A Framework for Stochastic Air Traffic Flow Modeling and Analysis

Traffic congestion in urban areas is posing many challenges, and a traffic flow model that accurately predicts traffic conditions can be useful in responding to them. With the limitation of infrastructure and the difficulty for real world experiment, traffic simulation is a good tool for the validation and future potential applications of the traffic flow model. This research presents a stochastic traffic flow model which uses a stochastic partial differential equation to describe the evolution of traffic flow on the highway. The stochastic model is calibrated and validated by real traffic data on a highway and is proved to have better predictive power than the deterministic model. Also, a microscopic traffic simulation is built and calibrated by the same highway data, and the validation result shows that the simulation is capable of representing the real traffic. By using traffic simulation to further explore the capability of the stochastic model, the validation demonstrated that the prediction works well at most locations, and the interpolation error may be improved by considering the influence of ramps and the change in the number of lanes.

There has been extensive research in traffic state estimation that accounts for the stochastic nature of traffic flow models. However, these studies often exhibit limitations such as an exclusive focus on motorway traffic and a reliance on a single data source. This paper departs from these methods by introducing a stochastic estimation framework that is specifically designed for urban arterial traffic. The framework has the capability to incorporate multiple data sources, which serves to improve its accuracy and robustness. The framework is composed of three components: (i) a stochastic traffic flow model, (ii) a filtering algorithm, and (iii) an algorithm for incorporating multi-source measurements. In terms of the traffic model, we introduce a new stochastic Switching Mode Model that can be applied to arterial roads that have both signalized and unsignalized intersections. This model does not consider uncertainty in the current mode of operation, which substantially reduces the computational complexity because there is only one mode at each time step. Furthermore, we propose three different filtering algorithms for multi-source traffic estimation, including the incremental stochastic Kalman Filter (SKF), the incremental stochastic Unscented Kalman Filter (SUKF), and the hybrid approach. Since the SKF can only deal with linear functions, non-linear measurement equations need to be linearized using first-order Taylor expansions. The SUKF is based on the Unscented Transform (UT), which enables it to work with a wider range of functions regardless of linearity, non-linearity, or non-differentiability. The hybrid algorithm is a combination of the SKF and the SUKF, in which linear equations are treated similarly to the SKF, and non-linear equations are handled with the UT in the same way as in the SUKF. The performances of these algorithms were similar when applied to the synthetic data of an urban arterial in Christchurch CBD, New Zealand. The hybrid algorithm, however, worked slightly better and was more stable than the other two.

This paper presents a real-time freeway network traffic surveillance tool RENAISSANCE. Based on a stochastic macroscopic freeway network traffic flow model and the extended Kalman filter, RENAISSANCE is fed with a limited amount of real-time traffic measurements to enable a number of freeway network traffic surveillance tasks, including traffic state estimation and prediction, travel time estimation and prediction, queue tail/head/length estimation and prediction (queue tracking), and incident alarm. The paper first introduces the stochastic macroscopic freeway network traffic flow model and a real-time traffic measurement model, upon which a complete dynamic system model for freeway network traffic is established, with a special attention to the handling of some important model parameters. The addressed traffic surveillance tasks are described along with the functional architecture of RENAISSANCE. A simulation test was conducted for the tool with respect to a hypothetical freeway network example, while the traffic state estimator of RENAISSANCE was also tested with real traffic measurement data collected from a Bavarian freeway.

Queueing Network Models (QNMs) with Finite Capacity provide powerful and realistic tools for the performance evaluation and prediction of discrete flow systems such as computer systems, communication networks and flexible manufacturing systems. Over recent years, there has been a great deal of progress towards the analysis and application of QNMs with finite capacity, and high quality research work has appeared in diverse scientific journals of learning and conference proceedings in the fields of Operations Research, Computer Science, Telecommunication Networks, Management and Industrial Engineering. However, there are still many important and interesting finite capacity queues and QNMs to be resolved, such as those involving multiple-job classes, bounds and theoretical properties, exact analysis, numerical solutions and approximate methods, as well as application studies to computer and distributed systems, high-speed networks and production systems.This volume of Annals of Operations Research on Queueing Networks with Finite Capacity presents 17 extended research papers, both from industry and academia, reflecting current original contributions in the theory and applications of finite capacity queues and networks worldwide. Earlier short versions of these papers were amongst those presented at QNets '95, The Third International Workshop on Queueing Networks with Finite Capacity, 6th-7th July, 1995, Ilkley, West Yorkshire, UK. The papers are classified into four parts covering exact analysis, approximate methods, error bounds and performance modelling studies.

