Hazard based models for freeway traffic incident duration

Assessing and prioritising cost-effective strategies to mitigate the impacts of traffic incidents and accidents on non-recurrent congestion on major roads represents a significant challenge for road network managers. This research examines the influence of numerous factors associated with incidents of various types on their duration. It presents a comprehensive traffic incident data mining and analysis by developing an incident duration model based on twelve months of incident data obtained from the Australian freeway network. Parametric accelerated failure time (AFT) survival models of incident duration were developed, including log-logistic, lognormal, and Weibul-considering both fixed and random parameters, as well as a Weibull model with gamma heterogeneity. The Weibull AFT models with random parameters were appropriate for modelling incident duration arising from crashes and hazards. A Weibull model with gamma heterogeneity was most suitable for modelling incident duration of stationary vehicles. Significant variables affecting incident duration include characteristics of the incidents (severity, type, towing requirements, etc.), and location, time of day, and traffic characteristics of the incident. Moreover, the findings reveal no significant effects of infrastructure and weather on incident duration. A significant and unique contribution of this paper is that the durations of each type of incident are uniquely different and respond to different factors. The results of this study are useful for traffic incident management agencies to implement strategies to reduce incident duration, leading to reduced congestion, secondary incidents, and the associated human and economic losses.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

Exact and approximate Bayesian inference for low count time series models with intractable likelihoods

In this paper we present a new simulation methodology in order to obtain exact or approximate Bayesian inference for models for low-valued count time series data that have computationally demanding likelihood functions. The algorithm fits within the framework of particle Markov chain Monte Carlo (PMCMC) methods. The particle filter requires only model simulations and, in this regard, our approach has connections with approximate Bayesian computation (ABC). However, an advantage of using the PMCMC approach in this setting is that simulated data can be matched with data observed one-at-a-time, rather than attempting to match on the full dataset simultaneously or on a low-dimensional non-sufficient summary statistic, which is common practice in ABC. For low-valued count time series data we find that it is often computationally feasible to match simulated data with observed data exactly. Our particle filter maintains $N$ particles by repeating the simulation until $N+1$ exact matches are obtained. Our algorithm creates an unbiased estimate of the likelihood, resulting in exact posterior inferences when included in an MCMC algorithm. In cases where exact matching is computationally prohibitive, a tolerance is introduced as per ABC. A novel aspect of our approach is that we introduce auxiliary variables into our particle filter so that partially observed and/or non-Markovian models can be accommodated. We demonstrate that Bayesian model choice problems can be easily handled in this framework.

Urban transit quality of service : user perception and behaviour

Despite its potential multiple contributions to sustainable policy objectives, urban transit is generally not widely used by the public in terms of its market share compared to that of automobiles, particularly in affluent societies with low-density urban forms like Australia. Transit service providers need to attract more people to transit by improving transit quality of service. The key to cost-effective transit service improvements lies in accurate evaluation of policy proposals by taking into account their impacts on transit users. If transit providers knew what is more or less important to their customers, they could focus their efforts on optimising customer-oriented service. Policy interventions could also be specified to influence transit users’ travel decisions, with targets of customer satisfaction and broader community welfare. This significance motivates the research into the relationship between urban transit quality of service and its user perception as well as behaviour. This research focused on two dimensions of transit user’s travel behaviour: route choice and access arrival time choice. The study area chosen was a busy urban transit corridor linking Brisbane central business district (CBD) and the St. Lucia campus of The University of Queensland (UQ). This multi-system corridor provided a ‘natural experiment’ for transit users between the CBD and UQ, as they can choose between busway 109 (with grade-separate exclusive right-of-way), ordinary on-street bus 412, and linear fast ferry CityCat on the Brisbane River. The population of interest was set as the attendees to UQ, who travelled from the CBD or from a suburb via the CBD. Two waves of internet-based self-completion questionnaire surveys were conducted to collect data on sampled passengers’ perception of transit service quality and behaviour of using public transit in the study area. The first wave survey is to collect behaviour and attitude data on respondents’ daily transit usage and their direct rating of importance on factors of route-level transit quality of service. A series of statistical analyses is conducted to examine the relationships between transit users’ travel and personal characteristics and their transit usage characteristics. A factor-cluster segmentation procedure is applied to respodents’ importance ratings on service quality variables regarding transit route preference to explore users’ various perspectives to transit quality of service. Based on the perceptions of service quality collected from the second wave survey, a series of quality criteria of the transit routes under study was quantitatively measured, particularly, the travel time reliability in terms of schedule adherence. It was proved that mixed traffic conditions and peak-period effects can affect transit service reliability. Multinomial logit models of transit user’s route choice were estimated using route-level service quality perceptions collected in the second wave survey. Relative importance of service quality factors were derived from choice model’s significant parameter estimates, such as access and egress times, seat availability, and busway system. Interpretations of the parameter estimates were conducted, particularly the equivalent in-vehicle time of access and egress times, and busway in-vehicle time. Market segmentation by trip origin was applied to investigate the difference in magnitude between the parameter estimates of access and egress times. The significant costs of transfer in transit trips were highlighted. These importance ratios were applied back to quality perceptions collected as RP data to compare the satisfaction levels between the service attributes and to generate an action relevance matrix to prioritise attributes for quality improvement. An empirical study on the relationship between average passenger waiting time and transit service characteristics was performed using the service quality perceived. Passenger arrivals for services with long headways (over 15 minutes) were found to be obviously coordinated with scheduled departure times of transit vehicles in order to reduce waiting time. This drove further investigations and modelling innovations in passenger’ access arrival time choice and its relationships with transit service characteristics and average passenger waiting time. Specifically, original contributions were made in formulation of expected waiting time, analysis of the risk-aversion attitude to missing desired service run in the passengers’ access time arrivals’ choice, and extensions of the utility function specification for modelling passenger access arrival distribution, by using complicated expected utility forms and non-linear probability weighting to explicitly accommodate the risk of missing an intended service and passenger’s risk-aversion attitude. Discussions on this research’s contributions to knowledge, its limitations, and recommendations for future research are provided at the concluding section of this thesis.

