Properties of a traffic control policy which ensure the existence of a traffic equilibrium consistent with the policy

We consider a network with interactions and capacity constraints at each junction. We give conditions on the interactions and constraints which, if satisfied at each separate junction, ensure that any feasible assignment problem has an equilibrium solution. Two illustrative examples are provided; the first arises naturally and does not satisfy our conditions, while the second does satisfy our conditions but is somewhat unnatural.     

Junction interactions and monotonicity in traffic assignment

We consider the traffic equilibrium problem when the travel demand is inelastic and stationary in time. Junction interactions, which abound in urban road networks, are permitted. We prove that the set of equilibria (solutions to the assignment problem) is convex when certain monotonicity and continuity conditions are statisfied at each junction.     

Two alternative definitions of traffic equilibrium

The paper shows that, under reasonable conditions, if there are junction or modal interactions then a Wardrop equilibrium exists but a user—optimised flow may well not.     

How flexible is flexible? Accounting for the effect of rescheduling possibilities in choice of departure time for work trips

In departure time studies it is crucial to ascertain whether or not individuals are flexible in their choices. Previous studies have found that individuals with flexible work times have a lower value of time for late arrivals. Flexibility is usually measured in terms of flexible work start time or in terms of constraints in arrival time at work. Although used for the same purpose, these two questions can convey different types of information. Moreover, constraints in departure time are often related not only to the main work activity, but to all daily activities. The objective of this paper is to investigate the effect of constraints in work and in other daily trips/activities on the willingness to shift departure time and the willingness to pay for reducing travel time and travel delay. We set up a survey to collect detailed data on the full 24-hour out-of-home activities and on the constraints for each of these activities. We then built a stated preference experiment to infer preferences on departure time choice, and estimated a mixed logit model, based on the scheduling model, to account for the effects of daily activity schedules and their constraints. Our results show that measuring flexibility in terms of work start time or constraints at work does not provide exactly the same information. Since one-third of the workers with flexible working hours in the survey indicated that they have restrictions on late work-arrival times, their willingness to pay will be overestimated (almost doubled) if flexibility information is asked only in terms of fixed/flexible working hours. This clearly leads to different conclusion in terms of demand sensitivity to reschedule to a later departure time. We also found that having other activities and constraints during the day increases the individuals’ willingness to pay to avoid being late at work, where the presence of constraints on daily activities other than work is particularly relevant for individuals with no constraints at work. The important impact of these findings is that if we neglect the presence of constraints, as is common practise in transport models, it will generally lead to biased value-of-time estimates. Results clearly show that the shift in the departure time, especially towards a late departure time, is strongly overestimated (the predicted shift is more than double) when the effect of non-work activities and their constraints is not accounted for.     

Open PFLOW: Creation and evaluation of an open dataset for typical people mass movement in urban areas

Understanding people flow at a citywide level is critical for urban planning and commercial development. Thanks to the ubiquity of human location tracking devices, many studies on people mass movement with mobility logs have been conducted. However, high cost and severe privacy policy constraints still complicate utilization of these data in practice. There is no dataset that anyone can freely access, use, modify, and share for any purpose. To tackle this problem, we propose a novel dataset creation approach (called Open PFLOW) that continuously reports the spatiotemporal positions of all individual’s in urban areas based on open data. With fully consideration of the privacy protection, each entity in our dataset does not match the actual movement of any real person, so that the dataset can be totally open to public as part of data infrastructure. Because the result is shown at a disaggregate level, users can freely modify, process, and visualize the dataset for any purpose. We evaluate the accuracy of the dataset by comparing it with commercial datasets and traffic census indicates that it has a high correlation with mesh population and link-based traffic volume.     

