Metamodels for estimating waterway delays through series of queues

A numerical method has been developed for estimating delays on congested waterways. Analytic and numerical results are presented for series of G/G/1 queues, i.e. with generally distributed arrivals and service times and single chambers at each lock. One or two-way traffic operations are modelled. A metamodelling approach which develops simple formulas to approximate the results of simulation models is presented. The structure of the metamodels is developed from queueing theory while their coefficients are statistically estimated from simulation results. The numerical method consists of three modules: (1) delays, (2) arrivals and (3) departures. The first estimates the average waiting time for each lock when the arrival and service time distributions at this lock are known. The second identifies the relations between the arrival distributions at one lock and the departure distributions from the upstream and downstream locks. The third estimates the mean and variance of inter-departure times when the inter-arrival and service time distributions are known. The method can be applied to systems with two-way traffic through common bi-directional servers as well as to one-way traffic systems. Algorithms for both cases are presented. This numerical method is shown to produce results that are close to the simulation results. The metamodels developed for estimating delays and variances of inter-departure times may be applied to waterways and other series of G/G/1 queues. These metamodels for G/G/1 queues may provide key components of algorithms for analyzing networks of queues.     

Simple analytical models for estimating the queue lengths from probe vehicles at traffic signals

As mobile traffic sensor technology gets more attention, mathematical models are being developed that utilize this new data type in various intelligent transportation systems applications. This study introduces simple analytical estimation models for queue lengths from tracked or probe vehicles at traffic signals using stochastic modeling approach. Developed models estimate cycle-to-cycle queue lengths by using primary parameters such as arrival rate, probe vehicle proportions, and signal phase durations. Valuable probability distributions and moment generating functions for probe information types are formulated. Fully analytical closed-form expressions are given for the case ignoring the overflow queue and approximation models are presented for the overflow case. Derived models are compared with the results from VISSIM-microscopic simulation. Analytical steady-state and cycle-to-cycle estimation errors are also derived. Numerical examples are shown for the errors of these estimators that change with probe vehicle market penetration levels, arrival rates, and volume-to-capacity ratios.     

Signalized intersections with variable flow rates: I analysis and simulation

One of the most common measures of signalized intersection operation is the amount of delay a vehicle incurs while passing through the intersection. Traditional models for estimating vehicle delay at intersections generally assume fixed signal timing and uniform arrival rates for vehicles approaching the intersection. One would expect that highly variable arrival rates would result in much longer delays than uniform arrival rates of the same average magnitude. Furthermore, one might expect that signal timing that is adjusted according to traffic volume would result in lower delay signal when variations in flow warrant such adjustable timing. This paper attempts to test several hypotheses concerning the effects of variable traffic arrival rates and adjusted signal timing through the use of simulation. The simulation results corroborate the hypothesis concerning the effect of varying arrival rates. As the variance of the arrival rate over time increases, the average delay per vehicle also increases. Signal timing adjustments based on traffic appear to decrease delay when flow rates vary greatly. As flow variations stabilize, the benefits of signal adjustments tend to diminish.     

An application-oriented model of passenger waiting time based on bus departure time intervals

This paper develops an application-oriented model to estimate waiting times as a function of bus departure time intervals. Bus stops are classified into Type A and B depending on whether they are connected with urban rail transit systems. Distributions of passenger arrival rates are analyzed based on field data for Beijing. The results indicate that the best fits for the distribution of passenger arrival rates for Type A and B bus stops are the lognormal distribution and gamma distribution, respectively. By analyzing relationships between passenger arrival rates and bus departure time intervals, it is demonstrated that parameters of the passenger arrival rate distribution can be expressed by the average and coefficient of variation of bus departure time intervals in functional relationships. The validation shows that the model provides a reliable estimation of the average passenger waiting time based on readily available bus departure time intervals.     

