Managing bottleneck congestion with tradable credits

We demonstrate the efficiency and effectiveness of a tradable credit system in managing the morning commute congestion with identical and nonidentical commuters. The credit system consists of a time-varying credit charged at the bottleneck and an initial credit distribution to the commuters, where the credits are universal in terms of time. Credits are tradable between the commuters and the credit price is determined by a competitive market. Under the assumption that late-arrival is not allowed, we prove that an optimal credit charging scheme, which completely eliminates the bottleneck queue, always exists despite how commuters vary in their value-of-time (VOT). The optimal charge rate is strictly increasing and convex with time, which therefore drives the commuters to depart in the increasing order of their VOT. The optimal credit charging scheme is pareto-improving, but may cause undesirable welfare distribution among the commuters. Our study shows that a combination of an initial credit distribution and an optimal credit charging scheme can simultaneously achieve system optimum and certain forms of equality (e.g., “numerical” or “proportional” equality), and that the commuters in the middle VOT bracket will receive the most credits under the proportionally equitable credit distribution.     

Optimally combined headway and timetable reliable public transport system

This paper presents a model-based multiobjective control strategy to reduce bus bunching and hence improve public transport reliability. Our goal is twofold. First, we define a proper model, consisting of multiple static and dynamic components. Bus-following model captures the longitudinal dynamics taking into account the interaction with the surrounding traffic. Furthermore, bus stop operations are modeled to estimate dwell time. Second, a shrinking horizon model predictive controller (MPC) is proposed for solving bus bunching problems. The model is able to predict short time-space behavior of public transport buses enabling constrained, finite horizon, optimal control solution to ensure homogeneity of service both in time and space. In this line, the goal with the selected rolling horizon control scheme is to choose a proper velocity profile for the public transport bus such that it keeps both timetable schedule and a desired headway from the bus in front of it (leading bus). The control strategy predicts the arrival time at a bus stop using a passenger arrival and dwell time model. In this vein, the receding horizon model predictive controller calculates an optimal velocity profile based on its current position and desired arrival time. Four different weighting strategies are proposed to test (i) timetable only, (ii) headway only, (iii) balanced timetable - headway tracking and (iv) adaptive control with varying weights. The controller is tested in a high fidelity traffic simulator with realistic scenarios. The behavior of the system is analyzed by considering extreme disturbances. Finally, the existence of a Pareto front between these two objectives is also demonstrated.     

Incorporating time and income constraints in dynamic agent-based models of activity generation and time use: Approach and illustration

Existing theories and models in economics and transportation treat households’ decisions regarding allocation of time and income to activities as a resource-allocation optimization problem. This stands in contrast with the dynamic nature of day-by-day activity-travel choices. Therefore, in the present paper we propose a different approach to model activity generation and allocation decisions of individuals and households that acknowledges the dynamic nature of the behavior. A dynamic representation of time and money allocation decisions is necessary to properly understand the impact of new technologies on day to day variations in travel and activity patterns and on performance of transportation systems. We propose an agent-based model where agents, rather than acting on the basis of a resource allocation solution for a given time period, make resource allocation decisions on a day-by-day basis taking into account day-varying conditions and at the same time respecting available budgets over a longer time horizon. Agents that share a household interact and allocate household tasks and budgets among each other. We introduce the agent-based model and formally discuss the properties of the model. The approach is illustrated on the basis of simulation of behavior in time and space.     

Dynamic system-optimal traffic assignment using a state space model

We propose a new mathematical formulation for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assume that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minimize the total travel time experienced by all the vehicles using the network. We model the traffic network over the time horizon as a discrete-time dynamical system. The system state at each time instant is defined in a way that, without loss of optimality, avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, link outflow functions, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied in the context of this model. These optimization problems are optimal control problems for nonlinear discrete-time dynamical systems, and thus they are amenable to algorithmic solutions based on dynamic programming. The computational challenges associated with the exact solution of these problems are discussed and some heuristics are proposed.     

