General solution scheme for the Static Link Transmission Model

Until the present day most static traffic assignment models are neither capacity constrained nor storage constrained. Recent studies have resulted in novel approaches that consider capacity constraints and sometimes storage constraints. We build upon the results of these works and the model formulated in our companion paper Bliemer and Raadsen (2018a) which comprises a static assignment model formulation that is both capacity constrained as well as storage constrained. The formulation of this model is derived from a continuous time dynamic network loading model proposed in Bliemer and Raadsen (2018b). The prospect of being able to capture spillback effects in static assignment provides new opportunities for making this modelling method more capable. It is well known that the absence of spillback typically results in significant underestimation of path travel times. This is especially true for paths that do not traverse bottleneck(s) directly, but that are affected by the space occupied of queues that are spilling back. Similar to Smith (2013) and Smith et al. (2013), Bliemer and Raadsen (2018a) did not provide a solution algorithm. In this paper, we take their model formulation and propose a general solution scheme suitable for large scale networks

Continuous-time general link transmission model with simplified fanning, Part II: Event-based algorithm for networks

In this paper a novel solution algorithm is proposed for solving general first order dynamic network loading (DNL) problems in general transport networks. This solution algorithm supports any smooth non-linear two regime concave fundamental diagram and adopts a simplified fanning scheme. It is termed eGLTM (event-based General Link Transmission Model) and is based on a continuous-time formulation of the kinematic wave model that adapts shockwave theory to simplify expansion fans. As the name suggests eGLTM is a generalisation of eLTM, which is a special case that solves the simplified first order model assuming a triangular fundamental diagram. We analyse the impact of modelling delay in the hypocritical branch of the fundamental diagram to assess the differences between the two models. In addition, we propose an additional stream of mixture events to propagate multi-commodity flow in event based macroscopic models, which makes both eLTM and eGLTM suitable for dynamic traffic assignment (DTA) applications. The proposed solution scheme can yield exact solutions as well as approximate solutions at a significantly lesser cost. The efficiency of the model is demonstrated in a number of case studies. Furthermore, different settings for our simplified fanning scheme are investigated as well as an extensive analysis on the effect of including route choice on the algorithms computational cost. Finally, a large scale case study is conducted to investigate the suitability of the model in a practical context and assess its efficiency compared to the simplified first order model

Continuous-time general link transmission model with simplified fanning, Part I: Theory and link model formulation

The kinematic wave theory is widely used to simulate traffic flows on road segments. Link transmission models are methods to find a solution to the kinematic wave model, however, their computational efficiency heavily relies on the shape of the fundamental diagram that is used as input. Despite the limitations and drawbacks of triangular and piecewise linear fundamental diagrams, they remain popular because they result in highly efficient algorithms. Using smooth nonlinear branches is often preferred in terms of realism and other desirable properties, but this comes at a significantly higher computational cost and requires time discretisation to find an approximate solution. In this paper we consider a nonlinear fundamental diagram as input and propose on-the-fly multi-step linearization techniques to simplify expansion fans. This leads to two simplified link transmission models that can be solved exactly in continuous time under the assumption of piecewise stationary travel demand. One of the models simplifies to shockwave theory in case of a single step. We show that embedding shockwave theory in the link transmission model allows for finding an exact solution in continuous time and we discuss the potential for the design of efficient event-based algorithms for general networks

Steady-state link travel time methods: formulation, derivation, and classification

Travel times are one of the most important outputs of transport planning models and this is unlikely to change in the future. It is therefore paramount that the methods that underpin the construction of travel times are well understood. However, while there exist many different travel time formulations to date, their relation to each other is not well researched, especially in the context of the three main types of macroscopic modelling paradigms: dynamic, semi-dynamic, and static traffic assignment. In this work, we provide consistent and general link travel time formulations across these three modelling paradigms, assuming steady state flow rates and by directly deriving them from a recent state-of-the-art continuous time macroscopic dynamic network loading model. We do so from two different perspectives; an experienced perspective, which actively tracks the tail of a physical queue, and a functional perspective, which does not. Based on the existing literature and our generalised link travel time formulations, a classification framework is proposed allowing one to compare existing (and future) methods in the literature in an objective fashion. We provide a number of explicit derivations of existing model formulations that can be considered special cases of our unified approach. In addition a number of representative existing methods in the literature has been classified based on the above mentioned framework for the reader’s convenience

An efficient event‐based algorithm for solving first order dynamic network loading problems

In this paper we will present a novel solution algorithm for the Generalised Link Transmission Model (G-LTM). It will utilise a truly event based approach supporting the generation of exact results, unlike its time discretised counterparts. Furthermore, it can also be configured to yield approximate results, when this approach is adopted its computational complexity decreases dramatically. It will be demonstrated on a theoretical as well as a real world network that when utilising fixed periods of stationary demands to mimic departure time demand fluctuations, this novel approach can be efficient while maintaining a high level of result accuracy. The link model is complemented by a generic node model formulation yielding a proper generic first order DNL solution algorithm