Pedestrian delay estimation at signalized intersections in developing cities

This paper proposes a pedestrian delay model suitable for signalized intersections in developing cities, on the basis of a field study conducted in Xi’an, China. The field study consisted of two parts: Part I involved only one crosswalk, and the signal cycle was divided into 13 subphases; Part II involved 13 crosswalks, but the signal cycles were only divided into green phases and non-green phases. It was found that pedestrian arrival rates were not uniform throughout cycles; pedestrians arriving during green phases might also receive delays; pedestrian signal non-compliance was so severe that delays were greatly reduced, but non-complying pedestrians might still receive delays; and for pedestrians walking different directions, though the relationships between average delay and arrival subphase were different, the overall average delays were almost the same. On the basis of the field study results, some assumptions are made about the relationship between average pedestrian delay and arrival subphase, and a new model is developed to estimate pedestrian delays at signalized intersections. The model is validated using the field data, and the validation results indicate that in Xi’an the new model provides much more accurate estimation than the existing models.     

Passenger arrival and waiting time distributions dependent on train service frequency and station characteristics: A smart card data analysis

Waiting time at public transport stops is perceived by passengers to be more onerous than in-vehicle time, hence it strongly influences the attractiveness and use of public transport. Transport models traditionally assume that average waiting times are half the service headway by assuming random passenger arrivals. However, research agree that two distinct passenger behaviour types exist: one group arrives randomly, whereas another group actively tries to minimise their waiting time by arriving in a timely manner at the scheduled departure time. This study proposes a general framework for estimating passenger waiting times which incorporates the arrival patterns of these two groups explicitly, namely by using a mixture distribution consisting of a uniform and a beta distribution. The framework is empirically validated using a large-scale automatic fare collection system from the Greater Copenhagen Area covering metro, suburban, and regional rail stations thereby giving a range of service headways from 2 to 60 min. It was shown that the proposed mixture distribution is superior to other distributions proposed in the literature. This can improve waiting time estimations in public transport models. The results show that even at 5-min headways 43% of passengers arrive in a timely manner to stations when timetables are available. The results bear important policy implications in terms of providing actual timetables, even at high service frequencies, in order for passengers to be able to minimise their waiting times.     

Evaluating the added-value of online bus arrival prediction schemes

Online predictions of bus arrival times have the potential to reduce the uncertainty associated with bus operations. By better anticipating future conditions, online predictions can reduce perceived and actual passenger travel times as well as facilitate more proactive decision making by service providers. Even though considerable research efforts were devoted to the development of computationally expensive bus arrival prediction schemes, real-world real-time information (RTI) systems are typically based on very simple prediction rules. This paper narrows down the gap between the state-of-the-art and the state-of-the-practice in generating RTI for public transport systems by evaluating the added-value of schemes that integrate instantaneous data and dwell time predictions. The evaluation considers static information and a commonly deployed scheme as a benchmark. The RTI generation algorithms were applied and analyzed for a trunk bus network in Stockholm, Sweden. The schemes are assessed and compared based on their accuracy, reliability, robustness and potential waiting time savings. The impact of RTI on passengers waiting times are compared with those attained by service frequency and regularity improvements. A method which incorporates information on downstream travel conditions outperforms the commonly deployed scheme, leading to a 25% reduction in the mean absolute error. Furthermore, the incorporation of instantaneous travel times improves the prediction accuracy and reliability, and contributes to more robust predictions. The potential waiting time gains associated with the prediction scheme are equivalent to the gains expected when introducing a 60% increase in service frequency, and are not attainable by service regularity improvements.     

