Frequency-based transit assignment considering seat capacities

This paper proposes a frequency-based assignment model that considers travellers probability of finding a seat in their perception of route cost and hence also their route choice. The model introduces a “fail-to-sit” probability at boarding points with travel costs based on the likelihood of travelling seated or standing. Priority rules are considered; in particular it is assumed that standing on-board passengers will occupy any available seats of alighting passengers before newly boarding passengers can fill any remaining seats. At the boarding point passengers are assumed to mingle, meaning that FIFO is not observed, as is the case for many crowded bus and metro stops, particularly in European countries. The route choice considers the common lines problem and an user equilibrium solution is sought through a Markov type network loading process and the method of successive averages. The model is first illustrated with a small example network before being applied to the inner zone of London’s underground network. The effect of different values passengers might attach to finding a seat are illustrated. Applications of the model for transit planning as well as for information provision at the journey planner stage are discussed.     

Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.     

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.     

Air itinerary shares estimation using multinomial logit models

ABSTRACT

The main goal of this study is the development of an aggregate air itinerary market share model. In order to achieve this, multinomial logit models are applied to distribute the city-pair passenger demand across the available itineraries. The models are developed at an aggregate level using open-source booking data for a large group of city-pairs within the US air transport system. Although there is a growing trend in the use of discrete choice models in the aviation industry, existing air itinerary share models are mostly focused on supporting carrier decision-making. Consequently, those studies define itineraries at a more disaggregate level using variables describing airlines and time preferences. In this study, we define itineraries at a more aggregate level, i.e. as a combination of flight segments between an origin and destination, without further insight into service preferences. Although results show some potential for this approach, there are challenges associated with prediction performance and computational intensity.     

A math-heuristic algorithm for the integrated air service recovery

A sophisticated flight schedule might be easily disrupted due to adverse weather, aircraft mechanical failures, crew absences, etc. Airlines incur huge costs stemming from such flight schedule disruptions in addition to the serious inconveniences experienced by passengers. Therefore, an efficient recovery solution that simultaneously decreases an airline's recovery cost while simultaneously mitigating passenger dissatisfaction is of great importance to the airline industry. In this paper, we study the integrated airline service recovery problem in which the aircraft and passenger schedule recovery problems are simultaneously addressed, with the objective of minimizing aircraft recovery and operating costs, passenger itinerary delay cost, and passenger itinerary cancellation cost.Recognizing the inherent difficulty in modeling the integrated airline service recovery problem within a single formulation (due to its huge solution space and quick response requirement), we propose a three-stage sequential math-heuristic framework to efficiently solve this problem, wherein the flight schedules and aircraft rotations are recovered in the first stage, Then, a flight rescheduling problem and passenger schedule recovery problems are iteratively solved in the next two stages. Time-space network flow representations, along with mixed-integer programming formulations, and algorithms that take advantages of the underlying problem structures, are proposed for each of three stages. This algorithm was tested on realistic data provided by the ROADEF 2009 challenge and the computational results reveal that our algorithm generated the best solution in nearly 72% of the test instances, and a near-optimal solution was achieved in the remaining instances within an acceptable timeframe. Furthermore, we also ran additional computational runs to explore the underlying characteristics of the proposed algorithm, and the recorded insights can serve as a useful guide during practical implementations of this algorithm.     

Some developments in equilibrium traffic assignment

A network optimization problem is formulated which yields a probabilistic equilibrated traffic assignment incorporating congestion effects and which as a special case, reduces to a user optimized equilibrium solution. In the resulting model, path choice is determined by a logit formula in which path costs are functions of the assigned flows. The article also demonstrates the similarity between some fixed demand incremental methods of traffic assignment and the minimization problem associated with computing the user equilibrium assignment.     

An integrated Bayesian approach for passenger flow assignment in metro networks

This paper proposes an integrated Bayesian statistical inference framework to characterize passenger flow assignment model in a complex metro network. In doing so, we combine network cost attribute estimation and passenger route choice modeling using Bayesian inference. We build the posterior density by taking the likelihood of observing passenger travel times provided by smart card data and our prior knowledge about the studied metro network. Given the high-dimensional nature of parameters in this framework, we apply the variable-at-a-time Metropolis sampling algorithm to estimate the mean and Bayesian confidence interval for each parameter in turn. As a numerical example, this integrated approach is applied on the metro network in Singapore. Our result shows that link travel time exhibits a considerable coefficient of variation about 0.17, suggesting that travel time reliability is of high importance to metro operation. The estimation of route choice parameters conforms with previous survey-based studies, showing that the disutility of transfer time is about twice of that of in-vehicle travel time in Singapore metro system.     

A semi-analytical approach for solving the bottleneck model with general user heterogeneity

This paper proposes a novel semi-analytical approach for solving the dynamic user equilibrium (DUE) of a bottleneck model with general heterogeneous users. The proposed approach makes use of the analytical solutions from the bottleneck analysis to create an equivalent assignment problem that admits closed-form commute cost functions. The equivalent problem is a static and asymmetric traffic assignment problem, which can be formulated as a variational inequality problem (VIP). This approach provides a new tool to analyze the properties of the bottleneck model with general heterogeneity, and to design efficient solution methods. In particular, the existence and uniqueness of the DUE solution can be established using the P-property of the Jacobian matrix. Our numerical experiments show that a simple decomposition algorithm is able to quickly solve the equivalent VIP to high precision. The proposed VIP formation is also extended to address simultaneous departure time and route choice in a single O–D origin-destination network with multiple parallel routes.     

