Capacity investment model for airport facilities under demand uncertainty

This paper addresses strategic airport facility planning under demand uncertainty. Existing studies are improved by (1) allowing capacity contraction and (2) adopting more flexible delay functions. A mixed‐integer nonlinear program, which incorporates scale economies in construction, time value of money, nonlinear congestion effect, and other factors, is proposed for optimizing the capacity expansion/contraction decisions over time for multiple airport components. The stochastic problem is converted into its deterministic equivalent because the number of demand scenarios considered is finite. A discrete approximation technique is used to remove the nonlinearities. Numerical studies are presented to demonstrate the capability of the proposed model and the computational efficiency of the solution method. The “Flaw of Averages” due to faulty decisions based on the average future condition is illustrated, and trade‐offs among various costs are discussed in the numerical analyses. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust Wardrop’s user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach

Various models of traffic assignment under stochastic environment have been proposed recently, mainly by assuming different travelers’ behavior against uncertainties. This paper focuses on the expected residual minimization (ERM) model to provide a robust traffic assignment with an emphasis on the planner’s perspective. The model is further extended to obtain a stochastic prediction of the traffic volumes by the technique of path choice approach. We show theoretically the existence and the robustness of the ERM solution. In addition, we employ an improved solution algorithm for solving the ERM model. Numerical experiments are carried out to illustrate the characteristics of the proposed model, by comparing with other existing models.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

Flight and passenger delay assignment optimization strategies

This paper compares different optimization strategies for the minimization of flight and passenger delays at two levels: pre-tactical, with on-ground delay at origin, and tactical, with airborne delay close to the destination airport. The optimization model is based on the ground holding problem and uses various cost functions. The scenario considered takes place in a busy European airport and includes realistic values of traffic. A passenger assignment with connections at the hub is modeled. Statistical models are used for passenger and connecting passenger allocation, minimum time required for turnaround and tactical noise; whereas uncertainty is also introduced in the model for tactical noise. Performance of the various optimization processes is presented and compared to ration by schedule results.     

A dual decomposition method for sector capacity constrained traffic flow optimization

An aggregate air traffic flow model based on a multicommodity network is used for traffic flow management in the National Airspace System. The problem of minimizing the total travel time of flights in the National Airspace System of the United States, subject to sector capacity constraints, is formulated as an Integer Program. The resulting solution achieves optimal delay control. The Integer Program implemented for the scenarios investigated has billions of variables and constraints. It is relaxed to a Linear Program for computational efficiency. A dual decomposition method is applied to solve the large scale Linear Program in a computationally tractable manner. A rounding algorithm is developed to map the Linear Program solution to a physically acceptable result, and is implemented for the entire continental United States. A 2-h traffic flow management problem is solved with the method.     

General stochastic user equilibrium traffic assignment problem with link capacity constraints

This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path‐specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.     

Sequential optimization approach for the multi‐class user equilibrium problem in a continuous transportation system

We consider a city region with several facilities that are competing for customers of different classes. Within the city region, the road network is dense, and can be represented as a continuum. Customers are continuously distributed over space, and they choose a facility by considering both the transportation cost and market externalities. More importantly, the model takes into account the different transportation cost functions and market externalities to which different customer classes are subjected. A logit‐type distribution of demand is specified to model the decision‐making process of users' facility choice. We develop a sequential optimization approach to decompose the complex multi‐class and multi‐facility problem into a series of smaller single‐class and single‐facility sub‐problems. An efficient solution algorithm is then proposed to solve the resultant problem. A numerical example is given to demonstrate the effectiveness and potential applicability of the proposed methodology.     

Multi-stage stochastic program to optimize signal timings under coordinated adaptive control

In the wake of traffic congestion at intersections, it is imperative to shorten delays in corridors with stochastic arrivals. Coordinated adaptive control can adjust green time flexibly to deal with a stochastic demand, while maintaining a minimum through-band for coordinated intersections. In this paper, a multi-stage stochastic program based on phase clearance reliability (PCR) is proposed to optimize base timing plans and green split adjustments of coordinated intersections under adaptive control. The objective is to minimize the expected intersection delay and overflow of the coordinated approach. The overflow or oversaturated effect is explicitly addressed in the delay calculation, which greatly increases the modeling complexity due to the interaction of overflow delays across cycles. The notion of PCR separates the otherwise related green time settings of consecutive cycles into a number of stages, in which the base timing plan and actual timing plan in different cycles are handled sequentially. We then develop a PCR based solution algorithm to solve the problem, and apply the model and the solution algorithm to actual intersections in Shanghai to investigate its performance as compared with Allsop’s method and Webster’s method. Preliminary results show the PCR-based method can significantly shorten delays and almost eliminates overflow for the coordinated approaches, with acceptable delay increases of the non-coordinated approaches. A comparison between the proposed coordinated adaptive logic and a coordinated actuated logic is also conducted in the case study to show the advantages and disadvantages.     

