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Curb space is one of the busiest areas in urban road networks. Especially in recent years, the rapid increase of ride-hailing trips and commercial deliveries has induced massive pick-ups/drop-offs (PUDOs), which occupy the limited curb space that was designed and built decades ago. These PUDOs could jam curbside utilization and disturb the mainline traffic flow, evidently leading to significant negative societal externalities. However, there is a lack of an analytical framework that rigorously quantifies and mitigates the congestion effect of PUDOs in the system view, particularly with little data support and involvement of confounding effects. To bridge this research gap, this paper develops a rigorous causal inference approach to estimate the congestion effect of PUDOs on general regional networks. A causal graph is set to represent the spatiotemporal relationship between PUDOs and traffic speed, and a double and separated machine learning (DSML) method is proposed to quantify how PUDOs affect traffic congestion. Additionally, a rerouting formulation is developed and solved to encourage passenger walking and traffic flow rerouting to achieve system optimization. Numerical experiments are conducted using real-world data in the Manhattan area. On average, 100 additional units of PUDOs in a region could reduce the traffic speed by 3.70 and 4.54 miles/hour (mph) on weekdays and weekends, respectively. Rerouting trips with PUDOs on curb space could respectively reduce the system-wide total travel time (TTT) by 2.44% and 2.12% in Midtown and Central Park on weekdays. A sensitivity analysis is also conducted to demonstrate the effectiveness and robustness of the proposed framework. Funding: The work described in this paper was supported by the National Natural Science Foundation of China [Grant 52102385], grants from the Research Grants Council of the Hong Kong Special Administrative Region, China [Grants PolyU/25209221 and PolyU/15206322], a grant from the Otto Poon Charitable Foundation Smart Cities Research Institute (SCRI) at the Hong Kong Polytechnic University [Grant P0043552], and a grant from Hong Kong Polytechnic University [Grant P0033933]. S. Qian was supported by a National Science Foundation Grant [Grant CMMI-1931827]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/trsc.2022.0195. [ABSTRACT FROM AUTHOR]

Microscopic traffic flow models enable predictions of traffic operations, which allows traffic engineers to assess the efficiency and safety effects of roadway designs. Modeling vehicle trajectories inside intersections is challenging because there is an infinite number of possible paths in a two-dimensional space, and drivers can simultaneously adapt their speeds as well. To date, human driver models for simultaneous longitudinal and lateral vehicle control based on the infrastructure characteristics and interactions with other drivers inside an intersection are still lacking. The contribution of this paper is threefold. First, it proposes an integrated microscopic traffic flow model to describe human-driven vehicle maneuvers under interactions. Drivers plan their heading and acceleration in the predicted future to minimize costs representing undesirable situations. The model works with a joint optimization for an interaction cost term. The weights associated with the interaction cost reflect how selfish or altruistic drivers are. Second, the proposed model endogenously gives the order of vehicles in case of crossing paths. Third, the paper develops a clustered validation method for microscopic traffic flow models with interacting vehicles, which account for interdriver variations. Results show that the model can accurately describe vehicle passing orders of interacting maneuvers, paths, and speeds against empirical data. The model can be applied to assess various intersection designs. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71971140 and 52122215] and the Natural Science Foundation of Shanghai [Grant 20ZR1439300]. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel data-driven optimization approach for trajectory-based air traffic flow management (ATFM). A key aspect of the proposed approach is the inclusion of airspace users' trajectory preferences, which are computed from traffic data by combining clustering and classification techniques. Machine learning is also used to extract consistent trajectory options, whereas optimization is applied to resolve demand-capacity imbalances by means of a mathematical programming model that judiciously assigns a feasible four-dimensional trajectory and a possible ground delay to each flight. The methodology has been tested on instances extracted from the Eurocontrol data repository. With more than 32,000 flights considered, we solve the largest instances of the ATFM problem available in the literature in short computational times that are reasonable from the practical point of view. As a by-product, we highlight the trade-off between preferences and delays as well as the potential benefits. Indeed, computing efficient solutions to the problem facilitates a consensus between the network manager and airspace users. In view of the level of accuracy of the solutions and the excellent computational performance, we are optimistic that the proposed approach can make a significant contribution to the development of the next generation of air traffic flow management tools. [ABSTRACT FROM AUTHOR]

Road traffic exhaust emission predictions are used to inform transport policy and investment decisions aimed at reducing emissions and achieving sustainable mobility. Emission predictions are also used as inputs when modeling air quality and human exposure to traffic-related air pollutants. To be effective, such policies and/or integration must be based on robust models that not only provide point-based predictions but also inform these with an interval of confidence that properly accounts for the propagation of uncertainties through the complex chain of models involved. This paper develops a data-driven methodological framework that enables calculating the uncertainty in average speed–based emission predictions induced by uncertainty in its traffic data inputs, which are most often predictions (or outputs) of traffic flow models. An ensemble-based optimisation approach is used to estimate both calibration and validation errors arising from uncertainty in the structure and parameterisation of the cell transmission model, a discretised first-order macroscopic traffic flow model that is often integrated with average speed–based emission models. A Monte Carlo sampling approach is proposed to propagate the uncertainty in traffic flow inputs to emission predictions. To ensure transferability of findings, this methodology has been tested using multiple real data sets on three motorway road networks, one of which operates under variable speed limits. The online appendix is available at https://doi.org/10.1287/trsc.2017.0787. [ABSTRACT FROM AUTHOR]

Connected technologies have engendered a paradigm shift in mobility systems by enabling digital platforms to coordinate large sets of vehicles in real time. Recent research has investigated how a small number of connected vehicles may be coordinated to reduce total system cost. However, platforms may coordinate vehicles to optimize a fleet-wide objective which is neither user nor system optimal. We study the behavior of optimized fleets in mixed traffic and find that, at small penetrations, fleets may worsen system cost relative to user equilibrium, and provide a concrete example of this paradox. Past a critical penetration level, however, optimized fleets reduce system cost in the network, up to achieving system optimal traffic flow, without need for an external subsidy. We introduce two novel notions of fleet-optimal mixed equilibria: critical fleet size for user equilibrium (CFS-UE) and critical fleet size for system optimum (CFS-SO). We demonstrate on the Sioux Falls and Pittsburgh networks that 33% and 83% of vehicles, respectively, must participate in the fleet to achieve system optimum. In Pittsburgh, we find that, although fleets permeate the network, they accumulate on highways and major arterials; the majority of origin-destination pairs are either occupied exclusively by users or by the fleet. Critical fleet size offers regulators greater insight into where fleet and system interests align, transportation planners a novel metric to evaluate road improvements, and fleet coordinators a better understanding of their efforts to optimize their fleet. History: This paper has been accepted for the Transportation Science Special Issue on Emerging Topics in Transportation Science and Logistics. Funding: This work was supported by the U.S. Department of Transportation [Mobility21] and the National Science Foundation [CMMI-1931827]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1189. [ABSTRACT FROM AUTHOR]

