A dynamic node model for point queue modelling

Abstract

Point-queuing and physical queuing are the two main assumptions that have been made in problems of Dynamic Network Loading (DNL) in order to mo-del 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.

Özet

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.