Managing network mobility with tradable credits

A system of tradable travel credits is explored in a general network with homogeneous travelers. A social planner is assumed to initially distribute a certain number of travel credits to all eligible travelers, and then there are link-specific charges to travelers using that link. Free trading of credits among travelers is assumed. For a given credit distribution and credit charging scheme, the existence of a unique equilibrium link flow pattern is demonstrated with either fixed or elastic demand. It can be obtained by solving a standard traffic equilibrium model subject to a total credit consumption constraint. The credit price at equilibrium in the trading market is also conditionally unique. The appropriate distribution of credits among travelers and correct selection of link-specific rates is shown to lead to the most desirable network flow patterns in a revenue-neutral manner. Social optimum, Pareto-improving and revenue-neutral, and side-constrained traffic flow patterns are investigated.     

Tradable credit schemes on networks with mixed equilibrium behaviors

This paper analyzes and designs tradable credit schemes on networks with two types of players, namely, a finite number of Cournot–Nash (CN) players and an infinite number of (infinitesimal) Wardrop-equilibrium (WE) players. We first show that there are nonnegative anonymous credit schemes that yield system optimum, when transaction costs are not considered. We then analyze how transaction costs would affect the trading and route-choice behaviors of both CN and WE players, and discuss the equilibrium conditions on the coupled credit market and transportation network in the presence of transaction costs. A variational inequality is formulated to describe the equilibrium and is subsequently applied to a numerical example to assess the impacts of transaction costs on a tradable credit system. As expected, transaction costs reduce the trading volume of credits and change their market price. They also change the way how players respond to credit charges in their route choices and cause efficiency losses to the credit schemes that are previously designed without considering transaction costs. With transaction costs, travel costs of WE players will likely increase while those of CN players may decrease due to their higher adaptability in routing strategies.     

Trial and error method for optimal tradable credit schemes: The network case

Recent studies on the new congestion reduction method―tradable credit scheme rely on the full information of speed‐flow relationship, demand function, and generalized cost. As analytical travel demand, functions are difficult to establish in practice. This paper develops a trial and error method for selecting optimal credit schemes for general networks in the absence of demand functions. After each trial of tradable credit scheme, the credit charging scheme and total amount of credits to be distributed are updated by both observed link flows at traffic equilibrium and revealed credit price at market equilibrium. The updating strategy is based on the method of successive averages and its convergence is established theoretically. Our numerical experiments demonstrate that the method of successive averages based trial and error method for tradable credit schemes has a lower convergence speed in comparison with its counterpart for congestion pricing and could be enhanced by exploring more efficient methods that make full use of credit price information. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlinear pricing for stochastic container leasing system

With the substantial upsurge of container traffic, the container leasing company thrives on the financial benefits and operational flexibility of leasing containers requested by shippers. In practice, container lease pricing problem is different from the consumer product pricing in consideration of the fair value of container, limited customer types and monopolistic supply market. In view of the durability of container and the diversified lease time and quantity, the pricing is a challenging task for the leasing company. This paper examines the monopolist’s nonlinear pricing problems in static and dynamic environments. In particular, the leasing company designs and commits a menu of price and hire quantity/time pairs to maximize the expected profit and in turn customers choose hire quantities/time to maximize their surpluses according to their hire preferences. In a static environment, closed-form solutions are obtained for different groups of customers with multiple types subject to capacity constraint. In a dynamic environment, we address two customer types and derive closed-form solutions for the problem of customers with hire time preference. Further, we show that the effect of the capacity constraint increases with time of the planning horizon when customers have the same hire time preference; while in the case with different hire time preferences, the capacity constraint has opposite effects on the low and high type customers. Last, the case of customers with hire quantity preference is discussed. We focus on the lease with alternative given sets of hire time and use dynamic programming to derive the numerical optimal hire time sequence.     

A multivariate cointegrating vector auto regressive model of freight transport demand: evidence from Indian railways

In this paper long run structural relationship for freight transport demand is derived for railways in India using annual time series data for 1960–1995. Some of the recent developments in multivariate dynamic econometric time series modelling have been employed such as estimation of long-run structural cointegrating relationship, short-run dynamics and measurement of the effects of shocks and their persistence during the evolution of dynamic freight transport demand system. The models are estimated using a cointegrating vector autoregressive (VAR) modelling framework, which allows for endogeneity of regressors. Results indicate high GDP elasticity and low price elasticity, with real freight rate, i.e. the price variable behaving exogenously with respect to the system. Any disequilibrium in the short-run is likely to be corrected in the long run via adjustments in freight transport demand and GDP. Further, the demand system seems to be stable in the long run and converges to equilibrium in a period of around 3 years after a typical system-wide shock.     

