Quasi-dynamic network loading: Adding queuing and spillback to static traffic assignment

For many years, static traffic assignment models have been widely applied in transport planning studies and will continue to be an important tool for strategic policy decisions. As is well known, in the traditional approach, the location of the delays and queues are not predicted correctly, and the resulting travel times do not correspond well with reality. Dynamic models can approach reality much better, but come at a computational cost. In this paper we propose a quasi-dynamic model which inherits most of the computational efficiency of static models, but aims to keep most of the important dynamic features, such as queuing, spillback, and shockwaves. Instead of adjusting the traditional static model or using heuristics, we theoretically derive the model from the dynamic link transmission model, assuming stationary travel demand and instantaneous flow. Furthermore, we present algorithms for solving the model. On a corridor network we illustrate the feasibility and compare it with other approaches, and on a larger network of Amsterdam we discuss the computational efficiency

Nokta kuyruk modellemesi için bir dinamik düğüm noktası modeli

Point-queuing and physical queuing are the two main assumptions that have been made in problems of Dynamic Network Loading (DNL) in order to model link and network performances. The queue spillback can only be captured by physical-queue approach, which is more realistic. Accordingly, the recent trend on traffic flow modeling for Dynamic Traffic Assignment (DTA) is to propose models with physical-queue assumption. However capturing the effects of physical-queuing in DNL modelling brings difficulties in obtaining an optimal solution of a DTA problem. As an alternative, the point-queue assumption handles vehicles as points without physical lengths. The storage capacity of each link can be ignored. The queue spillback on a link can be simulated by assuming the existence of a buffer area in the initial node of the link, for the temporary storage of vehicles exceeding the maximum density. Therefore, all links can contain unconstrained number of vehicles and capacity constraint on a link can be applied without numerical and computational difficulties. Moreover, the outflow rate of a link is only affected by its own flow considering that the downstream links will always have sufficient storage capacities. In the literature, point-queue assumption has been made in a varying structure of flow models adopting both exit-flow function approach, and in travel time function approach to perform DNL. In this paper, a mesoscopic dynamic node model for network loading is proposed, based on discrete packets, to model the point-queue process on a highway node with multiple merging and diverging links. The model is run using theoretical input data to simulate point-queuing in over-saturation condition. The presented dynamic node model has two components; a mesoscopic link model set with an exit link function formulation, and an algorithm written with a set of node rules considering the constraints of conservation, capacity, flow splitting rates and non-negativities. First, the time-varying flows that enter to multiple merging links (inflows) simultaneously are input to the mesoscopic link model. The link model component is developed by both considering the over-saturation phenomenon and improving the computational efficiency on a previously proposed link model. This model, is set out with link exit function formulation, discretisation on time dimension, defining capacity constraint rules for over-saturated states and uniformly accelerated speed assumption, which allows a realistic representation of outflow dynamics. Model has an iterative structure, which enables convergence to any target performance criteria with the coded algorithm. The flows that exit from these merging links (outflows) are computed regarding the link and flow characteristics. Then outflows of the merging links are input to a node as inflows. These conflicting flows are processed within the node component with predefined splitting rates and characteristics of the diverging links, and then the nodal exiting flows are computed. The main difference of the proposed dynamic node model in comparison to other models is that it respects capacity constraints regarding to splitting rules and consequently holds first-in-first-out rule. For the link model component of integrated model structure has been set out with the point-queuing assumption, the point-queues and the delays calculated in the presence of these vertical queues are considered instead of the physical queues and the delays occurring as a result of over-saturation. The node model problem is formulated as to maximize the total flow passing through the node subject to the constraints of conservation, capacity, flow splitting rates and non-negativities. The optimization problem is solved by simulation within the modelling horizon. Simulation process of the proposed model lasted as the inflows to merging links are wholly discharged from the entire node structure. The integrated model structure provided more realistic results in representing outflow dynamics. It is seen that the outflows of the link model component existed respecting to capacity constraints and the diagrams of these outflows seemed alike the sinusoidal inflow curves under the set node configuration. Despite the flows requiring to enter the diverging links are above over-saturation rates, the capacity restraint is respected. The results show that the model appears realistic in the representation of point-queuing process and diverging link flow dynamics, and is quite easy to calculate. The future extension of this study will be on the application of the proposed model to a general network. Keywords: Traffic networks, traffic flow, node model, simulation.Bu çalışmada; karayolu ağlarında akım yayılımını modelleyen ve bir dinamik ağ yükleme sürecinde tümleşik olarak kullanılabilen analitik bir dinamik düğüm noktası modeli yardımıyla, bağ girişlerinde meydana gelen nokta kuyruklanmanın modellemesi yapılmıştır. Önerilen dinamik düğüm noktası modelinin; bağ çıkış formülasyonu temelli bir karma-boyut bağ modeli bileşeni ve akım korunumu, kapasite, akım dağılımı ve negatif olmama kısıtlarını içeren bir düğüm noktası kuralları bileşeni vardır. Oluşturulan dinamik düğüm noktası formülasyonu, belirlenen kısıtlar altında benzetim yoluyla çözülmüştür. Nokta kuyruk varsayımı ile oluşturulan bağ modeli bileşeni; aşırı-doygun trafik akım durumunu değerlendiren bir yapıdadır. Zaman boyutunda yapılan ayrıklaştırma, aşırı-doygun duruma ilişkin konulan kapasite kısıtı ve düzgün ivmelenen taşıt hareketi varsayımı ile oluşturulan bağ modeli bileşeni, gerçekçi trafik akım dinamiklerinin temsiline olanak sağlamıştır. Bağ modeli ile belirlenen akımlar, düğüm noktası bileşenine girdi olmaktadır. Akımların düğüm noktası bileşeninde, önceden tanımlı dağılım oranları ve ayrılan bağ özellikleri ile işlenmesi ile ayrılan bağ giriş akımları hesaplanır. Modellenen nokta kuyrukların; i)  kapasitenin aşıldığı herhangi durumda ve ii) modeli çözmek için zaman düzeyinde yapılan ayrıklaştırmaya bağlı olarak, bir önceki hesaplama anından arta kalan akım hacmi varolduğu durumda belirdiği varsayılmıştır. Nokta kuyruk modellemesi için önerilen yeni dinamik düğüm noktası modeli, karma-boyut yaklaşımı temeli üzerinde yapılandırılmış tek düğüm noktası modelidir. Yeni modelin aşırı-doygunlukta gerçekçi sonuçlar verdiği görülmüştür. Anahtar Kelimeler: Ulaştırma ağı, trafik akımı, düğüm noktası modeli, benzetim

