel times. This paper describes a project in which the heavily congested model of NRM-West (the regional model of the Randstad containing Amsterdam, Rotterdam, The Hague and Utrecht) is used as a testcase for modelling improvements to the LMS/NRM to better fit with observed (big) data mentioned before.
In this project commissioned by Rijkswaterstaat – WVL, the traffic assignment model of LMS/NRM is replaced by the quasi dynamic traffic assignment model STAQ (first described in Brederode et al., 2010), and the OD matrices are recalibrated taking into account the flow metering effects of active bottlenecks as observed, together with the traditional calibration on observed flows from loop detector data.
Because implementation of a different assignment model in the LMS/NRM methodology implies a lot of (potential) side effects to the model system, we restrict ourselves in this project to not make any changes to the software (solve) used for the matrix estimation itself. Instead congestion effects are taken into account while generating assignment matrices (a.k.a. screenline matrices) based on STAQ output. This means that the methods tested within this project can easily be transferred to models using other matrix estimation methods intended to be used with static traffic assignment models. Incorporation of congestion effects into the assignment matrices also allows for direct comparison of flows from the assignment model with observed flows, instead of comparing unconstrained modelled demand with a ‘link demand’ (referred to as ‘wensvraag’ in dutch) estimated from the observed flow, as is currently the case for LMS/NRM.
The paper primarily presents (preliminary) results of the project in the form of comparisons of observed congestion patterns, speeds and travel times with assignment results. Furthermore, the paper describes what needed to be done to be able to use STAQ in NRM/LMS, how the flow metering effects on active bottlenecks as calculated by STAQ are used to construct assignment matrices that take flow metering into account, along with pitfalls, limitations and opportunities of the method in practice.
Furthermore, the paper provides a perspective on applicability of a matrix estimation method that can include observed travel times (from e.g. floating car data) and distribution patterns (from e.g. GSM data) in its objective function on top of the methodology described above. Depending on progress on this method, which is being undertaken as part of ongoing PhD research of the lead author of this paper, preliminary results on the NRM-West will be included. ... Read more

This paper presents a review and classification of traffic assignment models for strategic transport planning purposes by using concepts analogous to genetics in biology. Traffic assignment models share the same theoretical framework (DNA), but differ in capability (genes). We argue that all traffic assignment models can be described by three genes. The first gene determines the spatial capability (unrestricted, capacity restrained, capacity constrained, and capacity and storage constrained) described by four spatial assumptions (shape of the fundamental diagram, capacity constraints, storage constraints, and turn flow restrictions). The second gene determines the temporal capability (static, semi-dynamic, and dynamic) described by three temporal assumptions (wave speeds, vehicle propagation speeds, and residual traffic transfer). The third gene determines the behavioural capability (all-or-nothing, one shot, and equilibrium) described by two behavioural assumptions (decision-making and travel time consideration). This classification provides a deeper understanding of the often implicit assumptions made in traffic assignment models described in the literature. It further allows for comparing different models in terms of functionality, and paves the way for developing novel traffic assignment models. ... Read more

For decades congestion levels around the world are rising. To properly incorporate the effects of congestion into strategic transport models, a shift from static capacity restrained towards capacity constrained and dynamic traffic assignment models has occurred. In this paper we focus on quasi dynamic assignment models (more specific: static-capacity and storage constrained models by the definitions in Bliemer et al (2015)). These models explicitly capture the flow metering and spillback effects of congestion, but assume stationary demand during a single time period (e.g. a whole peak hour) and are therefore more scalable and mathematically tractable, both important properties for strategic transport models. Although computational capabilities of current hardware allow for large scale application of such models, the incorporation of capacity constraints causes route cost functions to be much more sensitive and to be inseparable over space (the latter occurs when routes share bottleneck nodes). Furthermore, the incorporation of storage constraints further increases inseparability (which occurs when queues spill back onto upstream links) and causes cost functions to become implicit. As such quasi dynamic models do not fully contain the favorable mathematical properties that are exploited in many algorithms to solve their capacity restrained counterparts and in fact do not necessarily comply with the requirements for existence and/or uniqueness of the user equilibrium (theorems 1.4 and 1.8 in Nagurney (1993)). Although in reality these unfavorable properties exist, a substantial body of research suggests that their (spatial) occurrence is limited and as such “…have minimal practical temporal and spatial consequences…” (Peeta and Zilliaskopoulos (2001)). However, several large scale applications using the quasi dynamic assignment model STAQ (first described in Brederode et al (2010)) have shown that especially the addition of storage constraints causes poor or non-convergence in real world applications. Further investigations in this paper will show that also the capacity constraints on their own can cause serious convergence issues. Contributions in this paper are (i) to give an overview of methods in literature and logical extensions to those methods that could improve convergence of quasi dynamic assignment models, (ii) to reveal and illustrate mechanisms that cause the convergence issues using examples on theoretical networks and (iii) to investigate to what extent enhancements to existing algorithms can be used to (partly) get around the convergence issues encountered. Ultimately, this research should lead to a method that generically solves quasi dynamic assignment models. ... Read more

A matrix estimation method using the semi dynamic assignment model STAQ is developed exploiting its methodological advantages over full DTA models. The matrix estimation problem is formulated as a bi-level problem and is solved on the node level taking flow metering into account. In the lower level the method uses marginal simulation of the node model within the assignment model to approximate the response function. The implicit relations between turn demand and link flows as defined by the directional capacity proportional node model are analyzed and made explicit. In the upper level an objective function minimizing differences between estimated and observed link flows and differences between prior and posterior ODmatrices is used, both components using a MSE distance function. The two components in the objective function are weighted and normalized. A method to prevent overshooting due to approximation errors is proposed as well as a method to correct the prior ODmatrix in case of insensitivity of the link flow due to supply constraints inconsistent with observed link flows. Test runs are conducted showing that the method finds (non-unique) solutions to the matrix estimation problem when only differences in link flows are taken into account, but may fail to converge when also differences between prior and estimated ODmatrix are taken into account. Further investigation suggests that secondary interaction effects should be included in the response function to solve the problem in these cases. ... Read more