Intermodal freight transport planning – A receding horizon control approach

This paper investigates intermodal freight transport planning problems among deep-sea terminals and inland terminals in hinterland haulage for a horizontally fully integrated intermodal freight transport operator at the tactical container flow level. An intermodal freight transport network (IFTN) model is first developed to capture the key characteristics of intermodal freight transport such as the modality change phenomena at intermodal terminals, physical capacity constraints of the network, time-dependent transport times on freeways, and time schedules for trains and barges. After that, the intermodal freight transport planning problem is formulated as an optimal intermodal container flow control problem from a system and control perspective with the use of the proposed IFTN model. To deal with the dynamic transport demands and dynamic traffic conditions in the IFTN, a receding horizon intermodal container flow control (RIFC) approach is proposed to control and to reassign intermodal container flows in a receding horizon way. This container flow control approach involves solving linear programming problems and is suited for transport planning on large-sized networks. Both an all-or-nothing approach and the proposed RIFC approach are evaluated through simulation studies. Simulation results show the potential of the proposed RIFC approach.     

Dynamic green bike repositioning problem – A hybrid rolling horizon artificial bee colony algorithm approach

This paper introduces a new dynamic green bike repositioning problem (DGBRP) that simultaneously minimizes the total unmet demand of the bike-sharing system and the fuel and CO₂ emission cost of the repositioning vehicle over an operational period. The problem determines the route and the number of bikes loaded and unloaded at each visited node over a multi-period operational horizon during which the cycling demand at each node varies from time to time. To handle the dynamic nature of the problem, this study adopts a rolling horizon approach to break down the proposed problem into a set of stages, in which a static bike repositioning sub-problem is solved in each stage. An enhanced artificial bee colony (EABC) algorithm and a route truncation heuristic are jointly used to optimize the route design in each stage, and the loading and unloading heuristic is used to tackle the loading and unloading sub-problem along the route in a given stage. Numerical results show that the EABC algorithm outperforms Genetic Algorithm in solving the routing sub-problem. Computation experiments are performed to illustrate the effect of the stage duration on the two objective values, and the results show that longer stage duration leads to higher total unmet demand and total fuel and CO₂ emission cost. Numerical studies are also performed to illustrate the effects of the weight and the loading and unloading times on the two objective values and the tradeoff between the two objectives.     

Managing rush hour travel choices with tradable credit scheme

This paper Analyzes a new tradable credit scheme (TCS) for managing commuters’ travel choices, which seeks to persuade commuters to spread evenly within the rush hour and between primary and alternative routes so that excessive traffic congestion can be alleviated. The scheme defines a peak time window and charges those who use the primary route within that window in the form of mobility credits. Those who avoid the peak-time window, by either traveling outside the peak time window or switching to the alternative route, may be rewarded credits. A market is created such that those who need to pay credits can purchase them from those who acquire them from their rewarding travel choices. A general analytical framework is proposed for a system of two parallel routes. The framework (1) considers a variety of assumptions about commuters’ behavior in response to the discontinuous credit charge introduced at the boundary of the peak-time window, (2) allows modeling congestion effects (or demand elasticity) on the alternative route, and (3) enables both the design of system optimal TCS and the analysis of the efficiency of any given TCS. Our analyses indicate that the proposed TCS not only achieves up to 33% efficiency gains in the base scenario, but also distributes the benefits among all the commuters directly through the credit trading. The results also suggest that very simple TCS schemes could provide substantial efficiency gains for a wide range of scenarios. Such simplicity and robustness are important to practicability of the proposed scheme. Numerical experiments are conducted to examine the sensitivity of TCS designs to various system parameters.     