Stochastic transit equilibrium

We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing in-vehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic common-lines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic common-lines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a real-size network case as the next step of this research.     

Latent temporal preferences: An application to airline travel

An essential element of demand modeling in the airline industry is the representation of time of day demand—the demand for a given itinerary as a function of its departure or arrival times. It is an important datum that drives successful scheduling and fleet decisions. There are two key components to this problem: the distribution of the time of day demand and how preferred travel time influences itinerary choice. This paper focuses on estimating the time of day distribution. Our objective is to estimate it in a manner that is not confounded with air travel supply; is a function of the characteristics of the traveler, the trip, and the market; and accounts for potential measurement errors in self-reported travel time preferences. We employ a stated preference dataset collected by intercepting people who were booking continental US trips via an internet booking service. Respondents reported preferred travel times as well as choices from a hypothetical set of itineraries. We parameterize the time of day distribution as a mixture of normal distributions (due to the strong peaking nature of travel time preferences) and allow the mixing function to vary by individual characteristics and trip attributes. We estimate the time of day distribution and the itinerary choice model jointly in a manner that accounts for measurement error in the self-reported travel time preferences. We find that the mixture of normal distributions fits the time of day distribution well and is behaviorally intuitive. The strongest covariates of travel time preferences are party size and time zone change. The methodology employed to treat self-reported travel time preferences as potentially having error contributes to the broader transportation time of day demand literature, which either assumes that the desired travel times are known with certainty or that they are unknown. We find that the error in self-reported travel time preferences is statistically significant and impacts the inferred time of day demand distribution.     

A bi‐level programming approach — Optimal transit fare under line capacity constraints

The fare of a transit line is one of the important decision variables for transit network design. It has been advocated as an efficient means of coordinating the transit passenger flows and of alleviating congestion in the transit network. This paper shows how transit fare can be optimized so as to balance the passenger flow on the transit network and to reduce the overload delays of passengers at transit stops. A bi‐level programming method is developed to optimize the transit fare under line capacity constraints. The upper‐level problem seeks to minimize the total network travel time, while the lower‐level problem is a stochastic user equilibrium transit assignment model with line capacity constraints. A heuristic solution algorithm based on sensitivity analysis is proposed. Numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Risk‐based stochastic equilibrium assignment model in augmented urban railway network

This study developed a methodology to model the passenger flow stochastic assignment in urban railway network (URN) with the considerations of risk attitude. Through the network augmentation technique, the urban railway system is represented by an augmented network in which the common traffic assignment method can be used directly similar to a generalized network form. Using the analysis of different cases including deterministic travel state, emergent event, peak travel, and completely stochastic state, we developed a stochastic equilibrium formulation to capture these stochastic considerations and give effects of risk aversion level on the URN performance, the passenger flow at transfer stations through numerical studies. Copyright © 2012 John Wiley & Sons, Ltd.     

Validation of a schedule‐based capacity restraint transit assignment model for a large‐scale network

This paper describes the application of a capacity restraint trip assignment algorithm to a real, large‐scale transit network and the validation of the results. Unlike the conventional frequency‐based approach, the network formulation of the proposed model is dynamic and schedule‐based. Transit vehicles are assumed to operate to a set of pre‐determined schedules. Passengers are assumed to select paths based on a generalized cost function including in‐vehicle and out‐of‐vehicle time and line change penalty. The time‐varying passenger demand is loaded onto the network by a time increment simulation method, which ensures that the capacity restraint of each vehicle during passenger boarding is strictly observed. The optimal‐path and path‐loading algorithms are applied iteratively by the method of successive averages until the network converges to the predictive dynamic user equilibrium. The Hong Kong Mass Transit Railway network is used to validate the model results. The potential applications of the model are also discussed.     

Simultaneous optimization of transit line configuration and passenger line assignment

Passenger transportation in most large cities relies on an efficient mass transit system, whose line configuration has direct impacts on the system operating cost, passenger travel time and line transfers. Unfortunately, the interplay between transit line configuration and passenger line assignment has been largely ignored in the literature. This paper presents a model for simultaneous optimization of transit line configuration and passenger line assignment in a general network. The model is formulated as a linear binary integer program and can be solved by the standard branch and bound method. The model is illustrated with a couple of minimum spanning tree networks and a simplified version of the general Hong Kong mass transit railway network.     