<p>Most of worldwide population lives in urban areas, demanding for air quality information with a high spatio-temporal resolution. The most promising approaches for estimating urban air quality within the complex urban topography are small sensor networks and simulation models.</p><p>The TRAFAIR project focuses on understanding the role of traffic emissions on urban air quality by the combination of dispersion modelling, space- and time-resolved gas monitoring by lower cost sensors and realistic traffic flow rates by dynamic traffic model based on real time traffic data. Test cities of TRAFAIR are Modena, Florence, Pisa, Livorno, Zaragoza and Santiago de Compostela.</p><p>Depending on the size of the urban area, from 6 to 13 sensors units are deployed across each city since August 2019, providing estimates of NO, NO<sub>2</sub>, CO and O<sub>3</sub>, along with RH and temperature. Metal oxide sensors are deployed in Tuscany (Florence, Pisa, Livorno) and electrochemical cells are used elsewhere. The units are calibrated on a regular basis by co-location at the air quality regulatory stations and subsequently deployed across the town to monitor several representative locations (e.g. Low Emission Zones, hospital surroundings). For each sensor the raw readings (e.g. mV for electrochemical cells) are collected and a regression model (e.g. Random Forest) is applied to derive a calibration function, exploiting the data from the regulatory stations during co-location periods; for instance in Modena, the first short-term calibration provided a model with a Mean Absolute Error between 5 – 6 ppb and 2 – 4 ppb for NO and NO<sub>2</sub> respectively.</p><p>The sensors are used for both real-time urban air quality mapping and to test and validate the 24hr forecast service of NOx by the microscale lagrangian dispersion model GRAL. The simulation domains, covering the urban area of each TRAFAIR city, have a horizontal resolution of 4 m and allow to account for the presence of buildings. The dispersion model mainly focuses on NOx by traffic emissions, although domestic heating will be also included in the analysis. Vehicular emissions are based either upon historical traffic data (e.g. induction loops), or upon previously available traffic flow simulation, or upon traffic pattern reconstruction using a traffic flow model followed by a cluster analysis to group streets with similar pattern.</p><p>The final goal of the project is the development of a tool to support local policymakers and to inform citizenship about the quality of air and the impact of urban emission sources, particularly traffic. A secondary goal of the project is the development of a valuable QA/QC protocol for small sensor units and the optimization of the modelling chain for the forecast of traffic and domestic heating impact on local air quality at the urban scale.</p>

A stochastic model of traffic flow: Gaussian approximation and estimation

Queueing networks have been widely used to evaluation performance of mainframe computer systems. In contrast, few results have been reported for modern open systems, so it was not clear whether queueing networks are useful for modern systems or not. We think this situation has partly been due to lack of handy evaluation tools. This paper presents tow tools that we developed to evaluate open system performance. On is a measuring tool that is capable of accurately obtaining the service times of system resources requested by an application transaction. The other is an estimating tool which calculates various performance measures based on queueing network models. This paper also describes a case study in which the performance of a medium‐sized UNIX client–server system (up to 24 clients) is estimated using the tools and these estimates are then compared with experimental results. The estimates closely agree with the measured results and are accurate enough for practical applications. Based on this, we conclude that queueing network models are also useful for modern systems.

Traffic state estimation using stochastic Lagrangian dynamics

En-route charging navigation system is significant for electric vehicle (EV) owners to relieve the range anxiety. Considering the limited battery capacity of EVs, accurate battery energy consumption prediction is crucial for charging navigation in that it determines the maximum traveling distance. This article develops a comprehensive EV energy consumption prediction model and the impacts of the traffic flow on the motor efficiency and driving resistances have been thoroughly considered. Moreover, a stochastic traffic flow model is proposed to improve the energy consumption prediction precision, in which the related uncertainties, such as travel time, vehicle speed, etc., are captured. Then, a novel cost-effective en-route EV charging navigation problem is formulated as a two-stage stochastic optimization problem. In addition, the EV charging behavior and its interaction with the routing selection are characterized in the navigation problem. Finally, an improved Benders Algorithm is modified to obtain the global optimal solution of the proposed navigation model. The simulation verification is carried out in the actual road network of a certain city and the IEEE 33-node coupling system. Results demonstrate the feasibility and effectiveness of the proposed model and solution algorithm.

Speed limit control at freeway bottlenecks is numerically studied on the basis of the Kerner-Klenov microscopic stochastic traffic flow model in the context of Kerner's three-phase traffic theory. It turns out that in some cases speed limit control, rather than preventing traffic breakdown, leads to induced congested pattern emergence at the bottleneck, whereas there is free flow at the bottleneck without speed limitation. In other cases, speed limit control can suppress moving jam emergence, which occurs without speed limitation. It is found that these effects are associated with the probabilistic character of traffic breakdown at a bottleneck as well as with complex spatiotemporal congested pattern features.

