Silvia Siri

Modelling and Optimal Receding-horizon Control of Maritime Container Terminals

The main objective of this paper consists in modelling, optimizing, and controlling container transfer operations inside intermodal terminals. More specifically, maritime container terminals are here considered, involving three kinds of transportation modes, i.e., maritime, rail, and road transport. Generally speaking, an intermodal port terminal can be seen as a system of container flows with two interfaces, towards the hinterland and towards the sea, respectively. Moreover, inside a terminal, unloading operations of inbound containers, container storage, and loading operations of outbound containers are carried out. A simple model for maritime container terminals is proposed in this paper. In the model, a system of queues represents the standing of containers and their movements inside the terminal. The dynamic evolutions of these queues are described by discrete-time equations, where the state variables represent the queue lengths and the control variables take into account the utilization of terminal resources such as load/unload handling rates. On the basis of the proposed model, an optimization problem is defined that consists in minimizing the transfer delays of containers in the terminal. The problem is stated as an optimal control problem whose solution is sought by adopting a receding-horizon strategy.

Modeling and solving the train load planning problem in seaport container terminals

In this paper we present two mathematical formulations and a heuristic approach for the train load planning problem of import containers at a seaport container terminal. The problem consists of determining how to assign a set of containers of different length and weight to the wagons of a train in order to satisfy capacity constraints of both the wagons and the train, while minimizing the rehandling operations in the stocking area where containers are waiting for being loaded on trains and maximizing the train utilization. Some computational results will be reported in the paper in which the heuristic approach is compared with the solution of the mathematical programming formulation.

An event-triggered Model Predictive Control scheme for freeway systems

Objective of this paper is to define an efficient control framework for freeway systems based on ramp metering. First of all, a Model Predictive Control (MPC) scheme is proposed in which the well known nonlinear cell transmission model (CTM) is used for the prediction. The model is then reformulated as a mixed logical dynamical (MLD) system, i.e. it is described by linear dynamic equations and linear inequalities in which both continuous and binary variables are present. In this way, the finite-horizon optimal control problem in the MPC scheme is transformed into a mixed integer quadratic programming problem whose objective function quadratically penalizes the deviation of the state variables from a specific equilibrium point. It is shown that the resulting control law stabilizes the system. Moreover, in order to make it more suitable for a real-time use, the foregoing control strategy is redesigned into an event-triggered control scheme. The idea is to update the control law only when the considered error exceeds a pre-specified threshold. Simulation results demonstrate how the use of the triggering rule allows to preserve the good performance of the proposed control scheme, while reducing the overall computational load.

Freeway networks as Systems of Systems: An event-triggered distributed control scheme

The objective of the present paper is the design of a control scheme for effectively managing congestion phenomena in freeways and interurban roadways. Such systems are typically made of several road stretches connected to compose a network and, of course, the dynamic behavior of traffic in each stretch influences the state of traffic in the overall network. In this sense a freeway network can be considered and analyzed as a “System of Systems”. A distributed Model Predictive Control Scheme in which clusters of freeway cells are separately regulated is proposed in the paper. Moreover, the definition of an event-triggered scheme is included in the paper as well: in the proposed scheme the control action is not computed at each time instant as in the classical Model Predictive Control framework, but only when the system state fulfils specific conditions,.

Freight transportation in railway networks with automated terminals: A mathematical model and MIP heuristic approaches

In this paper we propose a planning procedure for serving freight transportation requests in a railway network with fast transfer equipment at terminals. We consider a transportation system where different customers make their requests (orders) for moving boxes, i.e., either containers or swap bodies, between different origins and destinations, with specific requirements on delivery times. The decisions to be taken concern the route (and the corresponding sequence of trains) that each box follows in the network and the assignment of boxes to train wagons, taking into account that boxes can change more than one train and that train timetables are fixed. The planning procedure includes a pre-analysis step to determine all the possible sequences of trains for serving each order, followed by the solution of a 0-1 linear programming problem to find the optimal assignment of each box to a train sequence and to a specific wagon for each train in the sequence. This latter is a generalized assignment problem which is NP-hard. Hence, in order to find good solutions in acceptable computation times, two MIP heuristic approaches are proposed and tested through an experimental analysis considering realistic problem instances.

