This paper seeks traffic signal control policies which maximise long-run network throughput when demand is within network capacity and also when demand is beyond network capacity. The paper considers smooth versions of two well-known responsive traffic signal control policies: the P0 policy (see Smith, 1979b, 1980 or Smith et al., 2015) and the maxpressure or MP policy (see Varaiya, 2013a). The paper gives two simple example networks where both of these smooth responsive traffic control policies give rise to decreasing throughput for increasing demands; when these demands are beyond the network capacity. The paper then suggests a simple modification of the two responsive traffic control policies and shows that the two modified policies do maximise the long run throughput of the two signal-controlled networks; both when a steady input demand D is within network capacity and also when a steady demand exceeds network capacity. The modified version of P0 is as follows: for a certain positive number K, forD⩽Kuse responsive policyP0,and forD>Kuse the green-times generated byP0whenD=K. Thus in this modification the green-time proportions generated by responsive P0 are frozen as demand passes through K; and remain fixed for all demands D which exceed K. The paper shows that the above modification when applied to a continuous version of MP also maximises throughput in both networks for all values of the steady demand D. Finally the paper considers a signal controlled network with route choice. It is shown that if routes are chosen by travellers in their own best interests then the continuous version of MP does not always maximise throughput, even if the constant input demand D is within the network capacity, but P0 does always maximise throughput, even when the constant input demand D is beyond the network capacity.@en

Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport (PT), are increasingly becoming key objectives for policymakers worldwide. In this work we develop an optimal vehicle scheduling approach for next generation PT systems, considering the instance of mixed electric / hybrid fleet. Our objective is that of investigating to what extent electrification, coupled with optimal fleet management, can yield operational cost savings for PT operators. We propose a Mixed Integer Linear Program (MILP) to address the problem of optimal scheduling of a mixed fleet of electric and hybrid / non-electric buses, coupled with an ad-hoc decomposition scheme aimed at enhancing the scalability of the proposed MILP. Two case studies arising from the PT network of the city of Luxembourg are employed in order to validate the model; sensitivity analysis to fleet design parameters is performed, specifically in terms of fleet size and fleet composition. Conclusions point to the fact that careful modelling and handling of mixed-fleet conditions are necessary to achieve operational savings, and that marginal savings gradually reduce as more conventional buses are replaced by their electric counterparts. We believe the methodology proposed may be a key part of advanced decision support systems for policymakers and operators that are dealing with the on-going transition from conventional bus fleets towards greener transport solutions.@en

Traffic control performance on networks depends on the flow response to the policy adopted, which in turn contributes to determine the optimal signal settings. This paper focuses on the relationship between local and network wide traffic control policies within the combined traffic control and assignment problem. Through a full exploration of the solution space, an in depth cross comparison is performed between the well-known local policies P0 and Equisaturation, versus the global policies Maximum Throughput and Minimum Delay, to verify how the two local policies approximate the optimal settings for signalized intersections. Realistic traffic dynamics, such as congestion, multiple controllers and spillback are considered, to empirically determine the conditions under which the local policies are able to approximate global performances. After presenting the different local and global control policies, experiments are performed on simple toy networks. The complexity of the underlying network and, therefore, of the problems' boundary conditions is then increased, allowing us to showcase how the different metrics perform in different situations. Finally, conclusions on the results are drawn.@en

Reducing pollutant emissions and promoting sustainable mobility solutions, including Public Transport, are increasingly becoming key objectives for policymakers worldwide. In order to jointly achieve these goals, careful consideration should be put on the operational cost and management of PT services, in order to promote the adoption of green mobility solutions and advanced management techniques by operators. In this work we develop a dynamic fleet management approach for next generation Public Transportation systems, considering the instance of mixed electric / hybrid fleet. Our objective is that of investigating to what extent electrification, coupled with optimal fleet management, can yield operational cost savings for PT operators, explicitly considering real-Time disturbances, including delays, service disruptions etc. We propose a Mixed Integer Linear Program to address the problem of optimal scheduling of a mixed fleet of electric and hybrid / non-electric buses, and employ it as predictor in a Model Predictive Control approach. Test results based upon a real-life scenario showcase how the proposed approach is indeed capable of yielding a sizable reduction in operational costs, even when considerable disturbances arise from the underlying system.@en

