A08269

Edited byGaetano Fusco

MODELS AND TECHNOLOGIES FORINTELLIGENT TRANSPORTATION SYSTEMS

PROCEEDINGS OF THE INTERNATIONALCONFERENCE (ROME, 2009, JUNE 22-23)

Copyright © MMXARACNE editrice S.r.l.

www.aracneeditrice.itinfo@aracneeditrice.it

via Raffaele Garofalo, 133/A-B00173 Roma(06) 93781065

ISBN 978–88–548–3025–7

No part of this book may be reproduced in any form,by print, photoprint, microfilm, microfiche, or any other means,

without written permission from the publisher.

1st edition: March 2010

Preface

In the last decades, Intelligent Transportation Systems have been stimu-lating an intense research activity by the scientific community, which pro-duced a large number of models, methods and experimental applications re-garding traveler information, management systems, and vehicle control. Most of such models remained at a theoretical level because the technology required had not yet reached a sufficient maturity to provide effective and economically efficient applications. In recent years, technological advances have progressed considerably and many products and services are now com-ing onto the market. Those theoretical models can finally be applied and tested on actual implementations and, on the other hand, the large-scale commercialization of industrial products and services can exploit the results of these studies in order to provide stable and effective impacts on the trans-portation system.

The conference “Models and Technologies for Intelligent Transportation Systems” has been conceived with the aim of providing an opportunity for scholars engaged in basic or industrial research to meet and to discuss re-quirements for ITS applications, unsolved problems and future develop-ments.

This book of proceedings contains 65 extended abstracts of the presenta-tions at the conference, selected after an anonymous peer review process. The topics dealt with cover theoretical, technological and applicative issues that affect the deployment of Intelligent Transportation Systems and concern all ground transport modes: passenger car traffic, bus transit, railways and logistic systems, as well as their single components and the relative interac-tions. For an easier consultation, the book is organized in thematic sections. However, it is noteworthy that the various subjects treated here present many common aspects, regarding the methodological approach, the solution meth-ods and the technologies used. This suggests that the studies on Intelligent Transportation Systems have reached a good level of maturity and that they can be considered as a unitary discipline.

iiii

The contents of the papers allow us to define such a discipline as the de-sign of the functional characteristics and of the enabling technologies de-voted to provision of information, management and control of the transport system as a whole or of its single sub-systems. Such functions and technolo-gies can involve even very different elements of the transport system, like road and railway nodes, street arteries, or even a single vehicle.

However, in order to constitute an Intelligent Transportation System, it is required that a desired state of the elements of the system under control be defined and that the functions and technologies either provide an improved knowledge of the system, thus enabling decision-makers (e.g., transport managers, transit users, drivers) to perform the proper actions or, otherwise, enable the system to react to unpredicted perturbances automatically. Indeed, it is properly the design of strategies, functions and technologies applied to achieve predefined objectives efficiently that encompasses the intelligenceof the system.

GAETANO FUSCORoma, June 2009

Preface

iii

Acknowledgments

I wish to thank the anonymous referees for their quick and effective work aimed not only at selecting valuable papers but also at advising authors about possible improvements of their papers. I also wish to thank the mem-bers of the organizing committee and, in a special way, Dr. Chiara Co-lombaroni and Dr. Luigi Tatarelli, for his great contribute in the careful col-lection and review of these proceedings.

POST SCRIPTUM IN MEMORIAM OF PINO BELLEI

Prof. Giuseppe Bellei, one of the authors who contributed to this Confer-ence and our appreciated and esteemed colleague at Sapienza University of Roma, died on December 26th, a few days before the book was printed.

We are honoured to treasure in this book his last contribution to the disci-pline to which he dedicated his life of studies.

iviv

Committees

Scientific Committee

Prof. Alberto Broggi (Università di Parma, Italy) Prof. Giulio Erberto Cantarella (Università di Salerno, Italy) Prof. Michael Florian (Université de Montréal, Canada) Prof. Hani Mahmassani (Northwestern University, USA) Prof. Markos Papageorgiou (Technical University of Crete, Greece).