This paper addresses large-scale urban transportation optimization problems with time-dependent continuous decision variables, a stochastic simulation-based objective function, and general analytical differentiable constraints. We propose a meta- model approach to address, in a computationally efficient way, these large-scale dynamic simulation-based optimization problems. We formulate an analytical dynamic network model that is used as part of the metamodel. The network model formulation combines ideas from transient queueing theory and traffic flow theory. The model is formulated as a system of equations. The model complexity is linear in the number of road links and is independent of the link space capacities. This makes it a scalable model suitable for the analysis of large-scale problems. The proposed dynamic metamodel approach is used to address a time-dependent large-scale traffic signal control problem for the city of Lausanne. Its performance is compared to that of a stationary metamodel approach. The proposed approach outperforms the stationary approach. This comparison illustrates the added value of providing the algorithm with analytical dynamic problem-specific structural information. The performance of a signal plan derived by the proposed approach is also compared to that of an existing signal plan for the city of Lausanne, and to that of a signal plan derived by a mainstream commercial signal control software. The proposed method can systematically identify signal plans with good performance. [ABSTRACT FROM AUTHOR]

Presents a response by C. Hendrickson and G. Kocur to a letter to the editor about their article "Schedule Delay and Departure Time Decisions in a Deterministic Model," in the 15th vol. of the journal "Transportation Science."

Aggregated dynamic traffic models based on the network macroscopic fundamental diagram (MFD) have been founded on stationary or steady-state approximations. Theoretically, they are only qualified with slow-varying demand profiles as inputs. In practice, MFD models are often fed with fast-varying demand patterns classically observed during peak hours. This paper investigates the accuracy of existing MFD model outputs in such a case. It also provides a fresh look at hysteresis loops that may arise on MFD shapes and shows how they are connected to the demand profile. First derived are the exact solutions of the Lighthill, Whitham, and Richards (LWR) model for a simple but meaningful test case corresponding to the loading and the recovery of an arterial with a single bottleneck. The spatial integration of these solutions permits to derive the average flow- and outflow-MFD patterns. The average flow-MFD exhibits a clockwise hysteresis loop with higher flows during the network loading than during the recovery. The outflow MFD shows an opposite trend with a counterclockwise hysteresis loop. The detailed analysis of the LWR solution highlights that these patterns are fully driven by the congestion dynamics and different wave propagation during both periods. This complements existing studies that tend to explain hysteresis by heterogeneous network loading due to unbalanced flows at intersections. It should be noted that the size of the production-MFD hysteresis loop is influenced by the demand loading profile, which means that the MFD is more sensitive to the demand than initially expected. The second part of the paper is about the implications of these observations on the MFD simulation. The main conclusion is that the accumulation-based formulation captures properly the aggregate dynamics of the LWR model during saturation but not in free-flow. It should be calibrated with an average flow-MFD that does not account for the hysteresis pattern to properly estimate the outflow. On the contrary, the original formulation of the trip-based model is only valid in free-flow. During saturation, it should be patched to modify the outflow values. The best approach is a hybrid model that combines the trip-based model in free-flow and the accumulation-based model during saturation. Note that in free-flow the trip-based model is better fed by the average flow-MFD with hysteresis as it gives better estimation for the mean speed. Finally, some evidences are presented and tend to confirm that all the conclusions remain valid for more complex urban settings. [ABSTRACT FROM AUTHOR]

Observations of freeway traffic flow are usually quite scattered about an underlying curve when plotted versus density or occupancy. Although increasing the sampling intervals can reduce the scatter, whenever an experiment encompasses a rush hour with transitions in and out of congestion, some outlying data stubbornly remain beneath the ‘equilibrium’ curve. The existence of these nonequilibrium points is a poorly understood phenomenon that appears to contradict the simple kinematic wave (KW) model of traffic flow. This paper provides a tentative explanation of the phenomenon, based on experimental evidence. The evidence was a FIFO queue that grew and receded over two detector stations, generating typical flow-density scatter plots at both locations. The locations were far from other interacting traffic streams. The data revealed that a transition zone where vehicles decelerated gradually existed immediately behind the queue. The transition zone was quite wide (about 1 km at both locations), moved slowly (approximately with the ‘shock’ velocity of KW theory), and as a result spent many minutes over each detector station. Disequilibrium flow-density points arose only when the transition zone was over the detectors, suggesting that the transition zone explains their occurrence. The disequilibrium points drifted gradually from one branch of the curve to the other, as KW theory would have predicted if ‘shocks’ had a characteristic width equal to the dimension of the transition zone. Nothing was found in the data to contradict this view. This paper also shows that in our case, if one neglects the shocks' physical dimension, the position of every vehicle can be predicted with KW theory to within approximately five vehicle spacings. Thus, it appears that KW theory can predict rather accurately traffic behavior at the back of FTFO queues, i.e., when the lanes are equally attractive to all drivers. We end with a discussion offering some perspective on how the findings of this paper related to the traffic thinking found in the current literature. [ABSTRACT FROM AUTHOR]

A simple yet efficient traffic flow model, in particular one that describes vehicle longitudinal operational control and further characterizes a traffic flow fundamental diagram, is always desirable. Though many models have been proposed in the past with each having its own merits, research in this area is far from conclusive. This paper contributes a new model, i.e., the longitudinal control model, to the arsenal with a unique set of properties. The model is suited for a variety of transportation applications, among which a concrete example is provided in this paper. [ABSTRACT FROM AUTHOR]