Multi-scale perimeter control approach in a connected-vehicle environment

This paper proposes a novel approach to integrate optimal control of perimeter intersections (i.e. to minimize local delay) into the perimeter control scheme (i.e. to optimize traffic performance at the network level). This is a complex control problem rarely explored in the literature. In particular, modeling the interaction between the network level control and the local level control has not been fully considered. Utilizing the Macroscopic Fundamental Diagram (MFD) as the traffic performance indicator, we formulate a dynamic system model, and design a Model Predictive Control (MPC) based controller coupling two competing control objectives and optimizing the performance at the local and the network level as a whole. To solve this highly non-linear optimization problem, we employ an approximation framework, enabling the optimal solution of this large-scale problem to be feasible and efficient. Numerical analysis shows that by applying the proposed controller, the protected network can operate around the desired state as expressed by the MFD, while the total delay at the perimeter is minimized as well. Moreover, the paper sheds light on the robustness of the proposed controller. This multi-scale hybrid controller is further extended to a stochastic MPC scheme, where connected vehicles (CV) serve as the only data source. Hence, low penetration rates of CVs lead to strong noises in the controller. This is a first attempt to develop a network-level traffic control methodology by using the emerging CV technology. We consider the stochasticity in traffic state estimation and the shape of the MFD. Simulation analysis demonstrates the robustness of the proposed stochastic controller, showing that efficient controllers can indeed be designed with this newly-spread vehicle technology even in the absence of other data collection schemes (e.g. loop detectors).     

Stochastic dynamic itinerary interception refueling location problem with queue delay for electric taxi charging stations

A new facility location model and a solution algorithm are proposed that feature (1) itinerary-interception instead of flow-interception; (2) stochastic demand as dynamic service requests; and (3) queueing delay. These features are essential to analyze battery-powered electric shared-ride taxis operating in a connected, centralized dispatch manner. The model and solution method are based on a bi-level, simulation–optimization framework that combines an upper level multiple-server allocation model with queueing delay and a lower level dispatch simulation based on earlier work by Jung and Jayakrishnan. The solution algorithm is tested on a fleet of 600 shared-taxis in Seoul, Korea, spanning 603 km², a budget of 100 charging stations, and up to 22 candidate charging locations, against a benchmark “naïve” genetic algorithm that does not consider cyclic interactions between the taxi charging demand and the charger allocations with queue delay. Results show not only that the proposed model is capable of locating charging stations with stochastic dynamic itinerary-interception and queue delay, but that the bi-level solution method improves upon the benchmark algorithm in terms of realized queue delay, total time of operation of taxi service, and service request rejections. Furthermore, we show how much additional benefit in level of service is possible in the upper-bound scenario when the number of charging stations is unbounded.     

Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics

This paper investigates the nonlinear distance-based congestion pricing in a network considering stochastic day-to-day dynamics. After an implementation/adjustment of a congestion pricing scheme, the network flows in a certain period of days are not on an equilibrium state, thus it is problematic to take the equilibrium-based indexes as the pricing objective. Therefore, the concept of robust optimization is taken for the congestion toll determination problem, which takes into account the network performance of each day. First, a minimax model which minimizes the maximum regret on each day is proposed. Taking as a constraint of the minimax model, a path-based day to day dynamics model under stochastic user equilibrium (SUE) constraints is discussed in this paper. It is difficult to solve this minimax model by exact algorithms because of the implicity of the flow map function. Hence, a two-phase artificial bee colony algorithm is developed to solve the proposed minimax regret model, of which the first phase solves the minimal expected total travel cost for each day and the second phase handles the minimax robust optimization problem. Finally, a numerical example is conducted to validate the proposed models and methods.     

Preference-based evolutionary algorithm for airport surface operations

In addition to time efficiency, minimisation of fuel consumption and related emissions has started to be considered by research on optimisation of airport surface operations as more airports face severe congestion and tightening environmental regulations. Objectives are related to economic cost which can be used as preferences to search for a region of cost efficient and Pareto optimal solutions. A multi-objective evolutionary optimisation framework with preferences is proposed in this paper to solve a complex optimisation problem integrating runway scheduling and airport ground movement problem. The evolutionary search algorithm uses modified crowding distance in the replacement procedure to take into account cost of delay and fuel price. Furthermore, uncertainty inherent in prices is reflected by expressing preferences as an interval. Preference information is used to control the extent of region of interest, which has a beneficial effect on algorithm performance. As a result, the search algorithm can achieve faster convergence and potentially better solutions. A filtering procedure is further proposed to select an evenly distributed subset of Pareto optimal solutions in order to reduce its size and help the decision maker. The computational results with data from major international hub airports show the efficiency of the proposed approach.     

