Dynamic Modeling for Intelligent Transportation System Applications

Special Issue on Dynamic Modeling for Intelligent Transportation System Applicationspostprin

Joint buffer management and scheduling for input queued switches

Input queued (IQ) switches are highly scalable and they have been the focus of many studies from academia and industry. Many scheduling algorithms have been proposed for IQ switches. However, they do not consider the buffer space requirement inside an IQ switch that may render the scheduling algorithms inefficient in practical applications. In this dissertation, the Queue Length Proportional (QLP) algorithm is proposed for IQ switches. QLP considers both the buffer management and the scheduling mechanism to obtain the optimal allocation region for both bandwidth and buffer space according to real traffic load. In addition, this dissertation introduces the Queue Proportional Fairness (QPF) criterion, which employs the cell loss ratio as the fairness metric. The research in this dissertation will show that the utilization of network resources will be improved significantly with QPF. Furthermore, to support diverse Quality of Service (QoS) requirements of heterogeneous and bursty traffic, the Weighted Minmax algorithm (WMinmax) is proposed to efficiently and dynamically allocate network resources. Lastly, to support traffic with multiple priorities and also to handle the decouple problem in practice, this dissertation introduces the multiple dimension scheduling algorithm which aims to find the optimal scheduling region in the multiple Euclidean space

Road network maintenance and repair considering day-to-day traffic dynamics and transient congestion

Road maintenance and repair (M&R) are essential for keeping the performance of traffic infrastructure at a satisfactory level, and extending their lifetime to the fullest extent possible. For road networks, effective M&R plans should not be constructed in a myopic or ad-hoc fashion regardless of the subsequent benefits and costs associated with those projects considered. A hallmark of road M&R studies is the use of user equilibrium (UE) models to predict network traffic for a given set of road conditions with or without M&R. However, UE approaches ignore the traffic disequilibrium states and transient congestion as a result of M&R derived disruptions to network traffic on a day-to-day (DTD) time scale, which could produce additional substantial travel costs. As shown in the numerical studies on a M&R plan of the Sioux Falls network, the additional maintenance derived travel cost is about 4 billion, which is far exceed the actual M&R construction cost of 0.2 billion. Therefore, it is necessary to recognise the substantial social costs induced by maintenance-derived disruptions in the form of transient congestion when planning M&R. This realistic and pressing issue is not properly addressed by the road M&R planning problems with traffic equilibrium constraints. This thesis proposes a dual-time-scale road network M&R model aiming to simultaneously capture the long-term effects of M&R activities under traffic equilibria, and the maintenance-derived transient congestion using day-to-day (DTD) traffic evolutionary dynamics. The notion of ‘day’ is arbitrarily defined (e.g. weeks or months). The proposed M&R model consists of three sub-models: (1) a within-day dynamic network loading (DNL) model; (2) a day-to-day dynamic traffic assignment (DTD DTA) model; and (3) a day-to-day road quality model. The within-day traffic dynamics is captured by the Lighthill-Whitham-Richards (LWR) fluid dynamic network loading model. The day-to-day phase of the traffic dynamics specify travellers’ route and departure time choices in a stochastic manner based on a sequential mixed multinomial or nested Logit model. Travel information sharing behaviour is further integrated into this macroscopic doubly dynamic (both within-day and day-to-day dynamic) traffic assignment (DDTA) model to account for the impact of incomplete information on travel experiences. A deterministic day-to-day road quality model based on an exponential form of traffic flow is employed to govern the road deterioration process, where a quarter-car index (QI) is applied. All these dynamics are incorporated in a holistic dual-time-scale M&R model, which captures realistic phenomena associated with short-term and long-term effects of M&R, including physical queuing and spillback, road capacity reduction, temporal-spatial shift of congestion due to on-going M&R activities, and the tendency to converge to an equilibrium after M&R actions. Following the dual-time-scale road network M&R model, a bi-level road M&R optimisation model is proposed, where the aforementioned three sub-models are incorporated into the lower-level problem, while the upper-level is to minimise M&R expenditure and network travel costs while maintaining a satisfactory level of road quality. The M&R planning horizon is long yet finite (e.g. years or decades). A ‘quality-usage’ feedback mechanism is investigated in the proposed bi-level M&R model, namely, (1) the DTD road quality evolution as a result of DTD traffic loads and the M&R effectiveness; and (2) the evolution of DTD traffic in response to both DTD road deterioration and the improved road quality after M&R activities. The effectiveness of developed M&R optimisation model is demonstrated through case studies on the Sioux Falls network. A metaheuristic Genetic Algorithm (GA) approach is employed to solve the M&R problems given its highly nonlinear, nonconvex and non-differentiable nature. Explicit travellers’ choice behaviour dynamics and complex traffic phenomena such as network paradoxes arising from M&R activities are illustrated. Through a comparison with the results under the dynamic user equilibrium (DUE) method, the proposed DTD method achieves significant reduction in network travel cost of $ 25 million, approximately 20% of the total cost. This points to the benefit of using the DTD dynamics for capturing network’s responses to M&R in a more realistic way. The M&R model proposed in this thesis could provide valuable managerial insights for road M&R planning agencies.Open Acces