This paper explores some of the traffic phenomena that arise when drivers have to navigate a network in which queues back up past diverge intersections. If a diverge provides two alternative routes to the same destination and the shorter route has a bottleneck that generates a queue, one would expect that queue to stabilize at an equilibrium level where the travel time on both routes is roughly equal. If the capacity of the alternative route is unlimited then this network can accommodate any demand level. However, if the bottleneck is so close to the upstream end of the link that the equilibrium queue cannot be contained in the link, then the trip time on the queued route cannot grow to match that on the alternate route. This means that the alternative route can never be attractive, even if the queue spills back past the diverge, and that drivers approaching the diverge will act as if the alternative route did not exist. As a result, a steady flow into the system greater than the capacity of the bottleneck will cause a queue to grow all the way back to the origin (blocking it). The final result is an "oversaturated static state" where the queue regulates the input flow into the system. Curiously, if the bottleneck capacity of this network is reduced below a critical level (or is eliminated altogether) then the alternative route becomes attractive again and the system cannot reach the saturation point. This phenomenon is explored in the paper, where it is also shown that: i) a network can become permanently oversaturated / undersaturated as a result of a temporary increase / decrease in link capacity, ii) even under the most favorable assumptions, and in contrast to the equivalent assignment problem with point queues, a network can be stable both in an oversaturated and an undersaturated state, and iii) temporary endogenous disturbances can permanently reverse the saturation state of a network. These findings suggest that in certain situations the time-dependent traffic assignment problem with physical queues is chaotic in nature and that (as in weather forecasting) it may be impossible to obtain input data with the required accuracy to make reliable predictions of cumulative output flows. [ABSTRACT FROM AUTHOR]

This paper is concerned with the modeling of the Dynamic Traffic Assignment Problem (DTAP) for predicting the flows of urban transportation networks, mainly at peak periods. During the past 40 years, most of the research has been for the Static Traffic Assignment Problem (STAP) where it is assumed that demand is constant over time. This assumption is realistic for the analysis of intercity freight transportation networks over long periods of time, but it does not hold in an urban area, for simulating the flow variations during short periods (peak hours). Hence, during the past 20 years, the interest to the DTAP has been increasing. The seventies have been a transition period between heuristic models (where the demand is assigned to instantaneous minimum cost paths), and optimization models that take into account the demand over the whole study horizon of time, but all of them incorporate important limitations (only one destination; unrealistic conditions on the cost functions so that the flow "reaches" the destination; possible violation of the link capacities; etc.). In this paper, we propose a Dynamic Traffic Assignment Model which is mainly based on the following assumption: the time spent by a vehicle on a link may be decomposed into a fixed travel time plus a waiting time. The fixed travel time corresponds to the free or uncongested travel time over the link. Then the vehicle is put in an exit queue (which resides on the same link) until it becomes possible to enter a forward link; this decision is based on the link costs and their capacities. We show that this model leads to a network structure (a temporal expansion of the base network, including the queues) and therefore the DTAP may be viewed as a "simple" STAP over the expanded network. Hence, all the theories... [ABSTRACT FROM AUTHOR]

Linear data projection is widely used for unbiased traffic data estimation. Nevertheless, recent studies have proven that direct model estimation based on linearly projected data that ignores the scaling factor variability may lead to systematically biased parameters. Adjustment factors were derived for a generalised multivariate polynomial (GMP) function with fixed exponents to remove such biases. However, the methods have not been extended to generic nonlinear transport models necessitating nonlinear regressions. This paper scrutinises the mechanism of systematic data point distortion resulting from linear data projection and identifies the practical difficulties of the adjustment factor approach to other nonlinear models. To reduce such biases in nonlinear transport models, a generic mean value restoration (MVR) method, requiring only the first two moments of the scaling factor, and an extended MVR (EMVR) method, further incorporating higher-order moments by assuming a scaling factor distribution, are proposed. Simulation studies are conducted for both GMP functions with relaxed exponents and multivariate exponential decay functions, which are the most commonly adopted nonlinear functions for modeling traffic flow, to examine the effectiveness and robustness of the proposed methods for recovering the assumed true model parameters. Results reveal that the EMVR method generally can achieve higher level of accuracy. [ABSTRACT FROM AUTHOR]

Queueing because of congestion is an important aspect of road traffic. This paper provides a novel threshold queue that models the empirical shape of the fundamental diagram. In particular, we show that our threshold queue with two service phases captures the capacity drop that is eminent in the fundamental diagram of modern traffic. We use measurements on a Danish highway to illustrate that our threshold queue is indeed capable of capturing the fundamental diagram of real-world traffic systems. We furthermore indicate the modelling power of our threshold queue via a sensitivity study showing that our model is able to capture a wide range of shapes for the fundamental diagram. The online appendix is available at https://doi.org/10.1287/trsc.2018.0850. [ABSTRACT FROM AUTHOR]

This paper investigates the cell-transmission model (CTM)-based single destination system optimum dynamic traffic assignment (SO-DTA) problem, focusing attention on a case where the cell properties are time-invariant. We show the backward propagation of congestion in CTM does not affect the optimal arrival flow pattern of SO-DTA, if the fundamental diagram is of triangular/trapezoidal shape as in the CTM. We mathematically prove that the set of earliest arrival flows (EAFs) not constrained by the traffic wave propagation equations obtained on the node-arc network without cell division is a subset of the SO-DTA. This finding leads to a new approach to the SO-DTA that solves the EAF. Such an EAF can be obtained by merely applying static flow techniques and turning the static flows into dynamic flows over time. Therefore, SO-DTA can theoretically be solved with a run time at the link level depending polynomially on log T . We use numerical examples to verify the results and report the computational benefits of the proposed method by solving SO-DTA on a real-world network. [ABSTRACT FROM AUTHOR]

In this paper we propose a new estimator for calculating the probability of traffic breakdown as a function of traffic demand. Traffic breakdown is a well-studied phenomena within previous literature and is of great importance to traffic planners and controllers. The proposed estimator has an appealing intuition and is able to overcome several of the problems associated with previously proposed methodology. The input to the estimator is a set of aggregated (typically five minute) traffic observations classified to either a breakdown or nonbreakdown state, and a customized and fast algorithm for this purpose is proposed. Last, we apply the classification algorithm and breakdown probability estimator to a large data set consisting of several observation sites on the Norwegian road network, and we compare our estimator to a previously defined estimator. [ABSTRACT FROM AUTHOR]