Incentivized vehicle relocation in vehicle sharing systems

The asymmetric demand-offer problem represents a major challenge for one-way vehicle sharing systems (VSS) affecting their economic viability as it necessitates the engagement of considerable human (and financial) resources in relocating vehicles to satisfy customer demand. In this paper, we propose a novel approach which involves user-based vehicle relocations to address supply-and-demand mismatches; in our approach, VSS users are offered price incentives so as to accept picking up their vehicle from an oversupplied station and/or to drop it off to an under-supplied station. The system incentivizes users based on the priorities of vehicle relocations among stations, taking into account the fluctuating demand for vehicles and parking places at different stations over time. A graph-theoretic approach is employed for modeling the problem of allocating vehicles to users in a way that maximizes the profit of the system taking into account the budget the VSS can afford to spend for rewarding users, as well as the users’ strategic behavior. We present two different schemes for incentivizing users to act in favour of the system. Both schemes consider budget constraints and are truthful and budget-feasible. We have extensively evaluated our approach through simulations which demonstrated significant gain with respect to the number of completed trips and system revenue. We have also validated our approach through pilot trials conducted in a free-floating e-motorbike sharing system in the framework of an EU-funded research project.     

Dynamic user equilibrium in public transport networks with passenger congestion and hyperpaths

This paper presents a dynamic user equilibrium for bus networks where recurrent overcrowding results in queues at stops. The route-choice model embedded in the dynamic assignment explicitly considers common lines and strategies with alternative routes. As such, the shortest hyperpath problem is extended to a dynamic scenario with capacity constraints where the diversion probabilities depend on the time at which the stop is reached and on the expected congestion level at that time. In order to reproduce congestion for all the lines sharing a stop, the Bottleneck Queue Model with time-varying exit capacity, introduced in Meschini et al. (2007), is extended. The above is applied to separate queues for each line in order to satisfy the First-In-First-Out principle within every attractive set, while allowing overtaking among passengers with different attractive sets but queuing single file. The application of the proposed model to a small example network clearly reproduces the formation and dispersion of passenger queues due to capacity constraints and thus motivates the implementation of the methodology on a real-size network case as the next step for future research.     

Selection of roadway grades that minimize earthwork cost using linear programming

Roadway grades are normally established to satisfy the geometric specifications of the road. Once the grades are established, the earthwork allocations that minimize the cost are determined. This paper presents a model that links these two activities. The model selects the roadway grades that minimize the cost of earthwork and satisfy the geometric specifications. The geometric specifications pertain to the elements of the vertical alignment, elevation of grade line at specified stations, horizontal and vertical alignment relations, and type of vertical curve. The model enumerates all technically feasible grades and solves the linear programming problem to minimize earthwork allocation cost for those grade alternatives that satisfy borrow pit and landfill capacity constraints. The model incorporates important earthwork details and guarantees obtaining the global minimum earthwork cost. Application of the model is illustrated by a numerical example and model extensions to accomodate other design and construction aspects are presented.     

A note on the interpretation of the dual variables in estimating traffic capacity at signal- controlled road junctions

The values of the dual variables in a constrained optimisation problem can be used to estimate the sensitivity of the optimal value of the objective function to changes in the constraints. Allsop (1972) used standard methods of linear programming to derive expressions for the sensitivity of the reserve capacity at a signal-controlled road junction to various changes in the traffic engineering constraints. That analysis used the assumption that the maximum reserve capacity would be achieved when the cycle time used is maximal. While this normally occurs, some junctions have come to light where a reduction in the cycle time increases the capacity. Allsop's analysis is extended here to account for this possibility.     

Reducing the passenger travel time in practice by the automated construction of a robust railway timetable

Automatically generating timetables has been an active research area for some time, but the application of this research in practice has been limited. We believe this is due to two reasons. Firstly, some of the models in the literature impose artificial upper bounds on time supplements. This causes a high risk of generating infeasibilities. Secondly, some models that leave out these upper bounds often generate solutions that contain some very large time supplements because these supplements are not penalised in the objective function. The reason is that these objective functions often do not completely correspond to the true goal of a timetable. We solve both problems by minimising our objective function: total passenger travel time, expected in practice. Since this function evaluates and indirectly steers all time related decision variables in the system, we do not need to further restrict the ranges of any of these variables. As a result, our model does not suffer from infeasibilities generated by such artificial upper bounds for supplements.Furthermore, some measures are taken to significantly speed up the solver times of our model. These combined features result in our model being solved more quickly than previous models. As a result, our method can be used for timetabling in practice. We demonstrate our claims by optimising, in about two hours only, the timetable of all 196 hourly passenger trains in Belgium. Assuming primary delay-distributions with an average of 2% on the minima of each activity, the optimised timetable reduces expected passenger time in practice, as evaluated on the macroscopic level, by 3.8% during peak hours. This paper demonstrates that we added two important missing steps to make cyclic timetabling for passengers really useable in practice: (i) the addition of the objective function of expected passenger time in practice and (ii) the reduction of computation time by addition of well chosen additional constraints.     