The Time Dependent Traveling Salesman Planning Problem in Controlled Airspace

The integration of drones into civil airspace is one of the most challenging problems for the automation of the controlled airspace, and the optimization of the drone route is a key step for this process. In this paper, we optimize the route planning of a drone mission that consists of departing from an airport, flying over a set of mission way points and coming back to the initial airport. We assume that during the mission a set of piloted aircraft flies in the same airspace and thus the cost of the drone route depends on the air traffic and on the avoidance maneuvers used to prevent possible conflicts. Two air traffic management techniques, i.e., routing and holding, are modeled in order to maintain a minimum separation between the drone and the piloted aircraft. The considered problem, called the Time Dependent Traveling Salesman Planning Problem in Controlled Airspace (TDTSPPCA), relates to the drone route planning phase and aims to minimize the total operational cost. Two heuristic algorithms are proposed for the solution of the problem. A mathematical formulation based on a particular version of the Time Dependent Traveling Salesman Problem, which allows holdings at mission way points, and a Branch and Cut algorithm are proposed for solving the TDTSPPCA to optimality. An additional formulation, based on a Travelling Salesman Problem variant that uses specific penalties to model the holding times, is proposed and a Cutting Plane algorithm is designed. Finally, computational experiments on real-world air traffic data from Milano Linate Terminal Maneuvering Area are reported to evaluate the performance of the proposed formulations and of the heuristic algorithms.     

The punctuality performance of aircraft rotations in a network of airports

The aim of this paper is to investigate the influence of aircraft turnaround performance at airports on the schedule punctuality of aircraft rotations in a network of airports. A mathematical model is applied, composed of two sub-models, namely the aircraft turnaround model (turnaround simulations) and the enroute model (enroute flight time simulations). A Markovian type model is featured in the aircraft turnaround model to simulate the operation of aircraft turnarounds at an airport by considering operational uncertainties and schedule punctuality variance. In addition, stochastic Monte Carlo simulations are employed to carry out stochastic sampling and simulations in both the aircraft turnaround model and the enroute model. Results of simulations show the robustness of the aircraft rotation model in capturing uncertainties from aircraft rotations. The propagation of knock-on delays in aircraft rotations is found to be significant when the short-connection-time policy is used by an airline at its hub airport. It is also found that the proper inclusion of schedule buffer time in the aircraft rotation schedule helps control the propagation of knock-on delays and, therefore, stabilize the punctuality performance of aircraft rotations.     

A computational model for the probit‐based dynamic stochastic user optimal traffic assignment problem

This paper focuses on computational model development for the probit‐based dynamic stochastic user optimal (P‐DSUO) traffic assignment problem. We first examine a general fixed‐point formulation for the P‐DSUO traffic assignment problem, and subsequently propose a computational model that can find an approximated solution of the interest problem. The computational model includes four components: a strategy to determine a set of the prevailing routes between each origin–destination pair, a method to estimate the covariance of perceived travel time for any two prevailing routes, a cell transmission model‐based traffic performance model to calculate the actual route travel time used by the probit‐based dynamic stochastic network loading procedure, and an iterative solution algorithm solving the customized fixed‐point model. The Ishikawa algorithm is proposed to solve the computational model. A comparison study is carried out to investigate the efficiency and accuracy of the proposed algorithm with the method of successive averages. Two numerical examples are used to assess the computational model and the algorithm proposed. Results show that Ishikawa algorithm has better accuracy for smaller network despite requiring longer computational time. Nevertheless, it could not converge for larger network. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic system‐optimal traffic assignment for a city using the continuum modeling approach

This paper presents a continuum dynamic traffic assignment model for a city in which the total cost of the traffic system is minimized: the travelers in the system are organized to choose the route to their destinations that minimizes the total cost of the system. Combined with the objective function, which defines the total cost and constraints such as certain physical and boundary conditions, a continuum model can be formulated as an optimization scheme with a feasible region in the function space. To obtain an admissible locally optimal solution to this problem, we first reformulate the optimization in discrete form and then introduce a heuristic method to solve it. This method converges rapidly with attractive computational cost. Numerical examples are used to demonstrate the effectiveness of the method. Copyright © 2013 John Wiley & Sons, Ltd.     