Analysis of consumer response to fuel price fluctuations applying sample selection model to GPS panel data: Dynamics in individuals’ car use

The effects of fuel price increases on people’s car use have been widely discussed during the last few decades in travel behavior research. It is well recognized that fuel price has significant effects on driving distance and driving efficiency. However, most of this research assumed that these effects are invariant across individuals and weather conditions. Moreover, intrinsic variability in people’s preferences has not been given much attention due to the difficulty of collecting the necessary data. In this paper, we collected detailed travel behavior data of 276 respondents in the Netherlands, spanning a time period between one week and three months using GPS logs. These GPS data were fused with weather data, allowing us to estimate both exogenous (such as weather and fuel price) and endogenous effects (inertia and activity plans) on individual’s car use behavior. To further understand the effects of fuel price on the environment, we estimated the effects of fuel price fluctuation on CO₂ emissions by car. The results show a significant degree of inertia in car use behavior in response to increased fuel prices. Weather and fuel price showed significant effects on individual’s car using behavior. Moreover, fuel price shows two-week lagged effects on individual’s travel duration by car.     

Dynamic pricing for managed lanes with multiple entrances and exits

Priced managed lanes are increasingly being used to better utilize the existing capacity of the roadway to relieve congestion and offer reliable travel time to road users. In this paper, we investigate the optimization problem for pricing managed lanes with multiple entrances and exits which seeks to maximize the revenue and minimize the total system travel time (TSTT) over a finite horizon. We propose a lane choice model where travelers make online decisions at each diverge point considering all routes on a managed lane network. We formulate the problem as a deterministic Markov decision process and solve it using the value function approximation (VFA) method for different initializations. We compare the performance of the toll policies predicted by the VFA method against the myopic revenue policy which maximizes the revenue only at the current timestep and two heuristic policies based on the measured densities on the managed and general purpose lanes (GPLs). We test the results on four different test networks. The primary findings from our research suggest the usefulness of the VFA method for determining dynamic tolls. The best-found objective value from the method at its termination is better than other heuristics for all test networks with average improvements in the objective ranging between 10% and 90% for revenue maximization and 0–27% for TSTT minimization. Certain VFA initializations obtain best-found toll profiles within first 5–50 iterations which warrants computational time savings. Our findings also indicate that the revenue-maximizing optimal policies follow the “jam-and-harvest” behavior where the GPLs are pushed towards congestion in the earlier time steps to generate higher revenue in the later time steps, a characteristic not observed for the policies minimizing TSTT.     

Tradable credits scheme and transit investment optimization for a two‐mode traffic network

This paper proposes an optimization model to minimize the “system costs” and guide travelers' behavior by exploring the optimal bus investment and tradable credits scheme design in a bimodal transportation system. Travelers' transport mode choice behavior (car or bus) and the modal equilibrium conditions between these two forms of transport are studied in the tradable credits scheme. Public transport priority is highlighted by charging car travelers credits only. The economies of scale presented by the transit system under the tradable credit scheme are analyzed by comparing the marginal cost and average cost. Numerical examples are presented to demonstrate the model. Furthermore, the effects of tradable credits schemes on bus investment and travelers' modal choice behavior are explored based on scenario discussions. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic congestion pricing with day-to-day flow evolution and user heterogeneity

This paper investigates evolutionary implementation of congestion pricing schemes to minimize the system cost and time, measured in monetary and time units, respectively, with the travelers’ day-to-day route adjustment behavior and their heterogeneity. The travelers’ heterogeneity is captured by their value-of-times. First, the multi-class flow dynamical system is proposed to model the travelers’ route adjustment behavior in a tolled transportation network with multiple user classes. Then, the stability condition and properties of equilibrium is examined. We further investigate the trajectory control problem via dynamic congestion pricing scheme to derive the system cost, time optimum, and generally, Pareto optimum in the sense of simultaneous minimization of system cost and time. The trajectory control problem is modeled by a differential–algebraic system with the differential sub-system capturing the flow dynamics and the algebraic one capturing the pricing constraint. The explicit Runge–Kutta method is proposed to calculate the dynamic flow trajectories and anonymous link tolls. The method allows the link tolls to be updated with any predetermined periods and forces the system cost and/or time to approach the optimum levels. Both analytical and numerical examples are adopted to examine the efficiency of the method.     