Real time queue length estimation for signalized intersections using travel times from mobile sensors

We study how to estimate real time queue lengths at signalized intersections using intersection travel times collected from mobile traffic sensors. The estimation is based on the observation that critical pattern changes of intersection travel times or delays, such as the discontinuities (i.e., sudden and dramatic increases in travel times) and non-smoothness (i.e., changes of slopes of travel times), indicate signal timing or queue length changes. By detecting these critical points in intersection travel times or delays, the real time queue length can be re-constructed. We first introduce the concept of Queue Rear No-delay Arrival Time which is related to the non-smoothness of queuing delay patterns and queue length changes. We then show how measured intersection travel times from mobile sensors can be processed to generate sample vehicle queuing delays. Under the uniform arrival assumption, the queuing delays reduce linearly within a cycle. The delay pattern can be estimated by a linear fitting method using sample queuing delays. Queue Rear No-delay Arrival Time can then be obtained from the delay pattern, and be used to estimate the maximum and minimum queue lengths of a cycle, based on which the real-time queue length curve can also be constructed. The model and algorithm are tested in a field experiment and in simulation.     

Bus arrival time prediction at bus stop with multiple routes

Provision of accurate bus arrival information is vital to passengers for reducing their anxieties and waiting times at bus stop. This paper proposes models to predict bus arrival times at the same bus stop but with different routes. In the proposed models, bus running times of multiple routes are used for predicting the bus arrival time of each of these bus routes. Several methods, which include support vector machine (SVM), artificial neural network (ANN), k nearest neighbours algorithm (k-NN) and linear regression (LR), are adopted for the bus arrival time prediction. Observation surveys are conducted to collect bus running and arrival time data for validation of the proposed models. The results show that the proposed models are more accurate than the models based on the bus running times of single route. Moreover, it is found that the SVM model performs the best among the four proposed models for predicting the bus arrival times at bus stop with multiple routes.     

Slot misuse phenomena in capacity-constrained airports with seasonal demand: the Greek experience

Abstract

Airport slot misuse disturbs the efficient and continuous operation of capacity-constrained airports, leading to congestion and delay problems. Deviations from the coordinated schedule in regional airport systems that feature seasonal demand and delays in certain peak periods are studied in this article. The Greek airport system is considered as a case study. Deviations are quantified by computing the difference between scheduled and actual aircraft arrival times as well as the hourly slot capacity utilization ratio. Two collective indicators for airport benchmarking are proposed. An in-depth analysis of slot allocation deviations and the delays they cause is carried out for a representative sample of airports that are classified according to the proposed indicators. A brief discussion on potential measures to mitigate slot misuse is also presented.     

Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints

This paper focuses on how to minimize the total passenger waiting time at stations by computing and adjusting train timetables for a rail corridor with given time-varying origin-to-destination passenger demand matrices. Given predetermined train skip-stop patterns, a unified quadratic integer programming model with linear constraints is developed to jointly synchronize effective passenger loading time windows and train arrival and departure times at each station. A set of quadratic and quasi-quadratic objective functions are proposed to precisely formulate the total waiting time under both minute-dependent demand and hour-dependent demand volumes from different origin–destination pairs. We construct mathematically rigorous and algorithmically tractable nonlinear mixed integer programming models for both real-time scheduling and medium-term planning applications. The proposed models are implemented using general purpose high-level optimization solvers, and the model effectiveness is further examined through numerical experiments of real-world rail train timetabling test cases.     

Optimal transit routing with partial online information

This paper studies the routing strategy in a transit network with partial online information at stops. By partial online information, we mean that the arrival time of the incoming transit vehicles is available for a subset of the lines serving a stop. To cope with the partial information assumption, a new routing strategy is proposed and closed form formulae for computing expected waiting times and line boarding probabilities are derived. The proposed strategy unifies existing hyperpath-based transit route choice models that assume either no information or full information. Like many existing models, it ensures optimality when all information is available or the headway is exponentially distributed. The problem of determining the attractive set is discussed for each of the three information cases. In particular, a new heuristic algorithm is developed to generate the attractive set in the partial information case, which will always yield a solution no worse than that obtained without any information. The paper also reveals that, when information is available, an optimal hyperpath may contain cycles. Accordingly, the cause of such cycles is analyzed, and a sufficient condition that excludes cycles from optimal hyperpaths is proposed. Finally, numerical experiments are conducted to illustrate the impact of information availability on expected travel times and transit line load distributions. Among other findings, the results suggest that it is more useful to have information on faster lines than on slower lines.     