Harmonic quality of multilevel cascade inverters with random carrier phase pulse width modulation

The output harmonic quality of N series connected full-bridge dc-ac inverters is investigated. The inverters are pulse width modulated using a common reference signal but randomly phased carrier signals. Through analysis and simulation, probability distributions for inverter output harmonics and vector representations of N carrier phases are combined and assessed. It is concluded that a low total harmonic distortion is most likely to occur and will decrease further as N increases.

Harmonic quality of multilevel cascade inverters with random carrier phase pulse width modulation

The output harmonic quality of N series connected full-bridge dc-ac inverters is investigated. The inverters are pulse width modulated using a common reference signal but randomly phased carrier signals. Through analysis and simulation, probability distributions for inverter output harmonics and vector representations of N carrier phases are combined and assessed. It is concluded that a low total harmonic distortion is most likely to occur and will decrease further as N increases.

Exact series solutions of reactive transport models with general initial conditions

Exact solutions of partial differential equation models describing the transport and decay of single and coupled multispecies problems can provide insight into the fate and transport of solutes in saturated aquifers. Most previous analytical solutions are based on integral transform techniques, meaning that the initial condition is restricted in the sense that the choice of initial condition has an important impact on whether or not the inverse transform can be calculated exactly. In this work we describe and implement a technique that produces exact solutions for single and multispecies reactive transport problems with more general, smooth initial conditions. We achieve this by using a different method to invert a Laplace transform which produces a power series solution. To demonstrate the utility of this technique, we apply it to two example problems with initial conditions that cannot be solved exactly using traditional transform techniques.

A comparison of finite difference and finite volume methods for solving the space-fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non- classical diffusion or dispersion which is not adequately described by the classical theory of Brownian motion and Fick’s law. We consider a space-fractional advection-dispersion equation based on a fractional Fick’s law. Zhang et al. [Water Resources Research, 43(5)(2007)] considered such an equation with variable coefficients, which they dis- cretised using the finite difference method proposed by Meerschaert and Tadjeran [Journal of Computational and Applied Mathematics, 172(1):65-77 (2004)]. For this method the presence of variable coef- ficients necessitates applying the product rule before discretising the Riemann–Liouville fractional derivatives using standard and shifted Gru ̈nwald formulas, depending on the fractional order. As an alternative, we propose using a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Gru ̈nwald formulas are used to discretise the Riemann–Liouville fractional derivatives at control volume faces, eliminating the need for product rule expansions. We compare the two methods for several case studies, highlighting the convenience of the finite volume approach.

Weak conformance of process models with respect to data objects

Process models specify behavioral aspects by describing ordering constraints between tasks which must be accomplished to achieve envisioned goals. Tasks usually exchange information by means of data objects, i.e., by writing information to and reading information from data objects. A data object can be characterized by its states and allowed state transitions. In this paper, we propose a notion which checks conformance of a process model with respect to data objects that its tasks access. This new notion can be used to tell whether in every execution of a process model each time a task needs to access a data object in a particular state, it is ensured that the data object is in the expected state or can reach the expected state and, hence, the process model can achieve its goals.