To use efficiently the infrastructure of transportation networks, control strategies have been developed with the aim to reduce negative externalities, such as congestion and pollutant emissions. Previous works demonstrated that the maximum performance achievable by traffic control policies depends on the number and location of controllers employed, which implies the need to determine a set of controllers capable of fully controlling the underlying transportation network. Various approaches have been explored in the literature to locate controllers on networks, however a gap remains in terms of scalability as the methods proposed often exhibit heavy computational complexity. In this paper we aim to propose an approach capable of locating pricing controllers on transportation networks that is scalable, such that it can be applied on large instances, such as city-sized or regional networks. For this purpose, we propose a topology-based approach, adapted from the sensor location problem, as both problems share similar characteristics. We validate our proposed approach by analyzing the performance of controller sets produced on a wide range of artificially generated network ensembles. The analysis we provide reveals that the method proposed, while being easily applicable on large instances, is capable to locate an efficient controller set, and to redirect flows on the network so as to reduce the total time spent by road users.@en

Holding has been extensively used as control strategy to regulate public transport operations, especially to maintain even headways and prevent buses of the same line to bunch up. Applying holding to multiple lines requires however to deal with the transition between corridor and branching segments. In this study, we introduce a holding criterion for network configurations with lines that operate jointly along a common corridor and then diverge to individual branches serving different urban areas. The proposed holding decision rule accounts for all different passenger groups in the overlapping segment and considers the transition to individual line operation. The holding rule is evaluated using simulation for different demand levels and compositions and is compared with state-of-the-art control schemes for a real-world network. Results show that the proposed multi-line control yields performance improvements along the shared transit corridor as well as at the line level. The performance of the control scheme is affected by the demand composition and we provide indications regarding the conditions under which multi-line control is advisable.@en

In this work we extend our previously proposed cascading Kalman filtering technique, applied to the problem of urban network flow estimation, to adopt heterogeneous traf- fic data sources. Both static infrastructure detection (double induction loops) and Floating Car Data are collected from a given transportation network, and employed within separate stages of the cascading technique. The proposed approach relies upon notions of traffic flow inference (observability) to both i) determine the optimal set of locations in which sensors should be installed and ii) provide enhanced covariance information within the estimation technique. The impact of both penetration rates of Floating Car Data and sensor selection procedure is evaluated empirically, through a microscopic simulation software (SUMO) generating experimental data on a simple grid-like network. Test results showcase that the proposed extension to the cascading framework is indeed beneficial in reducing the overall estimation error on network segments where static infrastructure is unavailable. Furthermore, the importance of observability- based sensor locations is clearly demonstrated.@en

In transit corridors, multiple lines share a sequence of consecutive stops to provide higher joint frequency in higher demand areas. A key challenge is to coordinate the transition from single line to joint operation. A holding control strategy aimed at minimizing passenger travel times is introduced for lines merging into a shared corridor, accounting for the coordination of vehicle arrivals from the merging lines as well as the regularity of each line. The criterion is tested using an artificial network and a real-world network to analyze the impact of demand distribution and compare cooperative versus single line control. We illustrate how the real-time strategy yields overall passenger gains, depending on the composition of different user groups. Results are assessed based on operation and passenger performance indicators and show that coordination is achieved. When combined with joint control in the common part, the proposed approach achieves consistent network-wide travel time benefits.@en

In this work we develop a kalman filtering approach for the problem of traffic state estimation in urban networks. The proposed approach employs concepts developed in the field of traffic flow observability, to derive both i) a minimal set of locations wherein traffic sensing infrastructure the network should be equipped and ii) topological relationships to be employed in the filtering technique's error covariance matrices, to improve the estimation process. A Linear Time-Variant formulation of first-order traffic flow theory is employed to model node-node vehicle propagation, allowing to predict the evolution of Cumulative Vehicle Numbers at intersections. This model is then embedded in the proposed cascading Kalman Filter framework. Validation of the proposed filtering approach is performed on a simple grid-like network, bearing considerable congestion, spillback and rerouting behaviour. We generate experimental data through a microscopic simulation software (SUMO).Test results showcase how the proposed approach successfully exploits observability-based information to reconstruct data in unmeasured segments of the network. Particular care should however be devoted to appropriate inference of turning fractions at intersections, in order to achieve the lowest possible estimation error.@en

