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Advances in machine learning technology and the availability of big data from GPS systems have led to the development of effective methods for modelling transportation demand and forecasting the future. Most previous research concentrated on demand prediction using a variety of machine learning and deep learning models that took into account spatial and temporal relationships. This paper investigates the impact of spaces and time granularity for a Spatio-temporal demand modelling framework. Using taxi demand data from New York City, our study compares the prediction performance of deep learning models such as Long Short-Term Memory (LSTM), Convolution Neural Networks (CNN) and Temporal-Guided Networks (TGNet), modelled with a grid-based tessellation strategy. The findings of this study could assist researchers in better understanding how the granularity of space and time helps deep learning models perform better for demand forecasting problems.

To provide the optimal allocation of requests to the available fleet vehicles, routing algorithms typically assume the availability of complete and correct information about point-to-point travel times. Actually, in real applications non-recurrent events and traffic conditions make the estimation and the prediction of such travel times a difficult task, further complicated in real-time applications by the dynamicity of the information and the number of needed estimates. In this paper we present a complete methodology to achieve a computation of point-to-point travel times on a large network which proves to be both extremely fast and consistent with dynamically updated traffic information.

The usage of mobile phones is nowadays reaching full penetration rate in most countries. Smartphones are a valuable source for urban planners to understand and investigate passengers’ behavior and recognize travel patterns more precisely. Different investigations tried to automatically extract transit mode from sensors embedded in the phones such as GPS, accelerometer, and gyroscope. This allows to reduce the resources used in travel diary surveys, which are time-consuming and costly. However, figuring out which mode of transportation individuals use is still challenging. The main limitations include GPS, and mobile sensor data collection, and data labeling errors. First, this paper aims at solving a transport mode classification problem including (still, walking, car, bus, and metro) and then as a first investigation, presents a new algorithm to compute waiting time and access time to public transport stops based on a random forest model. Several public transport trips with different users were saved in Rome to test our access trip phase recognition algorithm. We also used Convolutional Neural Network as a deep learning algorithm to automatically extract features from one sensor (linear accelerometer), obtaining a model that performs well in predicting five modes of transport with the highest accuracy of 0.81%.

Trip patterns in terms of origin-to-destination (OD) traffic flows are a key input to traffic assignment models, namely to dynamic traffic assignment models. The trip patterns must also be dynamic – or at least time discretized – to properly approximate the time variability of the demand. However, OD matrices are not yet observable; in the best case, the measurements from Information and Communications Technologies (ICT) such as GPS vehicle tracking or mobile phone call detail records (CDR) can be used to collect samples that must then be used to infer or estimate the whole population. In order to perform this estimation, indirect processes that are usually based on mathematical models that take as input traffic counts are most commonly used. The problem of OD matrix estimation has been interesting for both researchers and practitioners for decades, (Van Zuylen and Willumsen, 1980). Furthermore, the aim of capturing the congestion effects of the changing OD flows during the OD estimation process conducted the research to an appealing mathematical formulation as a bi-level optimization problem. Moreover, in the recent years, the dynamic traffic assignments arise in order to capture the evolution of the traffic system according its dynamicity, leading to the dynamic OD matrix estimation problem. Peer Reviewed Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles::11.3 - Per a 2030, augmentar la urbanització inclusiva i sostenible, així com la capacitat de planificar i gestionar de manera participativa, integrada i sostenible els assentaments humans a tots els països Objectius de Desenvolupament Sostenible::11 - Ciutats i Comunitats Sostenibles

Modelling the within-day dynamic of passenger flows is crucial to optimize the service quality of public transport systems when supporting real-time operations and providing predictive information, as well as for off-line planning. Recurrent and non-recurrent congestion phenomena are increasingly affecting densely connected transit networks. In particular, the measures adopted to contain the spread of the COVID-19 pandemic affect significantly public transport capacity. Therefore, transit operators require a tool that can quickly forecast real- time capacity issues in the transit system to perform service recovery (e.g. introducing new runs) and to inform passengers about crowding at stops (e.g. through real-time information panels or trip planners). This research proposes an innovative congested run-based macroscopic dynamic assignment model, which simulates service degradation for passengers mingling at stops and strict capacity constraints. Fail-to-board probabilities are introduced at the diversion nodes of a diachronic hypergraph to represent service performances and passenger volumes on each run, in the framework of an implicit route enumeration model. This last aspect, jointly with the careful containment of the space- time network dimension, makes the model suitable for real-time applications in terms of computation time.