A linear programming-based method for the network revenue management problem of air cargo

One critical operational issue of air cargo operation faced by airlines is the control over the sales of their limited cargo space. Since American Airlines’ successful implementation in the post-deregulation era, revenue management (RM) has become a common practice for the airline industry. However, unlike the air passenger operation supported by well-developed RM systems with advanced decision models, the decision process in selling air cargo space to freight forwarders is usually based on experience, without much support from optimization techniques. This study first formulates a multi-dimensional dynamic programming (DP) model to present a network RM problem for air cargo. In order to overcome the computational challenge, this study develops two linear programming (LP) based models to provide the decision support operationally suitable for airlines. In addition, this study further introduces a dynamic adjustment factor to alleviate the inaccuracy problem of the static LP models in estimating resource opportunity cost. Finally, a numerical experiment is performed to validate the applicability of the developed model and solution algorithm to the real-world problems.     

A capacity restraint transit assignment with elastic line frequency

This paper proposes a new formulation for the capacity restraint transit assignment problem with elastic line frequency, in which the line frequency is related to the passenger flows on transit lines. A stochastic user equilibrium transit assignment model with congestion and elastic line frequency is proposed and the equivalent mathematical programming problem is also formulated. Since the passenger waiting time and the line capacity are dependent on the line frequency, a fixed point problem with respect to the line frequency is devised accordingly. The existence of the fixed point problem has been proved. A solution algorithm for the proposed model is presented. Finally, a numerical example is used to illustrate the application of the proposed model and solution algorithm.     

An activity-based approach for scheduling multimodal transit services

This paper proposes a new activity-based transit assignment model for investigating the scheduling (or timetabling) problem of transit services in multi-modal transit networks. The proposed model can be used to generate the short-term and long-term timetables of multimodal transit lines for transit operations and service planning purposes. The interaction between transit timetables and passenger activity-travel scheduling behaviors is captured by the proposed model, as the activity and travel choices of transit passengers are considered explicitly in terms of departure time choice, activity/trip chain choices, activity duration choice, transit line and mode choices. A heuristic solution algorithm which combines the Hooke–Jeeves method and an iterative supply–demand equilibrium approach is developed to solve the proposed model. Two numerical examples are presented to illustrate the differences between the activity-based approach and the traditional trip-based method, together with comparison on the effects of optimal timetables with even and uneven headways. It is shown that the passenger travel scheduling pattern derived from the activity-based approach is significantly different from that obtained by the trip-based method, and that a demand-sensitive (with uneven headway) timetable is more efficient than an even-headway timetable.     

Schedule-based transit assignment model with vehicle capacity and seat availability

In this paper, we propose a new schedule-based equilibrium transit assignment model that differentiates the discomfort level experienced by sitting and standing passengers. The notion of seat allocation has not been considered explicitly and analytically in previous schedule-based frameworks. The model assumes that passengers use strategies when traveling from their origin to their destination. When loading a vehicle, standing on-board passengers continuing to the next station have priority to get available seats and waiting passengers are loaded on a First-Come-First-Serve (FCFS) principle. The stimulus of a standing passenger to sit increases with his/her remaining journey length and time already spent on-board. When a vehicle is full, passengers unable to board must wait for the next vehicle to arrive. The equilibrium conditions can be stated as a variational inequality involving a vector-valued function of expected strategy costs. To find a solution, we adopt the method of successive averages (MSA) that generates strategies during each iteration by solving a dynamic program. Numerical results are also reported to show the effects of our model on the travel strategies and departure time choices of passengers.     

Toll pricing framework under logit‐based stochastic user equilibrium constraints

This paper addresses the toll pricing framework for the first‐best pricing with logit‐based stochastic user equilibrium (SUE) constraints. The first‐best pricing is usually known as marginal‐cost toll, which can be obtained by solving a traffic assignment problem based on the marginal cost functions. The marginal‐cost toll, however, has rarely been implemented in practice, because it requires every specific link on the network to be charged. Thus, it is necessary to search for a substitute of the marginal cost pricing scheme, which can reduce the toll locations but still minimize the total travel time. The toll pricing framework is the set of all the substitute toll patterns of the marginal cost pricing. Assuming the users' route choice behavior following the logit‐based SUE principle, this paper has first derived a mathematical expression for the toll pricing framework. Then, by proposing an origin‐based variational inequality model for the logit‐based SUE problem, another toll pricing framework is built, which avoids path enumeration/storage. Finally, the numerical test shows that many alternative pricing patterns can inherently reduce the charging locations and total toll collected, while achieving the same equilibrium link flow pattern. Copyright © 2013 John Wiley & Sons, Ltd.     

A microeconomic interpretation for the system optimal traffic assignment problem with nonadditive path cost

Using a Bergson–Samuelson welfare function, we outline a microeconomic interpretation of the effects of the non-linearity in the time/cost relationship for travellers in a congested transport network. It is demonstrated that a marginal cost traffic flow assignment following Wardrop's second principle, although it minimizes the total cost of a transport network, may reduce social welfare compared to the market equilibrium assignment based on Wardrop's first principle. A welfare-maximizing assignment model is presented and used to show that if the travellers' utility functions are linear, the assignment that maximizes social welfare will be the same as the assignment that minimizes total network cost, but if users' utility functions are non-linear (reflecting the traditional non-satiation and diminishing marginal utility axioms), the two assignments will be different. It is further shown that the effects of this non-linearity are such that a welfare-maximizing assignment will meet with less user resistance than a minimum total network cost assignment.