Hybrid predictive control for real-time optimization of public transport systems’ operations based on evolutionary multi-objective optimization

A hybrid predictive control formulation based on evolutionary multi-objective optimization to optimize real-time operations of public transport systems is presented. The state space model includes bus position, expected load and arrival time at stops. The system is based on discrete events, and the possible operator control actions are: holding vehicles at stations and skipping some stations. The controller (operator) pursues the minimization of a dynamic objective function to generate better operational decisions under uncertain demand at bus stops. In this work, a multi-objective approach is conducted to include different goals in the optimization process that could be opposite. In this case, the optimization was defined in terms of two objectives: waiting time minimization on one side, and impact of the strategies on the other. A genetic algorithm method is proposed to solve the multi-objective dynamic problem. From the conducted experiments considering a single bus line corridor, we found that the two objectives are opposite but with a certain degree of overlapping, in the sense that in all cases both objectives significantly improve the level of service with respect to the open-loop scenario by regularizing the headways. On average, the observed trade-off validates the proposed multi-objective methodology for the studied system, allowing dynamically finding the pseudo-optimal Pareto front and making real-time decisions based on different optimization criteria reflected in the proposed objective function compounds.     

Designing a home-to-work bus service in a metropolitan area

This paper presents a model and an algorithm for the design of a home-to-work bus service in a metropolitan area. This type of service must display an equilibrium between conflicting criteria such as efficiency, effectiveness, and equity. To this end, we introduce a multi-objective model in which, among other aspects, equity is considered by time windows on the arrival time of a bus at a stop. Time windows can have other uses such as, for example, guaranteeing synchronization of the service with other transportation modes. This is one of the guiding principles of the proposed model which is based on concepts that simultaneously tackle several issues at once. Along this line, we propose a cluster routing approach to model both bus stop location and routing in urban road networks where turn restrictions exist. The resulting multi-objective location-routing model is solved by a tabu search algorithm. As an application, we analyze a home-to-work bus service for a large research center located in Rome, Italy. This case study provides a benchmark for the algorithmic results, and shows the practical relevance of the proposed methodology.     

Analysis of real-time control strategies in a corridor with multiple bus services

Control strategies have been widely used in the literature to counteract the effects of bus bunching in passenger‘s waiting times and its variability. These strategies have only been studied for the case of a single bus line in a corridor. However, in many real cases this assumption does not hold. Indeed, there are many transit corridors with multiple bus lines interacting, and this interaction affects the efficiency of the implemented control mechanism.This work develops an optimization model capable of executing a control scheme based on holding strategy for a corridor with multiple bus lines.We analyzed the benefits in the level of service of the public transport system when considering a central operator who wants to maximize the level of service for users of all the bus lines, versus scenarios where each bus line operates independently. A simulation was carried out considering two medium frequency bus lines that serve a set of stops and where these two bus lines coexist in a given subset of stops. In the simulation we compared the existence of a central operator, using the optimization model we developed, against the independent operation of each line.In the simulations the central operator showed a greater reduction in the overall waiting time of the passengers of 55% compared to a no control scenario. It also provided a balanced load of the buses along the corridor, and a lower variability of the bus headways in the subset of stops where the lines coexist, thus obtaining better reliability for all types of passengers present in the public transport system.     

Real-time bus route state forecasting using particle filter and mesoscopic modeling

In the absence of system control strategies, it is common to observe bus bunching in transit operations. A transit operator would benefit from an accurate forecast of bus operations in order to control the system before it becomes too disrupted to be restored to a stable condition. To accomplish this, we present a general bus prediction framework. This framework relies on a stochastic and event-based bus operation model that provides sets of possible bus trajectories based on the observation of current bus positions, available via global positioning system (GPS) data. The median of the set of possible trajectories, called a particle, is used as the prediction. In particular, this enables the anticipation of irregularities between buses. Several bus models are proposed depending on the dwell and inter-stop running time representations. These models are calibrated and applied to a real case study thanks to the high quality data provided by TriMet (the Portland, Oregon, USA transit district). Predictions are finally evaluated by an a posteriori comparison with the real trajectories. The results highlight that only bus models accounting for the bus load can provide valid forecasts of a bus route over a large prediction horizon, especially for headway variations. Accounting for traffic signal timings and actual traffic flows does not significantly improves the prediction. Such a framework paves the way for further development of refined dynamic control strategies for bus operations.     