Despite various planning efforts, airspace capacity can sometimes be exceeded, typically because of disruptive events. Air traffic flow management (ATFM) is the process of managing flights in this situation. In this paper, we present an ATFM model that accounts for different rerouting options (path rerouting and diversion) and preexisting en route flights. The model proposes having a central authority to control all decisions, which is then compared with current practice. We also consider interflight and interairline fairness measures in the network. We use an exact approach to solve small- to medium-sized instances, and we propose a modified fix-and-relax heuristic to solve large-sized instances. Allowing a central authority to control all decisions increases network efficiency compared with the case where the ATFM authority and airlines control decisions independently. Our experiments show that including different rerouting options in ATFM can help reduce delays by up to 8% and cancellations by up to 23%. Moreover, ground delay cost has much more impact on network decisions than air delay cost, and network decisions are insensitive to changes in diversion cost. Furthermore, the analysis of the tradeoff between total network cost and overtaking cost shows that adding costs for overtaking can significantly improve fairness at only a small increase in total system cost. A balanced total cost per flight among airlines can be achieved at a small increase in the network cost (0.2%–3.0%) when imposing airline fairness. In conclusion, the comprehensiveness of the model makes it useful for analyzing a wide range of alternatives for efficient ATFM. [ABSTRACT FROM AUTHOR]

This note revisits a paper from Velan and Florian (Velan, S., M. Florian. 2002. A note on the entropy solutions of the hydrodynamic model of traffic flow. Transportation Sci. 36(4) 435-446) dealing with the entropy condition in traffic flow models. It aims to clarify the application of this condition for nondifferentiable fundamental diagrams and then to correct some misunderstandings that appear in the above-mentioned paper. This note clearly exhibits that the nonsmoothness of the fundamental diagram does not change the properties of the Lighthill-Whitham-Richards (LWR) solutions: (i) existence of a unique entropy solution and (ii) nonuniqueness of weak solutions. These precisions are important because piecewise linear fundamental diagrams appear to accurately fit with experimental observations and cannot be disproved on an alleged mathematical basis. [ABSTRACT FROM AUTHOR]

In this paper, congestion dynamics along crowded freeway corridors are modeled as a conservation law with a source term that is continuous in space. The source term represents the net inflow from ramps, postulated here as a location-dependent function of the demand for entering and exiting the corridor. Demands are assumed to be time-independent, which is appropriate for understanding the onset of congestion. Numerical and analytical results reveal the existence of four well-defined regions in time-space, two of which are transient. The conditions for the existence of congestion both in the freeway and in the on-ramps are identified, as well as the set of on-ramps that are most likely to become active bottlenecks. The results in this paper help explain the stochastic nature of bottleneck activation, and can be applied to devise effective system-wide ramp metering strategies that would prevent excessively long on-ramp queues. [ABSTRACT FROM AUTHOR]

In this paper we explicitly construct the entropy solutions for the Lighthill-Whitham-Richards (LWR) traffic flow model with a flow-density relationship which is piecewise quadratic, concave, but not continuous at the junction points where two quadratic polynomials meet, and with piecewise linear initial condition and piecewise constant boundary conditions. The existence and uniqueness of entropy solutions for such conservation laws with discontinuous fluxes are not known mathematically. We have used the approach of explicitly constructing the entropy solutions to a sequence of approximate problems in which the flow-density relationship is continuous but tends to the discontinuous flux when a small parameter in this sequence tends to zero. The limit of the entropy solutions for this sequence is explicitly constructed and is considered to be the entropy solution associated with the discontinuous flux. We apply this entropy solution construction procedure to solve four representative traffic flow cases, compare them with numerical solutions obtained by a high order weighted essentially nonoscillatory (WENO) scheme, and discuss the results from traffic flow perspectives. [ABSTRACT FROM AUTHOR]

By introducing the concept of speed elasticity of flow and density, this paper provides a generic characterization for a class of well-behaved equilibrium speed-flow curves that are differentiable and backward bending and possess monotone speed-density curves. We start with a comprehensive review on classical models, including Greenberg, Greenshields, and Underwood. A major limitation of these models is that the specification is uniquely determined by three road-specific parameters: the free-flow speed, the capacity flow, and the corresponding speed at the capacity flow, which makes the empirical application difficult due to lack of flexibility. Through a careful review of Del Castillo and Benitez [Del Castillo, J. M., F. G. Benitez. 1995. On the functional form of the speed-density relationship -- I: General theory, II: Empirical investigation. Transportation Res. Part B 29 373-406], we have provided a new characterization for the Newell-Frankin model and made a connection between the family of rational generating functions and the Greenshields-type models. Based on three primitive regularity conditions, we derive a generic characterization for well-behaved macroscopic equilibrium speed- flow curves that integrate all classical models. Using the generic characterization, we show that the equilibrium speed-flow curves derived from the car-following models can be classified as a two-parameter extension of the Greenshields-type model. We have also made an attempt in proposing a plausible rectification to the speed-flow models from the Highway Capacity Manual 2000 so that they possess the backward-bending property. A formal linkage between the generic characterization of speed-flow curves and the theory of congestion pricing is also established. [ABSTRACT FROM AUTHOR]

This paper deals with sensitivity analysis of static traffic user equilibrium problems. We apply some recently developed sensitivity analysis techniques for generalized equations to analyze the behavior of the equilibrium arc flow of such a problem when both the arc cost function and the travel demand vary. Our methods permit calculation of semiderivatives under general conditions and of derivatives under more restrictive conditions; we calculate the semiderivatives by solving a linear traffic user equilibrium problem and the derivatives by matrix multiplication together with the solution of a linear equation the dimension of which is at most the number of arcs. Three numerical examples show how to use these results in practice. [ABSTRACT FROM AUTHOR]

This paper deals with the fixed-cycle traffic-light (FCTL) queue, where vehicles arrive at an intersection controlled by a traffic light and form a queue. The traffic light alternates between green and red periods, and delayed vehicles are assumed to depart during the green period at equal time intervals. The key performance characteristic in the FCTL queue is the so-called mean overflow, defined as the mean queue length at the end of a green period. An exact solution for the mean overflow is available, but it has been considered to be of little practical value because it requires some numerical procedures. Therefore, most of the literature on the FCTL queue is about deriving approximations for the mean overflow. In deriving these approximations, most authors first approximate the FCTL queue by a bulk-service queue, approximate the mean overflow in the bulk-service queue, and use this as an approximation for the mean overflow in the FCTL queue. So far no quantitative comparison of both models has been given. We compare both models and assess the quality of the approximation for various settings of the parameter values. In this comparison and throughout the paper we do not restrict ourselves to Poisson arrivals, but consider a more general arrival process instead. We discuss the numerical issues that need to be resolved to calculate the exact expression for the mean overflow in both queues and show that clear computational schemes are available. Next, we present several bounds and approximations of the mean overflow that do not require numerical procedures. In particular, we derive a new approximation based on the heavy traffic limit and a scaling argument. We compare the new bounds and approximation with the existing ones. We elaborate on the impact of several parameters, like the length of the green and red period and the variance of the arrival distribution. [ABSTRACT FROM AUTHOR]