Frequency‐based transit assignment revisited

This working paper reformulates the Spiess and Florian frequency-based transit assignment method in matrix algebra revealing a new solution method. It is shown that the number of destination-specific passenger wait times at stops is equal to the number of flow conservation constraints (Proposition 1). The frequency-based transit assignment is found by matrix manipulation and when there are line capacity constraints the equilibrium effective frequencies are obtained iteratively. The existence of equilibrium effective frequencies is proven (Proposition 2). It is shown that a wider range of fare schemes, for example flat fares, can be modeled by the use of legs in the network representation. Numerical examples are presented and solved by R code

Introducing pattern graph rewriting in novel spatial aggregation procedures for a class of traffic assignment models

In this study two novel spatial aggregation methods are presented compatible with a class of traffic assignment models. Both methods are formalized using a category theoretical approach. While this type of formalization is new to the field of transport, it is well known in other fields that require tools to allow for reasoning on complex structures. The method presented stems from a method originally developed to deal with quantum physical processes. The first benefit of adopting this formalization technique is that it provides an intuitive graphical representation while having a rigorous mathematical underpinning. Secondly, it bears close resemblances to regular expressions and functional programming techniques giving insights in how to potentially construct solvers (i.e. algorithms). The aggregation methods proposed in this paper are compatible with traffic assignment procedures utilising a path travel time function consisting out of two components, namely (i) a flow invariant component representing free flow travel time, and (ii) a flow dependent component representing queuing delays. By exploiting the fact that, in practice, most large scale networks only have a small portion of the network exhibiting queuing delays, this method aims at decomposing the network into a constant free flowing part to compute once and a, much smaller, demand varying delay part that requires recomputation across demand scenarios. It is demonstrated that under certain conditions this procedure is lossless. On top of the decomposition method, a path set reduction method is proposed. This method reduces the path set to the minimal path set which further decreases computational cost. A large scale case study is presented to demonstrate the proposed methods can reduce computation times to less than 5% of the original without loss of accuracy

A lossless spatial aggregation procedure for a class of capacity constrained traffic assignment models incorporating point queues

In this paper two novel spatial aggregation procedures are proposed. A network aggregation procedure based on a travel time delay decomposition method and a zonal aggregation procedure based on a path redistribution scheme. The effectiveness of these procedures lies in the fact that they, unlike existing aggregation methods, exploit available information regarding the application context and the characteristics of the adopted traffic assignment procedure. The context considered involves all applications that require path and inter-zonal travel times as output. A typical example of such applications are quick-scan methods, which have become increasing popular in recent years. The proposed procedures are compatible with a class of traffic assignment procedures incorporating (residual) point queues. Furthermore, one can choose to combine network aggregation with zonal aggregation to increase the effectiveness of the procedure. Results are demonstrated via theoretical examples as well as a large-scale case study. In the case study it is shown that network loading times can be reduced to as little as 4% of the original situation without suffering any information loss

Requirements for traffic assignment models for strategic transport planning: A critical assessment

Transport planning models are used all over the world to assist in the decision making regarding investments in infrastructure and transport services. Traffic assignment is one of the key components of transport models, which relate travel demand to infrastructure supply, by simulating (future) route choices and network conditions, resulting in traffic flows, congestion, travel times, and emissions. Cost benefit analyses rely on outcomes of such models, and since very large monetary investments are at stake, these outcomes should be as accurate and reliable as possible. However, the vast majority of strategic transport models still use traditional static traffic assignment procedures with travel time functions in which traffic flow can exceed capacity, delays are predicted in the wrong locations, and intersections are not properly handled. On the other hand, microscopic dynamic traffic simulation models can simulate traffic very realistically, but are not able to deal with very large networks and may not have the capability of providing robust results for scenario analysis. In this paper we discuss and identify the important characteristics of traffic assignment models for transport planning. We propose a modelling framework in which the traffic assignment model exhibits a good balance between traffic flow realism, robustness, consistency, accountability, and ease of use. Furthermore, case studies on several large networks of Dutch and Australian cities will be presented

Genetics of traffic assignment models for strategic transport planning

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 functionality (genes). We argue that all traffic assignment models can be described by two genes. The first gene determines the spatial functionality (unrestricted, capacity restrained, capacity constrained, capacity and storage constrained) described by five spatial interaction assumptions, while the second gene determines the temporal functionality (static, semi-dynamic, dynamic) described by two temporal interaction assumptions. This classification provides a deeper understanding of the often implicit assumptions made in traffic assignment models described in the literature, particularly with respect to networking loading where the largest differences occur. It further allows for comparing different models in terms of functionality, and opens the way for developing novel traffic assignment models