We present the Information Comply Model (ICM) which extends the framework for macroscopic within-day DTA proposed by Gentile (2016) to represent the rerouting of drivers wrt a single traffic event. Rerouting is reproduced as a two-stage process: first, drivers become aware about the event and its consequences on traffic; second, drivers may decide to change path. At each arc, unaware drivers have a probability of being informed by multiple ATIS sources (radio, VMS, mobile apps), which depends not only on devise penetration rates, but also on users space and time coordinates wrt the position and interval of the event. At each node, aware drivers, who are somehow reluctant to change, may finally modify their path based on a random rerouting utility, which is composed of expected gains and avoided losses. ICM is thus capable of representing the evolution of rerouting phenomena in time and space when the information about a traffic event and its consequences on congestion spread among drivers and onto the network. This way, ICM extends the concept of dynamic user equilibrium to a case of imperfect information related to availability and awareness rather than to individual perception, as well as to a case of bounded rationality with prudent drivers. Besides the model architecture and specification, this paper provides a workable methodology which can be applied both off-line for transport planning and in real-time for traffic management on large size networks.

Come gia fatto nel caso dei sistemi lineari (cfr. il §2.2), anche nel caso di sistemi non lineari puo essere istruttivo studiare in dettaglio i sistemi planari, per i quali e facile visualizzare le traiettorie e le curve di livello, trattandosi di curve nel piano. Inoltre la bassa dimensionalita dello spazio in cui si svolge il moto ha forti implicazioni topologiche sulle orbite (dovute in ultima analisi al fatto che le traiettorie non si possono intersecare). Questo porta a risultati notevoli, tra cui spicca il teorema di Poincare-Bendixson, ricco di importanti conseguenze, illustrate nel seguito del paragrafo.

Come promesso all’inizio del §1.1, ci occupiamo ora dello studio delle equazioni differenziali ordinarie lineari definite su uno spazio vettoriale \(E\). Vedremo in maggiore dettaglio nel capitolo 3, che un’equazione differenziale ordinaria e un’equazione che lega una funzione \(x(t)\), dove \(t\) e una variabile reale, fisicamente interpretabile come ‘‘tempo’’, alle sue derivate rispetto a \(t\). Vedremo anche che e sempre possibile ricondursi al caso in cui compaia solo la derivata prima; l’equazione si dice allora del primo ordine. Un’equazione differenziale ordinaria lineare omogenea e un’equazione della forma \(\dot{x}=Ax\), con \(x\in E\) e \(A\in L(E)\), dove \(\dot{x}\) indica la derivata di \(x\) rispetto alla variabile \(t\). Nel prossimo capitolo considereremo casi piu generali in cui le equazioni siano non lineari, i.e. siano della forma \(\dot{x}=f(x)\), con \(f\colon W\subseteq E\to E\); a differenza del caso generale, comunque, se il sistema e lineare, la soluzione esiste sempre ed e unica. Perche tale risultato valga anche nel caso \(\dot{x}=f(x)\), occorre imporre opportune condizioni di regolarita sulla funzione \(f\).

Nel capitolo precedente abbiamo studiato un caso particolare di sistemi di equazioni differenziali ordinarie: i sistemi lineari. Abbiamo visto che in tal caso esiste un’unica soluzione, sempre definita globalmente nel caso omogeneo. Vogliamo ora vedere cosa si puo dire per sistemi della forma \(\dot{x}=f(x)\), dove \(f(x)\) e una funzione continua.