Influential vectors in fuel consumption by an urban bus operator: Bus route,driver behavior or vehicle type?

Energy costs account for an important share of the total costs of urban and suburban bus operators. The purpose of this paper is to expand empirical research on bus transit operation costs and identify the key factors that influence bus energy efficiency of the overall bus fleet of one operator and aid to the management of its resources.We estimate a set of multivariate regression models, using cross-section dataset of 488 bus drivers operating over 92 days in 2010, in 87 routes with different bus typologies, of a transit company operating in the Lisbon’s Metropolitan Area (LMA), Rodoviária de Lisboa, S.A.Our results confirm the existence of influential variables regarding energy efficiency and these are mainly: vehicle type, commercial speed, road grades over 5% and bus routes; and to a lesser extent driving events such as: sudden longitudinal decelerations and excessive engine rotation. The methodology proved to be useful for the bus operator as a decision-support tool for efficiency optimization purpose at the company level.     

Secrets of success: assessing the large increases in transit ridership achieved by Houston and San Diego transit providers

This paper summarizes and updates the findings from an earlier study by the same authors of transit systems in Houston (all bus) and San Diego (bus and light rail). Both systems achieved unusually large increases in transit ridership during a period in which most transit systems in other metropolitan areas were experiencing large losses. Based on ridership models estimated using cross section and time series data, the paper quantifies the relative contributions of policy variables and factors beyond the control of transit operators on ridership growth. It is found that large ridership increases in both areas are caused principally by large service increases and fare reductions, as well as metropolitan employment and population growth. In addition, the paper provides careful estimates of total and operating costs per passenger boarding and per passenger mile for Houston's bus operator and San Diego's bus and light rail operators. These estimates suggest that the bus systems are more cost-effective than the light rail system on the basis of total costs. Finally, the paper carries out a series of policy simulations to analyze the effects of transit funding levels and metropolitan development patterns on transit ridership and farebox recovery ratio.     

Analytical model for calibrating delay at congested bus stops

Abstract

A model is proposed to calculate the overall operating and delay times spent at bus stops due to passenger boarding and alighting and the time lost to queuing caused by bus stop saturation. A formula for line demand at each stop and the interaction between the buses themselves is proposed and applied to different bus stops depending on the number of available berths. The application of this model has quantified significant operational delays suffered by users and operator due to consecutive bus arrival at stops, even with flows below bus stop capacity.     

A systematic analysis of multimodal transport systems with road space distribution and responsive bus service

A smart design of transport systems involves efficient use and allocation of the limited urban road capacity in the multimodal environment. This paper intends to understand the system-wide effect of dividing the road space to the private and public transport modes and how the public transport service provider responds to the space changes. To this end, the bimodal dynamic user equilibrium is formulated for separated road space. The Macroscopic Fundamental Diagram (MFD) model is employed to depict the dynamics of the automobile traffic for its state-dependent feature, its inclusion of hypercongestion, and its advantage of capturing network topology. The delay of a bus trip depends on the running speed which is in turn affected by bus lane capacity and ridership. Within the proposed bimodal framework, the steady-state equilibrium traffic characteristics and the optimal bus fare and service frequency are analytically derived. The counter-intuitive properties of traffic condition, modal split, and behavior of bus operator in the hypercongestion are identified. To understand the interaction between the transport authority (for system benefit maximization) and the bus operator (for its own benefit maximization), we examine how the bus operator responds to space changes and how the system benefit is influenced with the road space allocation. With responsive bus service, the condition, under which expanding bus lane capacity is beneficial to the system as a whole, has been analytically established. Then the model is applied to the dynamic framework where the space allocation changes with varying demand and demand-responsive bus service. We compare the optimal bus services under different economic objectives, evaluate the system performance of the bimodal network, and explore the dynamic space allocation strategy for the sake of social welfare maximization.     

