Dynamic pricing and reservation for intelligent urban parking management

Despite rapid advances of information technologies for intelligent parking systems, it remains a challenge to optimally manage limited parking resources in busy urban neighborhoods. In this paper, we use dynamic location-dependent parking pricing and reservation to improve system-wide performance of an intelligent parking system. With this system, the parking agency is able to decide the spatial and temporal distribution of parking prices to achieve a variety of objectives, while drivers with different origins and destinations compete for limited parking spaces via online reservation. We develop a multi-period non-cooperative bi-level model to capture the complex interactions among the parking agency and multiple drivers, as well as a non-myopic approximate dynamic programming (ADP) approach to solve the model. It is shown with numerical examples that the ADP-based pricing policy consistently outperforms alternative policies in achieving greater performance of the parking system, and shows reliability in handling the spatial and temporal variations in parking demand.     

A dynamic pricing strategy for high occupancy toll lanes

High Occupancy Toll (HOT) lanes are emerging as a solution to the underutilization of High Occupancy Vehicle (HOV) lanes and also a means to generate revenue for the State Departments of Transportation. This paper proposes a method to determine the toll price dynamically in response to the changes in traffic condition, and describes the procedures for estimating the essential parameters. Such parameters include expected delays, available capacity for toll-paying vehicles and distribution of travelers’ value of time (VOT). The objective function of the proposed pricing strategy can be flexibly modified to minimize delay, maximize revenue or combinations of specified levels of delay and revenue. Real-world data from a 14-mile of freeway segment in the San Francisco Bay Area are used to demonstrate the applicability and feasibility of the proposed method, and findings and implications from this case study are discussed.     

Investigating preference heterogeneity in Value of Time (VOT) and Value of Reliability (VOR) estimation for managed lanes

This paper presents an empirical study in investigating user heterogeneity of Value of Time (VOT) and Value of Reliability (VOR). Combined Revealed Preference (RP) and Stated Preference (SP) data were used to understand traveler choice behavior regarding the usage of managed lanes (MLs). The data were obtained from the South Florida Expressway Stated Preference Survey, which focused on automobile drivers who had traveled on the I-75, I-95, or SR 826 corridors in South Florida. Mixed logit modeling was applied and indicated an average value of $13.55 per hour for VOT and $16.13 per hour for VOR. Potential sources of heterogeneity in user sensitivities to time, reliability, and cost were identified and quantified by adding interaction effects of the variables in the mixed logit model. The findings indicated that various socioeconomic demographic characteristics and trip attributes contributed to the variations in VOT and VOR at different magnitudes. The results of this study contribute to a better understanding on what attributes lead to higher or lower VOT and VOR and to what extent. These findings can be incorporated into the demand forecasting process and lead to better estimates and enhanced analytical capabilities in various applications, such as toll feasibility studies, pricing strategy and policy evaluations, and impact analysis.     

The dynamic shortest path problem with time-dependent stochastic disruptions

The dynamic shortest path problem with time-dependent stochastic disruptions consists of finding a route with a minimum expected travel time from an origin to a destination using both historical and real-time information. The problem is formulated as a discrete time finite horizon Markov decision process and it is solved by a hybrid Approximate Dynamic Programming (ADP) algorithm with a clustering approach using a deterministic lookahead policy and value function approximation. The algorithm is tested on a number of network configurations which represent different network sizes and disruption levels. Computational results reveal that the proposed hybrid ADP algorithm provides high quality solutions with a reduced computational effort.     

Development and comparison of choice models and tolling schemes for high-occupancy/toll (HOT) facilities

A high-occupancy/toll (HOT) lane is an increasingly popular form of traffic management strategy which reserves a set of freeway lanes for HOVs and transit users, while allowing low-occupancy vehicles (LOVs) to enter for a fee. In turn, HOT lanes maintain a minimal level of service by regulating the volume of entering LOVs. The focus of this paper is how to model the choice process of individual drivers, which dictates the volume of LOVs that choose to pay and take the HOT lane. Such models and the insights they provide can be very helpful for the toll setting process. Two simple formulations (an all-or-nothing assignment and an additive logit model) are compared with a proposed formulation based on the population value of time (VOT) distribution. Both static and dynamic toll setting algorithms are studied based on the proposed lane choice model, and their performance is compared under deterministic traffic behavior.     

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.     

Optimal joint distance and time toll for cordon-based congestion pricing

This paper addresses the optimal toll design problem for the cordon-based congestion pricing scheme, where both a time-toll and a nonlinear distance-toll (i.e., joint distance and time toll) are levied for each network user’s trip in a pricing cordon. The users’ route choice behaviour is assumed to follow the Logit-based stochastic user equilibrium (SUE). We first propose a link-based convex programming model for the Logit-based SUE problem with a joint distance and time toll pattern. A mathematical program with equilibrium constraints (MPEC) is developed to formulate the optimal joint distance and time toll design problem. The developed MPEC model is equivalently transformed into a semi-infinite programming (SIP) model. A global optimization method named Incremental Constraint Method (ICM) is designed for solving the SIP model. Finally, two numerical examples are used to assess the proposed methodology.     