We consider the problem of optimally determining the sequence of electric and hybrid buses departing from a multi-line bus terminal, considering both service constraints (schedule adherence) and energy constraints (electric bus charging status, bus recharging scheduling in capacitated facilities). The problem is formulated as a Mixed Integer Linear Program, with the objective of minimizing the total operational cost for the bus lines in question. System dynamics are captured by practical sets of constraints, ranging from scheduling adherence to discharge-recharge dynamics. Individual operational costs at the bus level and at the trip level are fully parametrized, allowing for extensive sensitivity analysis. We investigate a real-life case study based on the city of Luxembourg, where two charging stations have been installed in the central station's bus terminal. Experimental results show that, while full electrification is indeed possible, the required fleet size depends strongly on the given line(s) timetable.@en

Explicitly including the dynamics of users’ route choice behaviour in optimal traffic control applications has been of interest for researchers in the last five decades. This has been recognized as a very challenging problem, due to the added layer of complexity and the considerable non-convexity of the resulting problem, even when dealing with simple static assignment and analytical link cost functions. In this work we establish a direct behavioural connection between the different shapes and structures emerging in the solution space of such problems and the underlying route choice behaviour. We specifically investigate how changes in the active equilibrium route set exert direct influence on the solution space's structure and behaviour. Based on this result, we then formulate and validate a constrained version of the original problem, yielding desirable properties in terms of solution space regularity.@en

Explicitly including the dynamics of users' route choice behaviour in optimal traffic control applications has been of interest for researchers in the last five decades. This has been recognized as a very challenging problem, due to the added layer of complexity and the considerable non-convexity of the resulting problem, even when dealing with simple static assignment and analytical link cost functions. In this work we establish a direct behavioural connection between the different shapes and structures emerging in the solution space of such problems and the underlying route choice behaviour. We specifically investigate how changes in the active equilibrium route set exert direct influence on the solution space's structure and behaviour. Based on this result, we then formulate and validate a constrained version of the original problem, yielding desirable properties in terms of solution space regularity.@en

Public transport services are currently executing or planning a fundamental transition from traditional buses to electric buses. During this transition phase, the public transport offering is fulfilled with a mixed fleet across multiple bus terminals, which poses operational challenges for optimal vehicle scheduling, a problem not yet addressed in literature. As researchers in Transport Engineering and Operational Research at the University of Luxembourg, in collaboration with the Roma Tre University, we support the Ministry of Transport of Luxembourg and Volvo buses by modelling and simulating this transition phase, to help them managing and solving such challenges. In this work we develop a mixed-integer linear programming (MILP) formulation of the problem and implement a time-based decomposition framework, through which we can optimize real-life daily instances. This method is tested on the main urban bus lines that connect Central Station, Luxembourg Airport and ten other major terminals within Luxembourg City, providing (near) optimal solutions that explicitly consider the energy constraints arising from electric bus operations, while establishing an advantageous trade-off between delaying trips, to implement quick-charging of electric buses, and performing the same trip with costlier traditional buses. The results show a consistent decrease of operational costs as the percentage of e-buses in the fleet increases.@en

Sensor positioning is a fundamental problem in transportation networks, as the location of sensors strongly determines how traffic flows are observable and hence manageable. This paper aims to develop a methodology to determine sensor locations on a network such that an optimal trade-off solution is found between the amount of sensors installed and the resilience of the sensor set. In particular, we propose exact and heuristic solutions for identifying the optimal route sets such that no other route would include any additional information for finding optimal full and partial observability solutions. This is an important contribution to sensor location problems, as route-based link flow inference problems have non-unique solutions, strongly depending on the used link-route information. The properties of the new methodology are analyzed and illustrated through different case studies, and the advantages of the algorithms are quantified both for full and for partial observability solutions. Due to the route sets found by our approach, we are able to find full observability solutions characterized by a small number of sensors, while yet being efficient also in terms of partial observability. We perform validation tests on both small and real-life sized network instances.@en