The price of uncertainty in pavement infrastructure management planning: An integer programming approach

Currently there is a true dichotomy in the pavement maintenance and rehabilitation (M&R) literature. On the one hand, there are integer programming-based models that assume that parameters are deterministically known. On the other extreme, there are stochastic models, with the most popular class being based on the theory of Markov decision processes that are able to account for various sources of uncertainties observed in the real-world. In this paper, we present an integer programming-based alternative to account for these uncertainties. A critical feature of the proposed models is that they provide – a priori – probabilistic guarantees that the prescribed M&R decisions would result in pavement condition scores that are above their critical service levels, using minimal assumptions regarding the sources of uncertainty. By construction of the models, we can easily determine the additional budget requirements when additional sources of uncertainty are considered, starting from a fully deterministic model. We have coined this additional budget requirement the price of uncertainty to distinguish from previous related work where additional budget requirements were studied due to parameter uncertainties in stochastic models. A numerical case study presents valuable insights into the price of uncertainty and shows that it can be large.     

Survey and empirical evaluation of nonhomogeneous arrival process models with taxi data

Arrival processes are important inputs to many transportation system functions, such as vehicle prepositioning, taxi dispatch, bus holding strategies, and dynamic pricing. We conduct a comprehensive survey of the literature which shows that many transport systems employ basic homogeneous arrival process models or static nonhomogeneous processes. We conduct an empirical experiment to compare five state of the art arrival process short term prediction models using a common transportation system data set: New York taxi passenger pickups in 2013. Pickup data is split between 672 observations for model estimation and 96 observations for validation. From our experiment, we obtain evidence to support a recent model called FM‐IntGARCH, which is able to combine the benefits of both time series models and discrete count processes. Using a set of seven performance metrics from the literature, FM‐IntGARCH is shown to outperform the offline models—seasonal factor method, piecewise linear model—as well as the online models—ARIMA, Gaussian Cox process. Implications for operating data‐driven “smart” transit systems and urban informatics are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Reducing bias in probe-based arterial link travel time estimates

The use of probe vehicles to provide estimates of link travel times has been suggested as a means of obtaining travel times within signalized networks for use in advanced traveler information systems. Previous research has shown that bias in arrival time distributions of probe vehicles will lead to a systematic bias in the sample estimate of the mean. This paper proposes a methodology for reducing the effect of this bias. The method, based on stratified sampling techniques, requires that vehicle count data be obtained from an in-road loop detector or other traffic surveillance method. The effectiveness of the methodology is illustrated using simulation results for a single intersection approach and for an arterial corridor. The results for the single intersection approach indicate a correlation (R²) between the biased estimate and the population mean of 0.61, and an improved correlation between the proposed estimation method and the population mean of 0.81. Application of the proposed method to the arterial corridor resulted in a reduction in the mean travel time error of approximately 50%, further indicating that the proposed estimation method provides improved accuracy over the typical method of computing the arithmetic mean of the probe reports.     

Real-time queue length estimation for congested signalized intersections

How to estimate queue length in real-time at signalized intersection is a long-standing problem. The problem gets even more difficult when signal links are congested. The traditional input–output approach for queue length estimation can only handle queues that are shorter than the distance between vehicle detector and intersection stop line, because cumulative vehicle count for arrival traffic is not available once the detector is occupied by the queue. In this paper, instead of counting arrival traffic flow in the current signal cycle, we solve the problem of measuring intersection queue length by exploiting the queue discharge process in the immediate past cycle. Using high-resolution “event-based” traffic signal data, and applying Lighthill–Whitham–Richards (LWR) shockwave theory, we are able to identify traffic state changes that distinguish queue discharge flow from upstream arrival traffic. Therefore, our approach can estimate time-dependent queue length even when the signal links are congested with long queues. Variations of the queue length estimation model are also presented when “event-based” data is not available. Our models are evaluated by comparing the estimated maximum queue length with the ground truth data observed from the field. Evaluation results demonstrate that the proposed models can estimate long queues with satisfactory accuracy. Limitations of the proposed model are also discussed in the paper.     