A model and optimization-based heuristic for the operational aircraft maintenance routing problem

This paper investigates the Operational Aircraft Maintenance Routing Problem (OAMRP). Given a set of flights for a specific homogeneous fleet type, this short-term planning problem requires building feasible aircraft routes that cover each flight exactly once and that satisfy maintenance requirements. Basically, these requirements enforce an aircraft to undergo a planned maintenance at a specified station before accumulating a maximum number of flying hours. This stage is significant to airline companies as it directly impacts the fleet availability, safety, and profitability. The contribution of this paper is twofold. First, we elucidate the complexity status of the OAMRP and we propose an exact mixed-integer programming model that includes a polynomial number of variables and constraints. Furthermore, we propose a graph reduction procedure and valid inequalities that aim at improving the model solvability. Second, we propose a very large-scale neighborhood search algorithm along with a procedure for computing tight lower bounds. We present the results of extensive computational experiments that were carried out on real-world flight networks and attest to the efficacy of the proposed exact and heuristic approaches. In particular, we provide evidence that the exact model delivers optimal solutions for instances with up to 354 flights and 8 aircraft, and that the heuristic approach consistently delivers high-quality solutions while requiring short CPU times.     

Robust flight-to-gate assignment using flight presence probabilities

In this paper we present a novel method to improve the robustness of solutions to the Flight-to-Gate Assignment Problem (FGAP), with the aim to reduce the need for gate re-planning due to unpredicted flight schedule disturbances in the daily operations at an airport. We propose an approach in which the deterministic gate constraints are replaced by stochastic gate constraints that incorporate the inherent stochastic flight delays in such a way so as to ensure that the expected gate conflict probability of two flights assigned to the same gate at the same time does not exceed a user-specified value. The novel approach is integrated into an existing multiple time slot FGAP model that relies on a binary integer programming formulation and is tested using real-life data pertaining to Amsterdam Airport Schiphol. The results confirm that the proposed approach holds out great promise to improve the robustness of the FGAP solutions.     

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.     

Scheduling and platforming trains at busy complex stations

We consider the problem of train planning or scheduling for large, busy, complex train stations, which are common in Europe and elsewhere, though not in North America. We develop the constraints and objectives for this problem, but these are too computationally complex to solve by standard combinatorial search or integer programming methods. Also, the problem is somewhat political in nature, that is, it does not have a clear objective function because it involves multiple train operators with conflicting interests. We therefore develop scheduling heuristics analogous to those successfully adopted by train planners using “manual” methods. We tested the model and algorithms by applying to a typical large station that exhibits most of the complexities found in practice. The results compare well with those found by traditional methods, and take account of cost and preference trade-offs not handled by those methods. With successive refinements, the algorithm eventually took only a few seconds to run, the time depending on the version of the algorithm and the scheduling problem. The scheduling models and algorithms developed and tested here can be used on their own, or as key components for a more general system for train scheduling for a rail line or network.Train scheduling for a busy station includes ensuring that there are no conflicts between several hundred trains per day going in and out of the station on intersecting paths from multiple in-lines and out-lines to multiple platforms, while ensuring that each train is allowed at least its minimum required headways, dwell time, turnaround time and trip time. This has to be done while minimizing (costs of) deviations from desired times, platforms or lines, allowing for conflicts due to through-platforms, dead-end platforms, multiple sub-platforms, and possible constraints due to infrastructure, safety or business policy.     