The maximum level of performance reachable by traffic control policies is directly affected by the locations and types of controllers employed in the network. We therefore investigate methods to identify locations and types of controllers that guarantee that the highest possible level of performance can be reached, fully exploiting the available network capacity, while minimizing the overall installation costs. This condition is known as full controllability. In this work, based on an existing methodological contribution that allows to determine the optimal number and locations of Pricing controllers required to reach the maximal level of controllability in transportation networks, we investigate instances and conditions in which the same results can be achieved through Traffic Light controllers, which represent a more realistic and widespread technology. Due to the different impact of traffic lights and pricing controllers on the network, however, optimal locations for one set might differ from the optimal locations for the other. Consequently, replacing pricing controllers by traffic lights is not a straightforward task. Moreover, an enumeration of every possible combination of traffic light positions will result in combinatorial explosion. In order to avoid this problematic, in this work we study simple, atomic subnetwork structures, widely occurring in real-life networks, and assess whether it is possible to maintain the maximum level of controllability while replacing pricing controllers with traffic light controllers. We validated our approach on a set of increasing sized networks showcasing that our proposed substitution rule yields satisfactory results in more than 90 percents of instances. This first empirical step acts as the basis to study larger and more realistic transportation networks, therefore helping to develop a general methodology to substitute pricing controllers with traffic lights.@en

Developing traffic control strategies taking explicitly into account the route choice behavior of users has been widely recognized as a very challenging problem. Furthermore, the inclusion of user behavior in optimization based control schemes introduces strong irregularities in the solution space shape, such as non-convexity and non-smoothness. In this work, we propose an extended decomposition scheme for the anticipatory traffic control problem, based upon our previous contributions, which aims at i) reducing the computational complexity of the problem by approaching it in a controller-by-controller fashion, and ii) internalizing specific constraints in the objective function, guiding the optimization process away from non-significant minima, such as flat regions. Through two small scale test networks and different, randomly chosen initial points, we compare how the proposed extension influences optimization results with respect to our previously developed decomposed approach, as well as centralized schemes.@en

Coordination and integration of different traffic control policies have been of considerable interest in research in the last decades and, recently, have been object of large scale implementation trials. In the setting of peri-urban motorway systems, coordination of various kinds of controllers must however be accompanied by accurate prediction of both propagation of flows and queues in the network, as well as the users’ response in terms of route choice. In this paper, we showcase through a real-life case study how coordination and prediction are both essential when performing hybrid urban-motorway control. Simulation results of a Model Predictive Control application are compared to simpler local control approaches, and the impact of coordinated intersection control and, additionally, Ramp Metering is evaluated.@en

To be used efficiently, transportation networks require control strategies to optimize flow distribution. However, the location and type of controllers employed in a transportation network directly impact the level of performance reachable by traffic control policies. In order to guarantee that the highest level of performance is reachable, fully exploiting the available network capacity and reducing negative externalities, we explore methods to identify relevant controller locations in transportation networks while minimizing the number of controllers used. Previous work provided an exact approach to identify controller locations on complex networks. However, said approach exhibits complications when applied to transportation networks containing bi-directional links. We therefore propose simple heuristic algorithms relying only on topological information to solve this problem, while also avoiding heavy computation, thus being able to determine a solution to the minimal controller location set problem on large networks. Based on the existing framework, we aim to provide an experimental setup, with diverse network sizes and configurations to analyze the performances of different heuristic methods, in order to develop an efficient algorithm.@en

Editoral@en

Traffic control policies aim at reducing the negative externalities that ever-growing demand is causing on transportation networks, such as congestion and pollutant emissions. To achieve these goals, strategies coordinating and aligning the effects of several individual traffic controllers have received increasing attention in research and development in the past decades. However, a considerable gap still exists between the desired and experienced performance of advanced dynamic traffic management systems, resulting in failure to completely prevent the increasing peak-hour congestion in main urban areas worldwide. In this work we contribute to assessing whether this gap might be tied to inefficient network design, rather than algorithmic prowess. Based upon our earlier work, we investigate whether a trend can be found between determining locations of controllers in a network following control theoretical insights, and try to confirm our earlier intuitions when dealing with dynamic traffic assignment, featuring accurate propagation and spillback dynamics. To achieve these goals, we extend an existing synthetic network generation tool to allow us to test this hypothesis on real-life-like road networks, and extend our previously developed algorithms for the controller location problems allowing for sufficient generalization. Test results are presented on a simpler deterministic scenario and on 240 randomly generated networks, showcasing that placing controllers following controllability-based principles is advantageous from the perspective of model-based dynamic traffic management applications.@en