A simulation‐based reliability assessment approach for congested transit network

This paper is an attempt to develop a generic simulation‐based approach to assess transit service reliability, taking into account interaction between network performance and passengers' route choice behaviour. Three types of reliability, say, system wide travel time reliability, schedule reliability and direct boarding waiting‐time reliability are defined from perspectives of the community or transit administration, the operator and passengers. A Monte Carlo simulation approach with a stochastic user equilibrium transit assignment model embedded is proposed to quantify these three reliability measures of transit service. A simple transit network with a bus rapid transit (BRT) corridor is analysed as a case study where the impacts of BRT components on transit service reliability are evaluated preliminarily.     

Optimization of grid bus transit systems with elastic demand

Current analytic models for optimizing urban bus transit systems tend to sacrifice geographic realism and detail in order to obtain their solutions. The models presented here shows how an optimization approach can be successful without oversimplifying spatial characteristics and demand patterns of urban areas and how a grid bus transit system in a heterogeneous urban environment with elastic demand is optimized. The demand distribution over the service region is discrete, which can realistically represent geographic variation. Optimal network characteristics (route and station spacings), operating headways and fare are found, which maximize the total operator profit and social welfare. Irregular service regions, many‐to‐many demand patterns, and vehicle capacity constraints are considered in a sequential optimization process. The numerical results show that at the optima the operator profit and social welfare functions are rather flat with respect to route spacing and headway, thus facilitating the tailoring of design variables to the actual street network and particular operating schedule without a substantial decrease in profit. The sensitivities of the design variables to some important exogenous factors are also presented.     

Mixed RP/SP models incorporating interaction effects

In order to analyse the impact of a new train service in Cagliari (Italy) a databank including information from a revealed preference (RP) and a stated preference (SP) survey was set up. The RP data concern choice between car, bus and train; the SP data consider the binary choice between a new train service (quicker, more frequent, with a lower fare and more stations than the current one) and the alternative currently chosen by car and bus users. Logit models allowing for correlation among RP alternatives were estimated for this mixed RP/SP data set using the artificial tree structure method. The analysis included level-of-service variables measured with an unusually high level of precision, latent or second order variables (such as comfort), inertia and interaction variables. Different specifications of the utility function were tested, including the expenditure rate model, and the effects of these specifications on modelling results are highlighted. Our results show that for a population mainly composed of fixed income workers, the expenditure rate model is superior to the traditional wage rate model, yielding lower and more significant subjective values of time. Moreover, we found that the non-linear specifications appear to be more suitable as not only better model results were obtained, but also the real distribution of the error terms was revealed (i.e. highlighting correlation among public transport options).     

Passenger experience with quality-enhanced bus service: the tyne and wear ‘superoute’ services

This paper investigates the role that enhanced service quality introduced into a deregulated market has in improving the experience of bus travel by a sample of passengers in the Tyne and Wear area of England. A generalised ordered choice (GOC) model that accounts for preference heterogeneity through random parameters, as well as heteroscedasticity in unobserved variance, and random parameterisation of thresholds, is implemented to identify sources of influence on the overall experience of bus travel in the presence and absence of the quality-enhanced treatment of service. The GOC model is contrasted with a standard ordered logit model, and the marginal effects associated with the preferred GOC model are derived for each influencing attribute, taking into account the various ways in which each influence contributes to the utility associated with each level of bus experience. The paper supports a view that the introduction of quality improvements, via a Quality Bus Partnership, does contribute non-marginally to an increase in a positive bus experience, and signals a way forward through cooperative intervention, to grow patronage. Knowing which attributes successfully deliver a more positive experience (and those that do not) means that resources are effectively targeted at the aspect of service provision which will increase patronage and therefore revenues, satisfying the objectives of both the bus operator and the local authority partner.     