A control scheme for freeway traffic systems based on hybrid automata

In this paper a hybrid control scheme is devised in order to regulate traffic conditions in freeway systems. The considered control actions are ramp metering, i.e. using traffic lights at the on-ramps in order to regulate incoming traffic, and variable speed limits to be displayed on on-road variable message signs. The proposed scheme is composed of two levels: the lower level is characterized by different Model Predictive Control regulators, whereas at the higher level the different control actions are chosen according to a discrete-event dynamics. The overall scheme is then represented with the formalism of discrete-time discrete-event automata. More in detail, at the lower level, the prediction model used in the Model Predictive Control schemes is the first-order dynamical model of traffic flow in which we approximate the steady-state speed-density characteristic as a piecewise constant function. This approximation is motivated by the fact that we need a simpler finite-horizon problem to be solved on line, that in this case becomes a Mixed-Integer Linear programming problem. Depending on the system operating conditions, different regulators are determined by means of suitable Model Predictive Control schemes. The higher level of the control scheme has the function of identifying the present operating conditions and then switching to the suitable control action. The reported numerical results show the effectiveness of the proposed hybrid control framework.

An Event-Triggered Receding-Horizon Scheme for Planning Rail Operations in Maritime Terminals

This paper proposes a planning approach to optimize railway operations in seaport terminals by adopting a queue-based discrete-time model of the considered system. First, a mixed-integer linear mathematical programming problem is defined in order to optimize the timing of import trains and the use of the handling resources devoted to rail port operations. Second, in order to deal with unexpected situations or uncertainty in estimating some data necessary to the planning, an event-triggered receding-horizon planning approach is proposed, in which the finite horizon optimization problem is solved whenever a critical event happens or the real values of some problem data significantly differ from the predicted ones. Both these planning approaches are tested on data referred to a real terminal and deeply discussed in this paper.

Ramp metering control for two vehicle classes to reduce traffic emissions in freeway systems

In the paper a two-class ramp metering control strategy is proposed in order to minimize the traffic emissions in a freeway system. Two vehicle categories, i.e. cars and trucks, are explicitly represented in the dynamic model and separate control actions are devised for the two classes. The traffic emissions of vehicles are represented according to an average-speed model, assuming that the emission factor for a given pollutant depends only on the average speed during a trip. The considered control strategy is PI-ALINEA, suitably adapted to the two-class case, in which the occupancy set-point is set in order to reduce both the traffic emissions and the congestion level. The simulation tests have been realized in order to evaluate, for the one-class and for the two-class cases, how the total emissions and the total time spent by vehicles in the freeway system vary depending on the occupancy set-point, in different traffic scenarios.

Supervisory Model Predictive Control for freeway traffic systems

The application of Model Predictive Control schemes to real world complex plants, such as freeway traffic systems, is sometimes limited because of the necessity of tuning the control action depending on the system operating condition, and the significant computational burden inherent to the methodology. The MPC-based scheme presented in this paper aims at overcoming the mentioned limitations by using a supervisory control approach. The supervisor, at each time step, chooses among three possible actions: i) the controller needs to be changed and the new control action is computed, ii) no change is made to the controller, but it is necessary to recompute the control action, iii) neither is the controller varied, nor it is necessary to recompute the control action and the already determined control law is kept. In other terms, the control sequence is recomputed according to an event-triggered mechanism in which the control action is properly tuned to the system conditions. In the paper, the proposed control scheme is developed with reference to a class of non-linear systems admitting a model of Mixed Logical Dynamical type, which is suitable to describe freeway traffic systems, and the input-to-state practical stability of the controlled system is proved. Finally, the application of the proposed control scheme to a freeway traffic system is discussed and studied via simulation.

A New Emission Model Including On-ramps for Two-Class Freeway Traffic Control

The main objective of this paper is to propose a new two-class macroscopic emission model to describe the pollutant emissions produced by freeway traffic. The innovative aspect of the proposed model consists in considering the on-ramp emissions, which are explicitly modeled for different traffic scenarios. Next, a two-class local controller based on a ramp metering is reported with the aim of minimizing emissions and congestion in the freeway system. The relevance of the on-ramp emission model is in this way highlighted, since ramp metering may lead to creation of queues at the entering on-ramps and hence a concentration of pollutants on these on-ramps. Simulation results show the effectiveness of the proposed control strategy for a case of study.