International audience; The probabilistic forecasting method described in this study is devised to leverage spatial and temporal dependency of urban traffic networks, in order to provide predictions accurate at short term and meaningful for a horizon of up to several hours. By design, it can deal with missing data, both for training and running the model. It is able to forecast the state of the entire network in one pass, with an execution time that scales linearly with the size of the network. The method consists in learning a sparse Gaussian copula of traffic variables, compatible with the Gaussian belief propagation algorithm. The model is trained automatically from an historical dataset through an iterative proportional scaling procedure, that is well suited to compatibility constraints induced by Gaussian belief propagation. Results of tests performed on two urban datasets show a very good ability to predict flow variables and reasonably good performances on speed variables. Some understanding of the observed performances is given by a careful analysis of the model, making it to some degree possible to disentangle modeling bias from the intrinsic noise of the traffic phenomena and its measurement process.

Nel capitolo precedente ci siamo occupati dell’analisi qualitativa di sistemi meccanici conservativi unidimensionali. Una domanda legittima e se essa costituisca soltanto un utile esercizio matematico o se abbia invece rilevanza anche per problemi fisicamente piu realistici.

Quando si studia un sistema dinamico, in generale, non e possibile calcolare analiticamente la soluzione per ogni dato iniziale (cfr. i commenti a pag. 129). Tuttavia molte proprieta di un sistema dinamico possono essere studiate senza determinare, in maniera esplicita e dettagliata, l’insieme di tutte le traiettorie: si definisce analisi qualitativa lo studio di tali proprieta.

Nel capitolo precedente (cfr. il §9.7) abbiamo visto le formule che esprimono le leggi di variazione nel tempo della quantita di moto e del momento angolare di un corpo rigido. Se consideriamo un corpo rigido non soggetto ad altri vincoli che non siano quelli di rigidita, allora, come conseguenza del principio di d’Alembert, le equazioni del moto sono date dalle equazioni (9.43), dove \(\boldsymbol{f}\) e \(\boldsymbol{n}\) rappresentano, rispettivamente, la risultante delle forze attive agenti sul sistema e il risultante dei momenti di tale forze. In altre parole per il calcolo di \(\boldsymbol{f}\) e di \(\boldsymbol{n}\) possiamo ignorare le forze vincolari. Se al contrario il corpo rigido ha un punto fisso \(O\), occorre considerare in aggiunta la forza vincolare che si genera in \(O\), mentre il momento di tale forza rispetto al punto \(O\) e ovviamente nullo. Le corrispondenti equazioni del moto sono date dalle equazioni (9.53). Ci si riferisce a tale situazione talvolta, un po’ impropriamente, parlando di ‘‘corpo rigido libero con un punto fisso’’, dove ‘‘libero’’ indica l’assenza di forze esterne. Si noti che sia in assenza che in presenza di forze esterne la legge di variazione del momento angolare e la stessa.

We consider quasi-periodically systems in the presence of dissipation and study the existence of response solutions, i.e. quasi-periodic solutions with the same frequency vector as the forcing term. When the dissipation is large enough and a suitable function involving the forcing has a simple zero, response solutions are known to exist without assuming any non resonance condition on the frequency vector. We analyse the case of non-simple zeroes and, in order to deal with the small divisors problem, we confine ourselves to two-dimensional frequency vectors, so as to use the properties of continued fractions. We show that, if the order of the zero is odd (if it is even, in general no response solution exists), a response solution still exists provided the inverse of the parameter measuring the dissipation belongs to a set given by the union of infinite intervals depending on the convergents of the ratio of the two components of the frequency vector. The intervals may be disjoint and as a consequence we obtain the existence of response solutions in a set with "holes". If we want the set to be connected we have to require some non-resonance condition on the frequency: in fact, we need a condition weaker than the Bryuno condition usually considered in small divisors problems., Comment: 34 pages, 4 figures