Beyond tasks and gateways: discovering BPMN models with subprocesses, boundary events and activity markers

Existing techniques for automated discovery of process models from event logs largely focus on extracting flat process models. In other words, they fail to exploit the notion of subprocess, as well as structured error handling and repetition constructs provided by contemporary process modeling notations, such as the Business Process Model and Notation (BPMN). This paper presents a technique for automated discovery of BPMN models containing subprocesses, interrupting and non-interrupting boundary events, and loop and multi-instance markers. The technique analyzes dependencies between data attributes associated with events, in order to identify subprocesses and to extract their associated logs. Parent process and subprocess models are then discovered separately using existing techniques for flat process model discovery. Finally, the resulting models and logs are heuristically analyzed in order to identify boundary events and markers. A validation with one synthetic and two real-life logs shows that process models derived using the proposed technique are more accurate and less complex than those derived with flat process model discovery techniques.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Compressed sensing using hidden Markov models with application to vision based aircraft tracking

This paper investigates compressed sensing using hidden Markov models (HMMs) and hence provides an extension of recent single frame, bounded error sparse decoding problems into a class of sparse estimation problems containing both temporal evolution and stochastic aspects. This paper presents two optimal estimators for compressed HMMs. The impact of measurement compression on HMM filtering performance is experimentally examined in the context of an important image based aircraft target tracking application. Surprisingly, tracking of dim small-sized targets (as small as 5-10 pixels, with local detectability/SNR as low as − 1.05 dB) was only mildly impacted by compressed sensing down to 15% of original image size.

BPMN Miner: Automated Discovery of BPMN Process Models with Hierarchical Structure

Existing techniques for automated discovery of process models from event logs gen- erally produce flat process models. Thus, they fail to exploit the notion of subprocess as well as error handling and repetition constructs provided by contemporary process modeling notations, such as the Business Process Model and Notation (BPMN). This paper presents a technique for automated discovery of hierarchical BPMN models con- taining interrupting and non-interrupting boundary events and activity markers. The technique employs functional and inclusion dependency discovery techniques in order to elicit a process-subprocess hierarchy from the event log. Given this hierarchy and the projected logs associated to each node in the hierarchy, parent process and subprocess models are then discovered using existing techniques for flat process model discovery. Finally, the resulting models and logs are heuristically analyzed in order to identify boundary events and markers. By employing approximate dependency discovery tech- niques, it is possible to filter out noise in the event log arising for example from data entry errors or missing events. A validation with one synthetic and two real-life logs shows that process models derived by the proposed technique are more accurate and less complex than those derived with flat process discovery techniques. Meanwhile, a validation on a family of synthetically generated logs shows that the technique is resilient to varying levels of noise.

Alive SMC^2: Bayesian model selection for low-count time series models with intractable likelihoods

In this paper we present a new method for performing Bayesian parameter inference and model choice for low count time series models with intractable likelihoods. The method involves incorporating an alive particle filter within a sequential Monte Carlo (SMC) algorithm to create a novel pseudo-marginal algorithm, which we refer to as alive SMC^2. The advantages of this approach over competing approaches is that it is naturally adaptive, it does not involve between-model proposals required in reversible jump Markov chain Monte Carlo and does not rely on potentially rough approximations. The algorithm is demonstrated on Markov process and integer autoregressive moving average models applied to real biological datasets of hospital-acquired pathogen incidence, animal health time series and the cumulative number of poison disease cases in mule deer.

Bayesian parametric bootstrap for models with intractable likelihoods

In this paper it is demonstrated how the Bayesian parametric bootstrap can be adapted to models with intractable likelihoods. The approach is most appealing when the semi-automatic approximate Bayesian computation (ABC) summary statistics are selected. After a pilot run of ABC, the likelihood-free parametric bootstrap approach requires very few model simulations to produce an approximate posterior, which can be a useful approximation in its own right. An alternative is to use this approximation as a proposal distribution in ABC algorithms to make them more efficient. In this paper, the parametric bootstrap approximation is used to form the initial importance distribution for the sequential Monte Carlo and the ABC importance and rejection sampling algorithms. The new approach is illustrated through a simulation study of the univariate g-and- k quantile distribution, and is used to infer parameter values of a stochastic model describing expanding melanoma cell colonies.