Structure and dynamics of non-suburban passenger travel demand in Indian railways

In this paper we derive long run structural relationships for all the three classes, viz. upper, second and ordinary second class, of non-suburban long distance passenger transport demand for Indian railways using annual time series data for 1970–1995. We employ some of the recent developments in multivariate dynamic econometric time series modeling including estimation of long-run structural cointegrating relationships, short-run dynamics and measurement of the effects of shocks and their persistence on evolution of the dynamic passenger transport demand system. The models are estimated using a cointegrating vector autoregressive (VAR) modeling framework, which allows for endogeneity of regressors. The demand systems are found to be stable for all the classes in the long run and they converge to equilibrium in a period of around 2–4 years after a typical system-wide shock. Any disequilibrium in the short-run is corrected in the long-run with adjustments in passenger transport demand and the price variable, i.e. real rate charged per passenger kilometer. Results show that travel demand in all classes would rise with income, although the rise is less than proportionate in the case of ordinary class. High price elasticity in long-run and short-run impulse responses indicate that passenger fare hike could lead to substantial decline in travel demand leading to decline in revenue earnings of the railways. This revised version was published online in June 2006 with corrections to the Cover Date.     

Computing 4D near-optimal trajectories for dynamic air traffic flow management with column generation and branch-and-price

Abstract

The current air traffic system faces recurrent saturation problems. Numerous studies are dedicated to this issue, including the present research on a new dynamic regulation filter holding frequent trajectory optimisations in a real-time sliding horizon loop process. We consider a trajectory optimisation problem arising in this context, where a feasible four-dimensional (4D) trajectory is to be built and assigned to each regulated flight to suppress sector overloads while minimising the cost of the chosen policy. We model this problem with a mixed integer linear programme and solve it with a branch-and-price approach. The pricing sub-problem looks for feasible trajectories in a dynamic three-dimensional (3D) network and is solved with a specific algorithm based on shortest path labelling algorithms and on dynamic programming. Each algorithm is tested on real-world data corresponding to a complete traffic day in the European air traffic system; experimental results, including computing times measurement, validate the solution process.     

Auction-based tolling systems in a connected and automated vehicles environment: Public opinion and implications for toll revenue and capacity utilization

Autonomous and connected vehicles are expected to enable new tolling mechanisms, such as auction-based tolls, for allocating the limited roadway capacity. This research examines the public perception of futuristic auction-based tolling systems, with a focus on the public acceptance of such systems over current tolling practices on highways (e.g., dynamic and fixed tolling methodologies). Through a stated-preference survey, responses from 159 road-users residing in Virginia are elicited to understand route choice behavior under a descending price auction implemented on a hypothetical two-route network. Analysis of the survey data shows that there is no outright rejection of the presented auction-based tolling among those who are familiar with the current tolling methods. While males strongly support the new method, no clear pattern emerges among other demographic variables such as income and education level, and age. While high income respondents and regular commuters are more likely to pay higher tolls, no statistical significance between different genders, age groups, household sizes, and education levels is found. Based on the modeling results and the hypothetical road network, it is found that descending price tolling method yields higher average toll rates, and generates at least 70% more revenue when travel time saving is 30 min, and improves capacity utilization of the toll road significantly compared to fixed tolls.     

An empirical investigation on the dynamic processes of activity scheduling and trip chaining

Investigation of the dynamic processes of activity scheduling and trip chaining has been an interest of transportation researchers over the past decade because of its relevance to the effectiveness of congestion management and intelligent transportation systems. To empirically examine the processes, a computerized survey instrument is developed to collect household activity scheduling data. The instrument is unique in that it records the evolution of activity schedules from intentions to final outcomes for a weekly period. This paper summarizes the investigation on the dynamic processes of activity scheduling and trip chaining based on data collected from a pilot study of the instrument. With the data, ordered logit models are applied to identify factors that are pertinent to the scheduling horizon of activities. Results of the empirical analysis show that a daily schedule often starts with certain activities occupying a portion of the schedule and other activities are then arranged around these pre-occupants. Activities of shorter duration are more likely to be opportunistically inserted in a schedule already anchored by their longer duration counterparts. Persons with children often expect more constraining activities than those with no children. The analysis also shows that female respondents tend to be more structured in terms of how the week is planned. Additionally, analysis of travel patterns reveals that many trip-chains are formed opportunistically. Travel time required to reach an activity is positively related to the scheduling horizon for the activity, with more distant stops being planned earlier than closer locations.