Insertion heuristics have proven to be popular methods for solving a variety of vehicle routing and scheduling problems. In this paper, we focus on the impact of incorporating complicating constraints on the efficiency of insertion heuristics. The basic insertion heuristic for the standard vehicle routing problem has a time complexity of O(n³). However, straightforward implementations of handling complicating constraints lead to an undesirable time complexity of O(n4. We demonstrate that with careful implementation it is possible, in most cases, to maintain the O⊃3 complexity or, in a few cases, increase the time complexity to O(n⊃3 log n). The complicating constraints we consider in this paper are time windows, shift time limits, variable delivery quantities, fixed and variable delivery times, and multiple routes per vehicle. Little attention has been given to some of these complexities (with time windows being the notable exception), which are common in practice and have a significant impact on the feasibility of a schedule as well as the efficiency of insertion heuristics. [ABSTRACT FROM AUTHOR]

Many distribution centers use expensive, conveyor-based sorting systems that require large buildings to house them. In areas with tight space, robotic sorting systems offer a new type of solution to sort parcels by destination. Such systems are highly flexible in throughput capacity and are now gradually being introduced, particularly in express companies. This paper studies robotic sorting system with two layouts. The first layout has two tiers: robots drive on the top tier and sort parcels by destination on spiral conveyors connected to roll containers at the lower tier. The second layout has a single tier with input and output points located at the perimeter, connected by robots. For each layout, we consider both the shortest path topology via dual-lane aisles and the detour path topology via single-lane aisles. We build closed queueing networks for performance estimation, design an iterative procedure to investigate robot congestion in the two-tier layout, and use a traffic flow function to estimate robot congestion in the single-tier layout. Random, closest, dedicated, and shortest-queue robot-to-loading-station assignment rules are examined. We validate analytical models by both simulation and a real case of Deppon Express and analyze the optimal system size and operating policies for throughput capacity and operating cost. The results show that the system throughput capacity is significantly affected by robot congestion in the single-tier layout with the detour path topology, but it is only slightly affected in the other systems. A square layout fits the shortest path and a rectangular layout fits the detour path. Both the random assignment rule and the shortest-queue assignment rule are superior for a large number of robots, whereas the dedicated assignment rule is superior for a small number of robots. We apply these insights at Deppon Express for different allocations in peak and off-peak hours. Our analysis shows that a robotic sorting system typically has lower overall annual cost than a traditional cross-belt sorting system when the required throughput capacity is not too large. [ABSTRACT FROM AUTHOR]

The queueing-theoretical model for stationary traffic flow developed in a former paper is extended and modified for nonstationary flow. In particular it is shown how speed-flow-density relationships under nonstationary conditions may deviate from those obtained for stationary conditions.It is shown how the wide scatter which is often observed with empirical speed-flow-density data can be explained by nonstationarity. Furthermore, hysteresis loops,which may show up in speed-flow-density relationships, are interpreted by means of nonstationarity. [ABSTRACT FROM AUTHOR]

Over recent years, increasing attention has been devoted to the problem of estimating Origin/Destination (O/D) matrices by using traffic counts, named in the following O/D Count Based Estimation (ODCBE) problem. These methods combine traffic flow measures with other available information to "correct" and improve an initial estimate of the O/D trip matrix. Virtually all models and procedures proposed in the literature are formulated as mathematical programming problems. Most ODCBE models use a relationship relating traffic counts to the unknown O/D matrix; this relationship is often in the form of an explicit estimate of the assignment matrix, i.e., of the fractions of O/D flows using each link of the network for which traffic counts are available. The computation of the assignment matrix is not trivial for congested networks, where travel costs and path choice fractions depend on flows. This problem has been dealt with in relatively few papers in the literature, usually formulated as a bilevel optimisation model under the assumption of a Deterministic User Equilibrium (DUE) assignment model. In this paper, the general within-day static ODCBE problem for congested networks is formulated as a fixed-point problem of an implicit function which results from the solution of a mathematical programming problem. In other words, the solution of the ODCBE problem is an O/D matrix that, once assigned to the network, reproduces flows and costs consistent with the values used to compute the assignment matrix. Fixed-point theorems and algorithms have been extended to the problem at hand. Different fixed-point algorithms, namely, Functional Iteration, Method of Successive Averages, and Method of Successive Averages with Decreasing Reinitialisation are proposed, and their performances are compared on a small test network. It has been verified that all algorithms converge to the same solution, though with different speeds. Furthermore, the fixed-point solution outperforms the... [ABSTRACT FROM AUTHOR]

Collaborative decision making (CDM) is a joint Federal Aviation Administration (FAA)/ industry initiative aimed at improving traffic flow management when inclement weather reduces an airport's arrival capacity. CDM replaces the present Ground Delay Program and is expected to be fully implemented by or around the year 2000. Under CDM, during periods of undersupply, the FAA's role shifts from centralized decision-maker to information gatherer and resource arbiter. Filling the decision-making void are the airlines, now given the freedom to make rescheduling decisions according to their own priorities and objectives. In this paper, we present an integer model and a real-time solution algorithm that assist an airline in making these rescheduling decisions at its hub airport, the location with the largest number of operations and therefore the greatest opportunity for improvement. Our research improves the existing state-of-the-art by representing the real world more thoroughly and intuitively than existing models (a modeling contribution) and by exploiting the structure of our model to achieve optimal solutions to large-scale scenarios in real time (an algorithmic contribution). Furthermore, we present four different formulations of the model. Although the different formulations are equivalent in that they have identical integer feasible solution sets and optimal objective function values, they exhibit widely-varying optimization times when tested on large-scale scenarios, allowing us to compare the characteristics and desirability of the alternative formulation techniques. [ABSTRACT FROM AUTHOR]