BackgroundPreparation for a disaster or accident-related mass casualty events is often based on experience. The objective measures or tools for evaluating decision-making and effectiveness during such events are underdeveloped. Queueing theory has been suggested to evaluate the effectiveness of mass causality incidents (MCI) plans.ObjectiveUsing different types of real MCI, we aimed to determine if a queueing network model could be used as a tool to assist in preparing plans to address mass causality incidents.MethodsWe collected information from two types of mass casualty events: a motor vehicle accident and a dust explosion. Patient characteristics, time intervals of every working station, numbers of physicians and nurses attending, and time required by physicians and nurses during these two MCIs were collected and used for calculation in a queueing network model. Balanced efficiency was determined by calculating the numbers of server, i.e., nurses and physicians, in the two MCIs.ResultsEfficient patient flows were found in both MCIs. However, excessive medical manpower supply was revealed when the queueing network model was applied to assess the MCIs. The best fitting result, i.e., the most efficient man power utilization, can be calculated by the queueing network models. Furthermore, balanced efficiency may be a more suitable condition than the highest efficiency man power utilization when faced with MCIs.ConclusionThe queueing network model is a flexible tool that could be used in different types of MCIs to observe the degree of efficiency when handling MCIs.

In this paper, we present an approach for model transformation from Queueing Network Models (QNMs) into Queueing Petri Nets (QPNs). The performance of QPNs can be analyzed using a powerful simulation engine, SimQPN, designed to exploit the knowledge and behavior of QPNs to improve the efficiency of simulation. When QNMs are transformed into QPNs, their performance can be analyzed efficiently using SimQPN. To validate our approach, we apply it to analyze the performance of several queueing network models including a model of a database system. The evaluation results show that the performance analysis of the transformed QNMs has high accuracy and low overhead. In this context, model transformation enables the performance analysis of queueing networks using different ways that can be more efficient.

A variety of macroscopic traffic flow models have been applied to formulate the link-based system optimal dynamic traffic assignment (SO-DTA) problem in a many-to-one network. It is expected that SO-DTA models based on various traffic flow models usually result in different optimal link traffic evolution patterns, but whether and how traffic flow models affect the minimal system cost and the corresponding optimal arrival pattern at the destination is unclear. Three traffic flow models–point-queue, spatial-queue, and cell-transmission–are examined, and their resulted minimal system cost in many-to-one networks is compared. It is proved that for three simple networks–a linear network with two sequential bottlenecks, a two-in-one-out merge network, and a one-in-two-out diverge network–the minimal system costs for the SO-DTA models based on these three traffic flow models are identical. Numerical experiments show that this property appears to be held for general many-to-one networks. The reason may be that all three traffic flow models propagate the uncongested flows at the same speed and release the congested flows always at the link capacity. In SO-DTA applications where only the minimal system cost or arrival pattern at the destination is of major interest, the findings can be utilized to substantially expedite the solution procedure.

Unmanned Aerial Vehicles (UAVs) are opening up new opportunities for extensive applications. The traffic flow model is critical to evaluate the traffic needs of various applications in designing and deploying UAV system. However, the traffic flow model has not been explored in multi-services oriented UAV system. To this end, this paper proposes a general traffic flow model for multi-services orientated UAV system. Under such a model, the network services are first categorized into three subsets, each corresponding to one of telemetry, Internet of Things (IoT), and streaming data. According to the Pareto distribution, all UAVs are further partitioned into three subgroups relying on their network usages. We can measure the packet arrival rate for the nine segments, each of which represents one map relationship between a services subset and a UAV subgroup. Therefore, we can also obtain the number of packets for each network service and total data size. Simulation results are presented to illustrate that the number of packets and the data size predicted by our traffic model can well match with these in real scenarios with different network services.

According to the thought of intelligent forecasting and hybrid forecasting, an Intelligent Hybrid (IH) model for short-term traffic flow forecasting was presented. The IH model had three sub-models: History Mean (HM) model, Artificial Neural Network (ANN) model and the Fuzzy Combination (FC) model. By means of the good static stabilization character of HM method, the HM model predicted the traffic flow by the Single Exponential Smoothing method based on the historical traffic data. Otherwise, the ANN model was a 1.5-layer feed-forward neural network built by some common S-function neurons. Because of the strong dynamic nonlinear mapping ability of ANN, the ANN model can estimate the actual traffic flow in a very precise and satisfactory sense. The FC model mixed the two individual forecasting results by fuzzy logic and its output was regarded as the final forecasting of the traffic flow. Factual application results show that the IH model, which takes advantage of the unique strength of the HM model and the ANN model, can produce more precise forecasting than that of two individual models. Thus, the IH model can be an efficient method to the short-term traffic flow forecasting.