A scalable non-myopic dynamic dial-a-ride and pricing problem for competitive on-demand mobility systems

We propose a competitive on-demand mobility model using a multi-server queue system under infinite-horizon look-ahead. The proposed approach includes a novel dynamic optimization algorithm which employs a Markov decision process (MDP) and provides opportunities to revolutionize conventional transit services that are plagued by high cost, low ridership, and general inefficiency, particularly in disadvantaged communities and low-income areas. We use this model to study the implications it has for such services and investigate whether it has a distinct cost advantage and operational improvement. We develop a dynamic pricing scheme that utilizes a balking rule that incorporates socially efficient level and the revenue-maximizing price, and an equilibrium-joining threshold obtained by imposing a toll on the customers who join the system. Results of numerical simulations based on actual New York City taxicab data indicate that a competitive on-demand mobility system supported by the proposed model increases the social welfare by up to 37% on average compared to the single-server queuing system. The study offers a novel design scheme and supporting tools for more effective budget/resource allocation, planning, and operation management of flexible transit systems.     

System optimum and pricing for the day-long commute with distributed demand,autos and transit

The day-long system optimum (SO) commute for an urban area served by auto and transit is modeled as an auto bottleneck with a capacitated transit bypass. A public agency manages the system’s capacities optimally. Commuters are identical except for the times at which they wish to complete their morning trips and start their evening trips, which are given by an arbitrary joint distribution. They value unpunctuality – their lateness or earliness relative to their wish times – with a common penalty function. They must use the same mode for both trips. Commuters are assigned personalized mode and travel start times that collectively minimize society’s generalized cost for the whole day. This includes unpunctuality penalties, queuing delays, travel times and out-of-pocket costs for users, as well as travel supply costs and externalities for society.It is shown that in a SO solution there can be no queuing and that the set of SO solutions forms a convex set. Furthermore, if the schedule penalty that users suffer due to unpunctuality is separable into morning and evening components, then the set of commuters traveling by the same mode arrive at work and depart from work in the order of their wishes. These orders are in general different in the morning and the evening. It is also shown that there always is a SO solution in which users are at all times, and on both modes, either punctual or flowing at capacity. These problem properties are used to identify search methods, both, for SO solutions and for time-dependent tolls and transit fares that preserve the solutions as Nash equilibriums. In every case studied, these prices exist. They must peak concurrently for the two modes in both periods.In special cases involving only one mode, only one period or concentrated demand the solution to the complete problem decomposes by period conditional on the number of transit users, and this facilitates the solution. In these cases the day-long SO cost is the sum of the SO costs for the two peaks considered separately. However, this is not true in general – the solution obtained by combining the two single-period solutions can be infeasible. When this happens, the optimum day-long cost will exceed the sum of the single-period costs. The discrepancy is about 40% of the total schedule penalty for an example representing a large city. Thus, to develop realistic policies the day-long problem must be addressed head on. An approximate method that yields closed form formulas for the case with uniformly distributed wishes is presented.     

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.     

Dynamic charging-while-driving systems for freight delivery services with electric vehicles: Traffic and energy modelling

This paper presents a research on traffic modelling developed for assessing traffic and energy performance of electric systems installed along roads for dynamic charging-while-driving (CWD) of fully electric vehicles (FEVs).The logic adopted by the developed traffic model is derived from a particular simulation scenario of electric charging: a freight distribution service operated using medium-sized vans. In this case, the CWD service is used to recover the state of charge of the FEV batteries to shortly start with further activities after arrival at the depot.The CWD system is assumed to be implemented in a multilane ring road with several intermediate on-ramp entrances, where the slowest lane is reserved for the dynamic charging of authorized electric vehicles. A specific traffic model is developed and implemented based on a mesoscopic approach, where energy requirements and charging opportunities affect driving and traffic behaviours. Overtaking manoeuvres as well as new entries in the CWD lane of vehicles that need to charge are modelled according to a cooperative driving system, which manages adequate time gaps between consecutive vehicles. Finally, a speed control strategy is simulated at a defined node to create an empty time-space slot in the CWD lane, by delaying the arriving vehicles. This simulated control, implemented to allow maintenance operations for CWD that may require clearing a charging zone for a short time slot, could also be applied to facilitate on-ramp merging manoeuvres.     

A cooperative waiting strategy based on elliptical areas for the Dynamic Pickup and Delivery Problem with Time Windows

The purpose of this paper to present a cooperative scheduling algorithm for solving the Dynamic Pickup and Delivery Problem with Time Windows (DPDPTW). The idea behind cooperative waiting strategies is to calculate simultaneously the waiting times for all nodes in the solution. Classical non‐cooperative scheduling algorithms perform the scheduling for each route independently of the scheduling of the other routes. We present the Cooperative Scheduling Problem (CSP) based on the elliptical areas generated by vehicles waiting at their nodes. The CSP is solved by means of a genetic algorithm and is evaluated by using a set of benchmarks based on real‐life data found in the literature. Initially, two waiting strategies are presented: Wait‐Early‐Time scheduling and Balanced‐Departure scheduling. Extensive empirical simulations have been carried out by analyzing the degree of dynamism and the average waiting time, a new concept defined to take into account the gap between the time windows of pickup and delivery nodes. Copyright © 2016 John Wiley & Sons, Ltd.     

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.