Urban travel times are rather variable as a result of a lot of stochastic factors both in traffic flows, signals, and other conditions on the infrastructure. However, the most common way both in literature and practice is to estimate or predict only expected travel times, not travel time distributions. By doing so, it fails to provide full insight into the travel time dynamics and variability on urban roads. Another limitation of this common approach is that the effect of traffic measures on travel time reliability cannot be evaluated. In this paper, an analytical travel time distribution model is presented especially for urban roads with fixed-time controlled intersections by investigating the underlying mechanisms of urban travel times. Different from mean travel time models or deterministic travel time models, the proposed model takes stochastic properties of traffic flow, stochastic arrivals and departures at intersections, and traffic signal coordination between adjacent intersections into account, and therefore, is able to capture the delay dynamics and uncertainty at intersections. The queue spillback phenomenon is explicitly taken into account by applying shockwave theory in a probabilistic way. The proposed model was further validated with both VISSIM simulation data and field GPS data collected in a Chinese city. The results demonstrate that the travel time distributions derived from the analytical model can well represent those from VISSIM simulation. The comparison with field GPS data shows that the model estimated link and trip travel time distributions can also represent the field travel time distributions, though a small discrepancy can be observed in both middle range travel times and higher travel times. [ABSTRACT FROM AUTHOR]

This paper proposes an improved cellular automaton traffic flow model based on the brake light model, taking into account that the desired time gap of vehicles is larger than one second. Although the hypothetical steady state of vehicles in the deterministic limit corresponds to a unique relationship between speeds and gaps in the proposed model, the traffic states of vehicles dynamically span a two-dimensional region in the plane of speed versus gap, due to the various randomizations. We show that our model reproduces (i) the free flow, synchronized flow, wide moving jams, as well as transitions among the three phases; (ii) the evolution features of disturbances and the spatiotemporal patterns in a car-following platoon; (iii) the empirical time series of traffic speed obtained from Next Generation Simulation data. Furthermore, the basic feature of time headway distribution is also qualitatively reproduced. Therefore, we argue that a model has the potential to reproduce the empirical and experimental features of traffic flow, provided that the traffic states can dynamically span a 2D speed-gap region. [ABSTRACT FROM AUTHOR]

This paper presents the development of a macroscopic dynamic traffic assignment model for continuum transportation systems with elastic demand. A reactive dynamic user equilibrium model is extended to simulate network equilibrium problems for an urban area with multiple central business districts (CBDs). Each copy of traffic flow reactively makes route choice decisions to minimize the total travel cost from origin to destination, based on instantaneous traffic information from a radio broadcasting service or route guidance system. The elastic demand function for each copy of flow is associated with its total instantaneous travel cost. The model is solved by a cell-centered finite volume method for conservation law equations and a fast sweeping method for Eikonal-type equations on unstructured grids. Numerical experiments for an urban traffic network with two CBDs are presented to verify the rationality of the model and the validity of the numerical method. The numerical results indicate that the model captures some macroscopic characteristics of two copies of flow interacting in time-varying urban transportation systems, e.g., the spatial distributions of the flow density and flux and the path choice behavior in response to elastic demand, and can describe traffic equilibrium phenomena, such as self-organization and traffic congestion build-up and dissipation. [ABSTRACT FROM AUTHOR]

In the future, road traffic will incorporate a random mix of manual vehicles and cooperative adaptive cruise control (CACC) vehicles, where a CACC vehicle will degrade to an adaptive cruise control (ACC) vehicle when vehicle-to-vehicle communications are not available. This paper proposes a generalized framework of the Lighthill-Whitham-Richards (LWR) model for such mixed vehicular flow under different CACC penetration rates. In this approach, the kinematic wave speed propagating through the mixed platoon was theoretically proven to be the slope of mixed fundamental diagram. In addition, the random degradation from CACC to ACC was captured in mathematical expectation for traffic scenarios where the CACC only monitors one vehicle ahead. Three concrete car-following models, the intelligent driver model (IDM) and CACC/ACC models validated by Partners for Advanced Transit and Highways (PATH) program, were selected as examples to investigate the propagation of small perturbations and shock waves. Numerical simulations were also performed based on the selected car-following models. Moreover, the derived mixed LWR model was applied to solve some traffic flow problems. It indicates that the proposed LWR model is able to describe the propagation properties of both small perturbations and shock waves. The mixed LWR model can also be used to solve some practical problems, such as the queue caused by a traffic accident and the impact of a moving bottleneck. More importantly, the proposed generalized framework admits other CACC/ACC/regular car-following models, including those developed from further experiments. [ABSTRACT FROM AUTHOR]

In the realm of traffic assignment over a network involving rigid arc capacities, the aim of the present work is to generalize the model of Marcotte, Nguyen, and Schoeb [Marcotte P, Nguyen S, Schoeb A (2004) A strategic flow model of traffic assignment in static capacitated networks. Oper. Res. 52(2):191–212.] by casting it within a stochastic user equilibrium framework. The strength of the proposed model is to incorporate two sources of stochasticity stemming, respectively, from the users' imperfect knowledge regarding arc costs (represented by a discrete choice model) and the probability of not accessing saturated arcs. Moreover, the arc-based formulation extends the Markovian traffic equilibrium model of Baillon and Cominetti [Baillon JB, Cominetti R (2008) Markovian traffic equilibrium. Math. Programming 111(1-2):33–56.] through the explicit consideration of capacities. This paper is restricted to the case of acyclic networks, for which we present solution algorithms and numerical experiments. [ABSTRACT FROM AUTHOR]

On two-lane two-way roads overtaking opportunities are limited by the opposing traffic. For fixed volumes of traffic in both directions the opportunities for vehicles in one lane to overtake depend on the mean length of queues in the second lane, so that the mean queue length in the first lane is a function of the mean queue length in the second lane and vice versa. This paper takes an earlier procedure for determining the mean queue lengths in the two lanes at equilibrium and simplifies it by assuming that the distribution of queue lengths is known. The results obtained by assuming that the underlying distribution is Miller, Borel-Tanner, or geometric are then compared by a numerical evaluation. [ABSTRACT FROM AUTHOR]