A hierarchical line planning approach for a large-scale high speed rail network: The China case

Planning a set of train lines in a large-scale high speed rail (HSR) network is typically influenced by issues of longer travel distance, high transport demand, track capacity constraints, and a non-periodic timetable. In this paper, we describe an integrated hierarchical approach to determine line plans by defining the stations and trains according to two classes. Based on a bi-level programming model, heuristics are developed for two consecutive stages corresponding to each classification. The approach determines day-period based train line frequencies as well as a combination of various stopping patterns for a mix of fast trunk line services between major stations and a variety of slower body lines that offer service to intermediate stations, so as to satisfy the predicted passenger transport demand. Efficiencies of the line plans described herein concern passenger travel times, train capacity occupancy, and the number of transfers. Moreover, our heuristics allow for combining many additional conflicting demand–supply factors to design a line plan with predominantly cost-oriented and/or customer-oriented objectives. A range of scenarios are developed to generate three line plans for a real-world example of the HSR network in China using a decision support system. The performance of potential train schedules is evaluated to further examine the feasibility of the obtained line plans through graphical timetables.     

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

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

A hybrid controller for autonomous vehicles driving on automated highways

This paper addresses the problem of the hybrid control of autonomous vehicles driving on automated highways. Vehicles are autonomous, so they do not communicate with each other nor with the infrastructure. Two problems have to be dealt with: a vehicle driving in a single-lane highway must never collide with its leading vehicle; and a vehicle entering the highway at a designated entry junction must be able to merge from the merging lane to the main lane, again without any collision. To solve these problems, we equip each vehicle with a hybrid controller, consisting of several continuous control laws embedded inside a finite state automaton. The automaton specifies when a given vehicle must enter the highway, merge into the main lane, yield to other vehicles, exit from the highway, and so on. The continuous control laws specify what acceleration the vehicle must have in order to avoid collisions with nearby vehicles. By carefully designing these control laws and the conditions guarding the automaton transitions, we are able to demonstrate three important results. First, we state the initial conditions guaranteeing that a following vehicle never collides with its leading vehicle. Second, we extend this first result to a lane of autonomous vehicles. Third, we prove that if all the vehicles are equipped with our hybrid controller, then no collision can ever occur, and all vehicles either merge successfully or are forced to drop out when they reach the end of their merging lane. Finally, we show the outcome of a highway microsimulation modelled after the Katy Corridor near Houston, Texas: our single-lane highway can accommodate 4000 vehicles per hour with neither drop-outs nor traffic congestion. It is entirely programmed in SHIFT, a hybrid systems simulation language developed at UC Berkeley by the PATH group. This shows that SHIFT is a well suited language for designing safe control laws for autonomous highway systems, among others.     

Multi-commodity traffic assignment by continuum approximation of network flow with variable demand

Consider a city with several highly compact central business districts (CBD), and the commuters’ destinations from each of them are dispersed over the whole city. Since at a particular location inside the city the traffic movements from different CBDs share the same space and do not cancel out each other as in conventional fluid flow problems albeit travelling in different directions, the traffic flows from a CBD to the destinations over the city are considered as one commodity. The interaction of the traffic flows among different commodities is governed by a cost–flow relationship. The case of variable demand is considered. The primal formulation of the continuum equilibrium model is given and proved to satisfy the user optimal conditions, and the dual formulation of the problem and its complementary conditions are also discussed. A finite element method is then employed to solve the continuum problem. A numerical example is given to illustrate the effectiveness of the proposed method.     

Convergence of the Frank-Wolfe method for certain bounded variable traffic assignment problems

In two recent papers published in Transportation Research, Daganzo presented a modification of the Frank-Wolfe algorithm to solve certain link capacitated traffic assignment problems satisfying certain conditions. In order to show convergence of the modified algorithm, the assumption was made that the integral of the volume delay formula for each link tends to infinity as the link flow approaches the link capacity. In this paper we give a Theorem which establishes convergence of the modified algorithm under much weaker conditions. This result is then used to show convergence if the objective function of the assignment model is sufficiently large (not necessarily infinite) when the link flows are at capacity. Thus the modified method is applicable to a broader class of assignment problems. Two numerical examples illustrate (a) when the method converges and when it does not, and (b) that our Theorem provides a weaker condition for convergence of the method.