Assessment of large transport infrastructure projects: The CBA-DK model

This paper presents a newly developed decision support model to assess transport infrastructure projects: CBA-DK. The model combines use of conventional cost–benefit analysis to produce aggregated single point estimates, with quantitative risk analysis using Monte Carlo simulation to produce interval results. The embedded uncertainties within traditional CBA such as ex-ante based investment costs and travel time savings are of particular concern. The paper investigates these two impacts in terms of the Optimism Bias principle which is used to take account of the underestimation of construction costs and the overestimation of travel time savings. The CBA-DK methodological approach has been used to apply suitable probability distribution functions on the uncertain parameters, thus resulting in feasibility risk assessment moving from point to interval results. The proposed assessment model makes use of both deterministic and stochastic based information. Decision support as illustrated in this paper aims to provide assistance in the development and ultimately the choice of action, while accounting for the uncertainties surrounding transport appraisal schemes. The modelling framework is illustrated by the use of a case study appraising airport and runway alternatives in the capital of Greenland – Nuuk. The case study has been conducted in cooperation with the Home Rule Authorities of Greenland.     

Optimal location of advance warning for mandatory lane change near a two-lane highway off-ramp

Improper mandatory lane change (MLC) maneuvers in the vicinity of highway off-ramp will jeopardize traffic efficiency and safety. Providing an advance warning for lane change necessity is one of the efficient methods to perform systematic lane change management, which encourages smooth MLC maneuvers occurring at proper locations to mitigate the negative effects of MLC maneuvers on traffic flow nearby off-ramp. However, the state of the art indicates the lack of rigorous methods to optimally locate this advance warning so that the maximum benefit can be obtained. This research is motivated to address this gap. Specifically, the proposed approach considers that the area downstream of the advance warning includes two zones: (i) the green zone whose traffic ensures safe and smooth lane changes without speed deceleration (S-MLC); the start point of the green zone corresponding to the location of the advance warning; (ii) the yellow zone whose traffic leads to rush lane change maneuvers with speed deceleration (D-MLC). An optimization model is proposed to search for the optimal green and yellow zones. Traffic flow theory such as Greenshield model and shock wave analysis are used to analyze the impacts of the S-MLC and D-MLC maneuvers on the traffic delay. A grid search algorithm is applied to solve the optimization model. Numerical experiments conducted on the simulation model developed in Paramics 6.9.3 indicate that the proposed optimization model can identify the optimal location to set the advance MLC warning nearby an off-ramp so that the traffic delay resulting from lane change maneuvers is minimized, and the corresponding capacity drop and traffic oscillation can be efficiently mitigated. Moreover, the experiments validated the consistency of the green and yellow zones obtained in the simulation traffic flow and from the optimization model for a given optimally located MLC advance warning under various traffic regimes. The proposed approach can be implemented by roadside mobile warning facility or on-board GPS for human-driven vehicles, or embedded into lane change aid systems to serve connected and automated vehicles. Thus it will greatly contribute to both literature and engineering practice in lane change management.     

A model and a solution algorithm for airport common use check-in counter assignments

In this research we develop an integer programming model to assist airport authorities to assign common use check-in counters. Due to the many complicated factors that have to be considered in such a model, the problem size is expected to be huge, making its solution difficult and therefore not applicable to the real world. Therefore, we develop a heuristic method, containing three heuristic models, to solve the model. These heuristic models are formulated as zero–one integer programs that can be solved using the simplex method and the branch-and-bound technique. To test how well the proposed models and the solution method may be applied in the real world, we perform a case study concerning the operations of a major airport in Taiwan.     

A robust optimization approach for dynamic traffic signal control with emission considerations

We consider an analytical signal control problem on a signalized network whose traffic flow dynamic is described by the Lighthill–Whitham–Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956). This problem explicitly addresses traffic-derived emissions as constraints or objectives. We seek to tackle this problem using a mixed integer mathematical programming approach. Such class of problems, which we call LWR-Emission (LWR-E), has been analyzed before to certain extent. Since mixed integer programs are practically efficient to solve in many cases (Bertsimas et al., 2011b), the mere fact of having integer variables is not the most significant challenge to solving LWR-E problems; rather, it is the presence of the potentially nonlinear and nonconvex emission-related constraints/objectives that render the program computationally expensive.To address this computational challenge, we proposed a novel reformulation of the LWR-E problem as a mixed integer linear program (MILP). This approach relies on the existence of a statistically valid macroscopic relationship between the aggregate emission rate and the vehicle occupancy on the same link. This relationship is approximated with certain functional forms and the associated uncertainties are handled explicitly using robust optimization (RO) techniques. The RO allows emissions-related constraints and/or objectives to be reformulated as linear forms under mild conditions. To further reduce the computational cost, we employ a link-based LWR model to describe traffic dynamics with the benefit of fewer (integer) variables and less potential traffic holding. The proposed MILP explicitly captures vehicle spillback, avoids traffic holding, and simultaneously minimizes travel delay and addresses emission-related concerns.