Forecasting traffic over a long period of time is of considerable interest and usefulness, but accurate forecasting is very difficult. Traditional projection and factoring methods for mid- and long-term cumulative traffic forecasting are deterministic and only provide a point prediction without specifying a statistical measure of prediction reliability. This paper constructs a stochastic projection and factoring method by casting long-term traffic volume counts into an integrated and rigorous framework of a more refined structural time series component model with piecewise stationary renewal processes capturing time-of-day, day-of-week, monthly, and yearly variations. By doing so, the new method roots itself in a solid theoretical foundation and generates two advantages. First, it results in a more accurate point prediction of cumulative traffic by taking into account the time-of-day traffic count variation in the modeling of unobservable future long-term traffic flow at temporary count stations or at a site under investigation as a mixture of piecewise stationary renewal processes with different means and variances. Second, it allows an interval prediction to be estimated by incorporating uncertainty into the modeling and forecasting process. [ABSTRACT FROM AUTHOR]

In this paper, we evaluate the performance of a dynamic approach to classifying flow patterns reconstructed by a switching-mode macroscopic flow model considering a multivariate clustering method. To remove noise and tolerate a wide scatter of traffic data, filters are applied before the overall modeling process. Filtered data are dynamically and simultaneously input to the density estimation and traffic flow modeling processes. A modified cell transmission model simulates traffic flow to explicitly account for flow condition transitions considering wave propagations throughout a freeway test stretch. We use flow dynamics specific to each of the cells to determine the mode of prevailing traffic conditions. Flow dynamics are then reconstructed by neural methods. By using two methods in part, i.e., dynamic classification and nonhierarchical clustering, classification of flow patterns over the fundamental diagram is obtained by considering traffic density as a pattern indicator. The fundamental diagram of speed-flow is dynamically updated to specify the current corresponding flow pattern. The dynamic classification approach returned promising results in capturing sudden changes on test stretch flow patterns as well as performance compared to multivariate clustering. The dynamic methods applied here are open to use in practice within intelligent management strategies, including incident detection and control and variable speed management. [ABSTRACT FROM AUTHOR]

For a predetermined set of an upper bound of link flows, this paper proposes a price-based congestion control scheme for achieving such a restraint target of traffic flow that evolves from day to day. On each day, drivers have to pay a toll selected from a feasible set. The tolls on each day are determined by the link flows and toll charges on the previous day and the predetermined upper bound of link flows. Several properties of the dynamical system model with the control scheme are analyzed, including the invariance of its evolutionary trajectories; the equivalence between its stationary state and user equilibrium under toll charge; the uniqueness, existence, and boundedness of its stationary state; and the convergence of its evolutionary trajectories. A special case of the model and implementation of the control scheme for several alternative targets are also given. Finally, application of the model to a traffic network is demonstrated with a numerical example. The study is helpful for better understanding the mechanism of congestion control under day-to-day traffic flow dynamics. [ABSTRACT FROM AUTHOR]

Vehicles on roads can be distinguished, each defined by its own set of properties (e.g., fleet length and free-flow speed). The traffic states on roads can be attributed to the longitudinal heterogeneity in vehicles. Vehicles slower than prevailing vehicles are defined as moving bottlenecks. On a multilane road section with multiple vehicle types, slower vehicles create moving bottlenecks and induce overtaking by faster vehicles so as to maintain their higher desired speed. The influence of single-class moving bottlenecks has been studied in the past. However, the impacts of multiple classes of moving bottlenecks have not yet been fully explored. This paper categorizes vehicles into passenger cars, medium trucks, and heavy trucks. By defining medium trucks and heavy trucks as moving bottlenecks, we develop analytical formulas for the fundamental diagram on a multilane road section with heterogeneous moving bottlenecks. The formula confirms that the composition of traffic and the longest truck platoon length influence the fundamental diagram. We then conduct simulations using a first-order kinematic wave model in Lagrangian coordinates to validate the fundamental diagram developed with the analytical formula and obtain promising results. This study provides fundamental knowledge for multiclass traffic modeling and multilane traffic operations. [ABSTRACT FROM AUTHOR]

Private enterprises and governments around the world use speed cameras to control traffic flow and limit speed excess. Cameras may be exposed to difficult weather conditions and typically require frequent maintenance. When deciding the order in which maintenance should be performed, one has to consider both the traveling times between the cameras and the traffic flow that each camera is supposed to monitor. In this paper, we study the problem of routing a set of technicians to repair cameras by minimizing the total weighted latency, that is, the sum of the weighted waiting times of each camera, where the weight is a parameter proportional to the monitored traffic. The resulting problem, called the weighted k-traveling repairman problem (wkTRP), is a generalization of the well-known traveling repairman problem and can be used to model a variety of real-world applications. To solve the wkTRP, we propose an iterated local search heuristic and an exact branch-and-cut algorithm enriched with valid inequalities. The effectiveness of the two methods is proved by extensive computational experiments performed both on instances derived from a real-world case study and on benchmark instances from the literature on the wkTRP and on related problems. [ABSTRACT FROM AUTHOR]

Efficient and exact algorithms are important for performing fast and accurate traffic network simulations with macroscopic traffic models. In this paper, we extend the semianalytical Lax–Hopf algorithm in order to compute link inflows and outflows with the Lighthill–Whitham–Richards (LWR) model. Our proposed fast Lax–Hopf algorithm has a very low computational complexity. We demonstrate that some of the original algorithm's operations (associated with the initial conditions) can be discarded, leading to a faster computation of boundary demands/supplies in network simulation problems for general concave fundamental diagrams (FDs). Moreover, the computational cost can be further reduced for triangular FDs and specific space–time discretizations. The resulting formulation has a performance comparable to the link transmission model and because it solves the original LWR model for a wide range of FD shapes, with any initial configuration, it is suitable to solve a broad range of traffic operations problems. As part of the analysis, we compare the performance of the proposed scheme with that of other well-known computational methods. [ABSTRACT FROM AUTHOR]

There has been extensive research on the optimal design of road congestion pricing schemes based on traffic network equilibrium models. Since travel demands are closely related to the locations of workplace and residence, it is of both theoretical and practical importance to extend the optimization approach to treat location choices as well as travel route choices. This paper addresses the problem of optimal location of housing supply and transportation network pricing in an integrated location and transportation model with heterogeneous households that have different values of travel time. In the model, housing exhibits external economies and diseconomies of scale, depending on the population density in residential zones. It is shown that in such a model the marginal cost pricing principle applied to internalize these externalities in general results in local optima of social surplus. Optimization algorithms based on sensitivity analysis are proposed to find combinations of housing supply patterns and road tolls that optimize social surplus under various conditions. A numerical example is given to illustrate the proposed method. The potential policy implications of the optimization approach are examined and compared with that of the marginal cost pricing principle. [ABSTRACT FROM AUTHOR]