Characterizing corridor-level travel time distributions based on stochastic flows and segment capacities

abstract: Trip travel time reliability is an important measure of transportation system performance and a key factor affecting travelers’ choices. This paper explores a method for estimating travel time distributions for corridors that contain multiple bottlenecks. A set of analytical equations are used to calculate the number of queued vehicles ahead of a probe vehicle and further capture many important factors affecting travel times: the prevailing congestion level, queue discharge rates at the bottlenecks, and flow rates associated with merges and diverges. Based on multiple random scenarios and a vector of arrival times, the lane-by-lane delay at each bottleneck along the corridor is recursively estimated to produce a route-level travel time distribution. The model incorporates stochastic variations of bottleneck capacity and demand and explains the travel time correlations between sequential links. Its data needs are the entering and exiting flow rates and a sense of the lane-by-lane distribution of traffic at each bottleneck. A detailed vehicle trajectory data-set from the Next Generation SIMulation (NGSIM) project has been used to verify that the estimated distributions are valid, and the sources of estimation error are examined.The final version of this article, as published in Cogent Engineering, can be viewed online at: https://www.cogentoa.com/article/10.1080/23311916.2014.99067

A Finite Time Combinatorial Algorithm for Instantaneous Dynamic Equilibrium Flows

Instantaneous dynamic equilibrium (IDE) is a standard game-theoretic concept in dynamic traffic assignment in which individual flow particles myopically select en route currently shortest paths towards their destination. We analyze IDE within the Vickrey bottleneck model, where current travel times along a path consist of the physical travel times plus the sum of waiting times in all the queues along a path. Although IDE have been studied for decades, several fundamental questions regarding equilibrium computation and complexity are not well understood. In particular, all existence results and computational methods are based on fixed-point theorems and numerical discretization schemes and no exact finite time algorithm for equilibrium computation is known to date. As our main result we show that a natural extension algorithm needs only finitely many phases to converge leading to the first finite time combinatorial algorithm computing an IDE. We complement this result by several hardness results showing that computing IDE with natural properties is NP-hard.Comment: 27 pages, 11 figure

Dynamic system-optimal traffic assignment using a state space model

We propose a new mathematical formulation for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assume that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minimize the total travel time experienced by all the vehicles using the network. We model the traffic network over the time horizon as a discrete-time dynamical system. The system state at each time instant is defined in a way that, without loss of optimality, avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, link outflow functions, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied in the context of this model. These optimization problems are optimal control problems for nonlinear discrete-time dynamical systems, and thus they are amenable to algorithmic solutions based on dynamic programming. The computational challenges associated with the exact solution of these problems are discussed and some heuristics are proposed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30420/1/0000041.pd

Dynamic Flows with Adaptive Route Choice

We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest path length by current waiting times in queues plus physical travel times. As our main results, we show: 1. existence and constructive computation of IDE flows for single-source single-sink networks assuming constant network inflow rates, 2. finite termination of IDE flows for multi-source single-sink networks assuming bounded and finitely lasting inflow rates, 3. the existence of IDE flows for multi-source multi-sink instances assuming general measurable network inflow rates, 4. the existence of a complex single-source multi-sink instance in which any IDE flow is caught in cycles and flow remains forever in the network.Comment: 40 pages, shorter version published in the "Proceedings of the 20th Conference on Integer Programming and Combinatorial Optimization, 2019