Dynamic traffic assignment: model classifications and recent advances in travel choice principles

Dynamic Traffic Assignment (DTA) has been studied for more than four decades and numerous reviews of this research area have been conducted. This review focuses on the travel choice principle and the classification of DTA models, and is supplementary to the existing reviews. The implications of the travel choice principle for the existence and uniqueness of DTA solutions are discussed, and the interrelation between the travel choice principle and the traffic flow component is explained using the nonlinear complementarity problem, the variational inequality problem, the mathematical programming problem, and the fixed point problem formulations. This paper also points out that all of the reviewed travel choice principles are extended from those used in static traffic assignment. There are also many classifications of DTA models, in which each classification addresses one aspect of DTA modeling. Finally, some future research directions are identified.postprin

Road network equilibrium approaches to environmental sustainability

Environmental sustainability is closely related to transportation, especially to the road network, because vehicle emissions and noise damage the environment and have adverse effects on human health. It is, therefore, important to take their effect into account when designing and managing road networks. Road network equilibrium approaches have been used to estimate this impact and to design and manage road networks accordingly. However, no comprehensive review has summarized the applications of these approaches to the design and management of road networks that explicitly address environmental concerns. More importantly, it is necessary to identify this gap in the literature so that future research can improve the existing methodologies. Hence, this paper summarizes these applications and identifies potential future research directions in terms of theories, modelling approaches, algorithms, analyses, and applications.postprin

A nonlinear equation system approach to the dynamic stochastic user equilibrium simultaneous route and departure time choice problem

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Stochastic process models for dynamic traffic assignment

This research explored the idea of unifying the deterministic and stochastic process approaches together, and developing a generalised framework of dynamic traffic assignment models to include day-to-day and within day variations in traffic flow. The framework of models is also aimed at capturing individual drivers’ adaptation of route choices based on the route costs experienced through suitable driver learning models. In this thesis, the route flows within a day in a given departure period are modelled as random variables, and their evolution over a period of time (a number of days) is modelled as stochastic processes based on the laws of probability. The interactions among the route flows from various departure periods over the network links in space and time, are modelled through dynamic link loading procedures. Stochastic processes under certain mild conditions admit a unique stationary probability distribution which can be modelled by using simulation techniques. Alternatively, the moments (e.g., mean and variance) of the equilibrium (stationary) probability distribution can also be estimated. This research has advanced the idea of estimating the properties of equilibrium probability distribution by making a particular contribution in formulating the methodology for computing the Jacobians of route travel times with respect to the route inflows in a doubly dynamic assignment context using an analytical procedure, which are necessary for estimating the variance-covariance matrices of stationary route flows. In this modelling framework, there are three modules - the first one is a day-to-day route choice model defined as a discrete time stochastic process, the second is a continuous time dynamic network loading of the route flows considering the complete spatio-temporal effects of the traffic flows that use the road links at the same time, and the third is the drivers’ learning and adjusting model based on a linear filter. The main idea of estimating the properties of stationary probability distribution in this research builds on two earlier results: firstly, when the demand is sufficiently large, the equilibrium probability distribution converges approximately to a Multivariate Normal distribution and its mean coincides with the SUE flows; secondly, the variance can be estimated by an approximation procedure. The equilibrium probability distribution can also be worked out using the commonly followed Monte Carlo simulation technique, which involves simulating the route choice process as a multinomial probability distribution over a number of days, and then summarising the properties e.g., the mean and the variance of the stationary probability distribution. This procedure though simple, is time consuming and the main difficulty lies in detecting the stationarity of the process. Based on the necessary conditions, simple and practically useable tests for identifying the stationarity of a stochastic process have been introduced. These tests involve analysing autocorrelations and computing large lag standard errors in autocorrelations. The stationary variance-covariance of route flows obtained by the variance approximation model, was compared with that computed by the simulation procedure. Overall, the variance approximation model performs satisfactorily. Variance-covariance of route flows has been found sensitive primarily to the input logit choice parameter, which defines the boundaries of the validity of the variance approximation model. Variance-covariance is also affected by the memory length with the shorter memory systems essentially producing highly variant systems. Similarly, the variance-covariance of route flows is also sensitive to the memory weight, and the lower memory weight (0 < memory weight « 1) produces the same effect as that of shorter memory systems. The Jacobians of the travel times worked out in this thesis have much wider applicability, and a few possible situations have been listed here among many others. Firstly, the optimisation based user equilibrium programs can be speeded up by defining the descent direction with the help of the Jacobians. Secondly, the Jacobians may be found very useful in defining the dynamic road user pricing problems. Finally, the sensitivity analysis of user equilibrium problems requires the computation of the Jacobians