Diverging junctions are important network bottlenecks, and a better understanding of diverging traffic dynamics has both theoretical and practical implications. In this paper, we present a new framework for constructing kinematic wave solutions to the Riemann problem of kinematic wave models of diverging traffic with jump initial conditions. Within this framework, the function space of weak solutions is enlarged to include interior states that occur with stationary discontinuities, and various discrete flux functions in cell transmission models of diverging traffic are used as entropy conditions to pick out unique physical solutions. Then in demand-supply space, we prove that the Riemann problem can be uniquely solved for existing discrete flux functions, in the sense that stationary states and, therefore, shock or rarefaction waves on all links, can be uniquely determined under given initial conditions. We show that the two diverge models by Lebacque and Daganzo are asymptotically equivalent. We also prove that the supply proportional and priority-based diverge models are locally optimal evacuation strategies. With numerical examples, we demonstrate the validity of the analytical solutions of interior states, stationary states, and corresponding kinematic waves. This study presents a unified framework for analyzing traffic dynamics arising at diverging junctions and could be helpful for developing emergency evacuation strategies. [ABSTRACT FROM AUTHOR]

In traffic systems where driving is on the left, right-turning movements tend to be difficult to efficiently accommodate at signal controlled junctions. A hook turn is one potential solution for this. A hook turn is where a right turn is made from the nearside lane rather than an offside lane at a four-leg signalised junction. After entering the junction, the turning vehicle waits at a nearside position in front of the side road stop line, and then proceeds toward the exit arm when the side road signal turns green. The research described in this paper uses microscopic simulation modelling in an innovative way to compare the traffic performance of a hypothetical hook-turn junction with an equivalent conventional junction with opposed right turns. The simulation model evaluated traffic performance under various combinations of demand flow, turning proportions, and signal timings. It was found that hook turns reduced delays to through traffic from the same approach in nearly all cases. Overall junction performance depended on the scale of any increased delays to left-turning traffic and side road traffic resulting from the hook-turn movement. It is concluded that hook turns could be used much more widely than at present--including where driving is on the right--offering significant operational benefits in the right circumstances. [ABSTRACT FROM AUTHOR]

In the future world of self-driving vehicles, intersections will be managed by computers that send individual commands to each passing vehicle. This paper proposes to make traffic priority contingent on the self-reported value of time of vehicle occupants. A model of two merging roads with stochastic traffic is developed. Algorithms for calculation of optimal exit sequences, accounting for time value heterogeneity, are characterized. Welfare costs of a limited planning horizon are assessed. An incentive-compatible scheme of payment for priority is calculated. Under mild conditions, the mechanism is Pareto improving, that is, benefits all parties. The optimality of the traffic volume and composition under the optimal exit regulation is established. [ABSTRACT FROM AUTHOR]

Unmanned aircraft systems (UASs) are a promising new mode of transportation for cargo delivery. Although control, navigation, and communication technologies are becoming available on individual flight units, system-level motion management for dense UAS traffic remains an open question. This paper presents a motion-planning model based on nonlinear optimization techniques to centrally coordinate paths for all vehicles traversing a shared two-dimensional (2D) space. An exact bound is derived to characterize the discrete-time separation constraints, and a set of new metrics is proposed to measure 2D traffic flow efficiency. The grand goal is to make all vehicles that come under dispatch reach their respective destinations quickly and efficiently while maintaining a safe intervehicle separation at all times. This infinite-horizon operational problem is formulated as a nonlinear nonconvex optimization model that must be solved in a progressive, receding-horizon fashion. To ensure feasibility and overcome path deadlocks attributed to local optima, a series of heuristic measures are developed. By pivoting on artfully coined intermediate feasibility, the algorithm is able to circumvent imminent deadlocks in a predictive manner and progressively construct the solution with guaranteed feasibility. Simulation experiments are performed at various traffic density levels to generate useful insights for airspace regulators and traffic managers. [ABSTRACT FROM AUTHOR]

In this paper, we develop models for adjusting or setting fares on a transit system to encourage passengers to choose travel strategies that lead to the least travel delay for the entire system. In our problem setting, these fares vary with time of day. Similar to the one used to reduce congestion on vehicular traffic networks, our goal is to adjust or set fares so that a user equilibrium solution under the new fares yields the least delay or is system optimal. On the other hand, pricing frameworks for traffic networks such as marginal cost pricing do not readily apply because the travel delay in transit systems involves factors different from those in vehicular traffic and cannot be expressed in closed functional forms. The models herein are schedule based and account for loading priorities and individual vehicle capacities explicitly. Differences among the proposed models are illustrated with a small network. [ABSTRACT FROM AUTHOR]

Recently, Aw and Rascle and Zhang introduced a new second-order macroscopic model, following the theoretical investigations on the Payne-Whitham second-order modelling by Daganzo. The conserved variables in this model are the density and the relative flow. The aim of this paper is to solve the Riemann problem for the Aw-Rascle-Zhang (ARZ) model for all possible initial conditions, using an extended fundamental diagram. The resolution of the Riemann problem provides the user of the model with a set of nontrivial analytical solutions; it is also a prerequisite for the construction of numerical solution schemes. Some examples are given in which analytical solutions of the Riemann problem are discussed and compared to numerical solutions. The ARZ model shows better fit to real data than the embedded Lighthill-Whitham-Richards (LWR) model for the same set of physical parameters. [ABSTRACT FROM AUTHOR]

We study in this paper some consequences of queue spillback in a simple road network with a steady demand and provide exact formulas for traffic flow patterns. This one origin-destination pair, two-route network contains a diverge and a merge, and the interaction of queues formed at the merge produces several interesting traffic flow patterns, of which two types of oscillatory solutions are of particular interest. One of the oscillatory solutions is decaying, and the other is perfectly periodic. The latter resembles the stop-and-go pattern found in real-world traffic. Because a general road network usually contains many components like the simple network studied here, interaction of queues at junctions provides an alternative explanation to the formation of stop-and-go traffic. [ABSTRACT FROM AUTHOR]