Real options and flexibility analysis in design and management of one-way mobility on-demand systems using decision rules

This study explores the concepts of real options and flexibility analysis as an approach to address uncertain demand growth in mobility on-demand (MoD) vehicle-sharing systems, with the goal of improving expected lifecycle performance. As MoD systems are gaining popularity worldwide, they inevitably face significant uncertainty in terms of needs and customer demands. Designing, planning capacity deployment, and operating such system can be challenging, and require significant capital investments for companies and cities. Two distinct real options analysis (ROA) models are developed to evaluate and optimize flexible strategies for these systems, relying on a novel methodological approach to value flexibility based on decision rules. The decision-rule-based approach differs from standard ROA approaches used to quantify the value of flexibility in irreversible investment projects, typically based on dynamic programming. It emulates the decision-making process by capturing mathematically a triggering mechanism that determines when it is best to exercise the flexibilities embedded in the system design. Two prevalent types of MoD systems are studied in this paper as demonstration of the methodological framework: a station-based system where customers must pick up and return the vehicle at specific locations, and a free-floating system, where customers may pick up and drop the car anywhere within a certain area. A simulation-based approach is used to analyze the station-based system, which models the rebalancing operations from a micro-level perspective. The approach consists of a discrete event simulator for performance estimation, and an optimization algorithm for design space exploration that integrates a population-based search algorithm with Optimal Computing Budget Allocation (OCBA). For the free-floating system, an analytical model is developed where the decision rule is formulated into and solved using stochastic mixed integer programming (MIP). The study provides guidance to system operators on potential strategies for deploying MoD systems, considering explicitly uncertainty and flexibility as a value enhancing mechanism.     

Balancing energy consumption and risk of delay in high speed trains: A three-objective real-time eco-driving algorithm with fuzzy parameters

Eco-driving is an energy efficient traffic operation measure that may lead to important energy savings in high speed railway lines. When a delay arises in real time, it is necessary to recalculate an optimal driving that must be energy efficient and computationally efficient.In addition, it is important that the algorithm includes the existing uncertainty associated with the manual execution of the driving parameters and with the possible future traffic disturbances that could lead to new delays.This paper proposes a new algorithm to be executed in real time, which models the uncertainty in manual driving by means of fuzzy numbers. It is a multi-objective optimization algorithm that includes the classical objectives in literature, running time and energy consumption, and as well a newly defined objective, the risk of delay in arrival. The risk of delay in arrival measure is based on the evolution of the time margin of the train up to destination.The proposed approach is a dynamic algorithm designed to improve the computational time. The optimal Pareto front is continuously tracked during the train travel, and a new set of driving commands is selected and presented to the driver when a delay is detected.The algorithm evaluates the 3 objectives of each solution using a detailed simulator of high speed trains to ensure that solutions are realistic, accurate and applicable by the driver. The use of this algorithm provides energy savings and, in addition, it permits railway operators to balance energy consumption and risk of delays in arrival. This way, the energy performance of the system is improved without degrading the quality of the service.     

A stochastic model of traffic flow: Theoretical foundations

In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.     

Uncertainty modeling for bus selection and allocation in a private transportation system

ABSTRACT

This paper describes the development of a probabilistic formulation that provides global optimum selection and allocation of a fleet of buses in a private transportation system of an organization where a third party is hired to provide transportation for its employees and their dependents. In this private transportation system, a fleet of buses is to be selected and allocated to serve employees and their independents on different prescheduled trips along different routes from the organization’s headquarters and residential compound where round-trip times of scheduled trips are subject to uncertainty due to random delays. We propose a probabilistic approach based on 0-1 integer programming for the selection and allocation to determine the optimal number and size of buses assigned to a set of prescheduled trips in a particular time interval. Examples and a case study are presented to illustrate the applicability and suitability of the proposed approach.