Bi-level GA and GIS for Multi-objective TSP Route Planning

Abstract

Route planning is usually carried out to achieve a single objective such as to minimize transport cost, distance traveled or travel time. This article explores an approach to multi-objective route planning using a genetic algorithm (GA) and geographical information system (GIS) approach. The method is applied to the case of a tourist sight-seeing itinerary, where a route is planned by a tour operator to cover a set of places of interest within a given area. The route planning takes into account four criteria including travel time, vehicle operating cost, safety and surrounding scenic view quality. The multi-objective route planning in this paper can be viewed as an extension of the traditional traveling salesman problem (TSP) since a tourist needs to pass through a number of sight points. The four criteria are quantified using the spatial analytic functions of GIS and a generalized cost for each link is calculated. As different criteria play different roles in the route selection process, and the best order of the multiple points needs to be determined, a bi-level GA has been devised. The upper level aims to determine the weights of each criterion, while the lower level attempts to determine the best order of the sights to be visited based on the new generalized cost that is derived from the weights at the upper level. Both levels collaborate during the iterations and the route with the minimal generalized cost is thus determined. The above sight-seeing route planning methodology has been examined in a region within the central area of Singapore covering 19 places of interest.     

A connected-vehicle-based dynamic control model for managing the bus bunching problem with capacity constraints

This paper describes a connected-vehicle-based system architecture which can provide more precise and comprehensive information on bus movements and passenger status. Then a dynamic control method is proposed using connected vehicle data. Traditionally, the bus bunching problem has been formulated into one of two types of optimization problem. The first uses total passenger time cost as the objective function and capacity, safe headway, and other factors as constraints. Due to the large number of scenarios considered, this type of framework is inefficient for real-time implementation. The other type uses headway adherence as the objective and applies a feedback control framework to minimize headway variations. Due to the simplicity in the formulation and solution algorithms, the headway-based models are more suitable for real-time transit operations. However, the headway-based feedback control framework proposed in the literature still assumes homogeneous conditions at all bus stations, and does not consider restricting passenger loads within the capacity constraints. In this paper, a dynamic control framework is proposed to improve not only headway adherence but also maintain the stability of passenger load within bus capacity in both homogenous and heterogeneous situations at bus stations. The study provides the stability conditions for optimal control with heterogeneous bus conditions and derives optimal control strategies to minimize passenger transit cost while maintaining vehicle loading within capacity constraints. The proposed model is validated with a numerical analysis and case study based on field data collected in Chengdu, China. The results show that the proposed model performs well on high-demand bus routes.     

Modeling intermodal equilibrium for bimodal transportation system design problems in a linear monocentric city

This paper investigates the intermodal equilibrium, road toll pricing, and bus system design issues in a congested highway corridor with two alternative modes - auto and bus - which share the same roadway along this corridor. On the basis of an in-depth analysis of the demand and supply sides of the bimodal transportation system, the mode choice equilibrium of travelers along the continuum corridor is first presented and formulated as an equivalent variational inequality problem. The solution properties of the bimodal continuum equilibrium formulation are analytically explored. Two models, which account for different infrastructure/system regulatory regimes (public and private), are then proposed. In the public regulatory model, the road toll location and charge level are simultaneously optimized together with the bus service fare and frequency. In the private regulatory model, the fare and frequency of bus services, which are operated by a profit-driven private operator, are optimized for exogenously given toll pricing schemes. Finally, an illustrative example is given to demonstrate the application of the proposed models. Sensitivity analysis of residential/household distribution along the corridor is carried out together with a comparison of four different toll pricing schemes (no toll, first best, distance based, and location based). Insightful findings are reported on the interrelationships among modal competition, market regulatory regimes, toll pricing schemes, and urban configurations as well as their implications in practice.     

Multiple period optimization of bus transit systems

Analytic models are developed for optimizing bus services with time dependence and elasticity in their demand characteristics. Some supply parameters, i.e. vehicle operating costs and speeds are also allowed to vary over time. The multiple period models presented here allow some of the optimized system characteristics (e.g. route structure) to be fized at values representing the best compromise over different time periods, while other characteristics (e.g. service headways) may be optimized within each period. In a numerical example the demand is assumed to fluctuate over a daily cycle (e.g. peak, offpeak and night), although the same models can also be used for other cyclical or noncyclical demand variations over any number of periods. Models are formulated and compared for four types of conditions, which include steady fixed demand, cyclical fixed demand, steady equilibrium demand and cyclical equilibrium demand. When fixed demand is assumed, the optimization objective is minimum total system cost, including operator cost and user cost, while operator profit and social welfare are the objective functions maximized for equilibrium demand. The major results consist of closed form solutions for the route spacings, headways, fares and costs for optimized feeder bus services under various demand conditions. A comparison of the optimization results for the four cases is also presented. When demand and bus operating characteristics are allowed to vary over time, the optimal functions are quite similar to those for steady demand and supply conditions. The optimality of a constant ratio between the headway and route spacing, which is found at all demand densities if demand is steady, is also maintained with a multi-period adjustment factor in cyclical demand cases, either exactly or with a relatively negligible approximation. These models may be used to analyze and optimize fairly complex feeder or radial bus systems whose demand and supply characteristics may vary arbitrarily over time.     