An intersection-movement-based stochastic dynamic user optimal route choice model for assessing network performance

Different from traditional methods, this paper formulates the logit-based stochastic dynamic user optimal (SDUO) route choice problem as a fixed point (FP) problem in terms of intersection movement choice probabilities, which contain travelers’ route information so that the realistic effects of physical queues can be captured in the formulation when a physical-queue traffic flow model is adopted, and that route enumeration and column generation heuristics can be avoided in the solution procedure when efficient path sets are used. The choice probability can be either destination specific or origin–destination specific, resulting into two formulations. To capture the effect of physical queues in these FP formulations, the link transmission model is modified for the network loading and travel time determination. The self-regulated averaging method (SRAM) was adopted to solve the FP formulations. Numerical examples were developed to illustrate the properties of the problem and the effectiveness of the solution method. The proposed models were further used to evaluate the effect of information quality and road network improvement on the network performance in terms of total system travel time (TSTT) and the cost of total vehicle emissions (CTVE). Numerical results show that providing better information quality, enhancing link outflow capacity, or constructing a new road can lead to poor network performance.postprin

Approximation and Control of Skill Based Parallel Service Systems with Homogeneous Service

A skill base parallel service system is comprised of a set of customers of different classes that arrive randomly for service, a set of servers that serve those customers and a set of qualifications that defines which customer classes can be served by which server. Systems of this kind appear in a wide range of applications from the assignment of jobs to employees with different skills to network traffic routing. Literature regarding these systems has almost exclusively been focused on the asymptotic heavy traffic regime. The reason being that such an asymptotic regime is convenient to analyze and allows the derivation of exact results. However, although many applications can be well approximated by an asymptotic regime, many others can not. In this work we are especially concerned with large scale sparse systems where, despite the system being large of scale, each customer class can only be served by a small subset of the servers. After laying foundations for the model in Chapter 1 and exploring structural properties in Chapter 2 we go on to present the two main contributions of this work. In Chapter 3 we develop a set of approximations that compile to a , first of its kind, approximation scheme of matching rates of skill based parallel service system operating under the \textit{first-come-first-serve} or \textit{longest-queue-first} policies. The accuracy of the approximation is verified with extensive simulation experiments where it is shown to provide matching rate estimates with an absolute error of $3\%-5\%$ for a wide range of traffic intensities. Later, in Chapter 4 we use insights provided by the new approximation to derive weighted versions of the \textit{first-come-first-serve} or \textit{longest-queue-first} and show, through comprehensive simulation testing, that these weighted polices dramatically reduce the waiting time of customers in congested system compared to the original unweighted versions. Finally, we extend the use of the weighted policies to systems with matching rewards and show that, by appropriate choice of weights, these policies can be used by a controller to efficiently trade-off between the rate of reward accumulation and waiting time experienced by the customer