Modeling and optimizing urban bus transit considering headway variation for cost and service reliability analysis

Due to the stochastic nature of traffic conditions and demand fluctuations, it is a challenging task for operators to maintain reliable services, and passengers often suffer from longer travel times. A failure to consider this issue while planning bus services may lead to undesirable results, such as higher costs and a deterioration in level of service. Considering headway variation at route stops, this paper develops a mathematical model to optimize bus stops and dispatching headways that minimize total cost, consisting of both user and operator costs. A Genetic Algorithm is applied to search for a cost-effective solution in a real-world case study of a bus transit system, which improves service reliability in terms of a reduced coefficient of variation of headway.     

Evaluation of an existing bus network using a transit network optimisation model: a case study of the Hiroshima City Bus network

This study evaluates an existing bus network from the perspectives of passengers, operators, and overall system efficiency using the output of a previously developed transportation network optimisation model. This model is formulated as a bi-level optimisation problem with a transit assignment model as the lower problem. The upper problem is also formulated as bi-level optimisation problem to minimise costs for both passengers and operators, making it possible to evaluate the effects of reducing operator cost against passenger cost. A case study based on demand data for Hiroshima City confirms that the current bus network is close to the Pareto front, if the total costs to both passengers and operators are adopted as objective functions. However, the sensitivity analysis with regard to the OD pattern fluctuation indicates that passenger and operator costs in the current network are not always close to the Pareto front. Finally, the results suggests that, regardless of OD pattern fluctuation, reducing operator costs will increase passenger cost and increase inequity in service levels among passengers.     

Mitigation of disruptions in public transit by Bee Colony Optimization

Dispatchers in many public transit companies face the daily problem of assigning available buses to bus routes under conditions of bus shortages. In addition to this, weather conditions, crew absenteeism, traffic accidents, traffic congestion and other factors lead to disturbances of the planned schedule. We propose the Bee Colony Optimization (BCO) algorithm for mitigation of bus schedule disturbances. The developed model takes care of interests of the transit operator and passengers. The model reassigns available buses to bus routes and, if it is allowed, the model simultaneously changes the transportation network topology (it shortens some of the planned bus routes) and reassigns available buses to a new set of bus routes. The model is tested on the network of Rivera (Uruguay). Results obtained show that the proposed algorithm can significantly mitigate disruptions.     

Estimation of bus dwell time using univariate time series models

A significant proportion of bus travel time is contributed by dwell time for passenger boarding and alighting. More accurate estimation of bus dwell time (BDT) can enhance efficiency and reliability of public transportation system. Regression and probabilistic models are commonly used in literatures where a set of independent variables are used to define the statistical relationship between BDT and its contributing factors. However, due to technical and monetary constraints, it is not always feasible to collect all the data required for the models to work. More importantly, the contributing factors may vary from one bus route to another. Time series based methods can be of great interest as they require only historical time series data, which can be collected using a facility known as automatic vehicle location (AVL) system. This paper assesses four different time series based methods namely random walk, exponential smoothing, moving average (MA), and autoregressive integrated moving average to model and estimate BDT based on AVL data collected from Auckland. The performances of the proposed methods are ranked based on three important factors namely prediction accuracy, simplicity, and robustness. The models showed promising results and performed differently for central business district (CBD) and non‐CBD bus stops. For CBD bus stops, MA model performed the best, whereas for non‐CBD bus stops, ARIMA model performed the best compared with other time series based models. Copyright © 2014 John Wiley & Sons, Ltd.