Organizing Committee

Prof. Gaetano Fusco (Sapienza Università di Roma, chair) Dr. Adriano Alessandrini (Sapienza Università di Roma, Italy) Dr. Maurizio Bielli (CNR-IASI, Italy) Dr. Chiara Colombaroni (Sapienza Università di Roma, Italy) Prof. Guido Gentile (Sapienza Università di Roma, Italy) Dr. Riccardo Licciardello (Sapienza Università di Roma, Italy) Dr. Lorenzo Meschini (Sapienza Università di Roma, Italy) Dr. Marialisa Nigro (Università Roma Tre, Italy) Dr. Luca Persia (Sapienza Università di Roma, Italy) Prof. Stefano Ricci (Sapienza Università di Roma, Italy)

v

Contents

Part I Theory and models for ITS deployment ..................................1 Effects of ITS on surplus day-to-day dynamics in transportation networks Giulio E. Cantarella...........................................................................................2

Dynamic Traffic Assignment with a New Flow Propagating Model Based on First-Order Traffic Flow Theory N.C. Balijepalli, D. Ngoduy, D. Watling .......................................................... 14

On Dynamic Information and Patterns of Cooperative Behaviours: a Probabilistic Model with Economic Analysis Fabien Leurent, Thai Phu Nguyen ................................................................... 21

Multi objective optimization of traffic systems using dynamic traffic management measures Luc J.J.Wismans , Eric C.Van Berkum, Michiel C.J Bliemer ............................ 29

Dynamic Network Loading models and their impact on DTA-based OD-matrix estimation Rodric Frederix .............................................................................................. 35

Robust paths in urban transportation networks Ludovica Adacher, Marta Flamini, Gaia Nicosia............................................. 39

Simulation of network traffic in a time-of-day scale Ming-Chorng Hwang ...................................................................................... 45

An Algorithm for Network Loading in Dynamic Assignment Hilmi Berk Celikoglu, Mauro Dell’Orco.......................................................... 48

Towards global solutions in the calibration of micro-simulation models: a verification approach Vincenzo Punzo, Biagio Ciuffo ........................................................................ 54

Empirical Laws for Urban Car Mobility S. Rambaldi, L. Giovannini, A. Bazzani and B.Giorgini ................................... 59

vivi

Part II Traveler Information and Road Traffic Management Systems ...........................................................................................65

Optimal Mainstream Traffic Flow Control of Motorway Networks Markos Papageorgiou, Rodrigo C. Carlson, Ioannis Papamichail, Albert Messmer ............................................................................................... 66

FREEFLOW, Data and Intelligent Decision Support: the York Demonstration and a Theoretical Observation Mike Smith, Robert Shepherd........................................................................... 74

An Intelligent Traffic Management System for Coordinated Routing Decisions Inspired by Honey Bee Communication H. F. Wedde, S. Lehnhoff, S. Senge, A. M. Lazarescu ....................................... 81

Integrated macroscopic traffic flow and emission model based on METANET and VT-micro S.K. Zegeye, B. De Schutter, J. Hellendoorn, E.A. Breunesse............................ 86

Capturing state variations by optimal detector positions Francesco Viti, Chris M.J. Tampère ................................................................ 90

Traffic State Identification Using Loop Detector Data Jiang Han, Rajesh Krishnan, John Polak ......................................................... 95

Use of Data Fusion to Update Information When Modeling Drivers’ Choice Behavior Mauro Dell’Orco, Mario Marinelli.................................................................. 98

Traffic state estimation and prediction in urban networks through online modelling Chris M.J. Tampère, Francesco Viti, Ben L.H. Immers................................... 109

Real-time traffic monitoring and forecast through OPTIMA - Optimal Path Travel Information for Mobility Actions Lorenzo Meschini, Guido Gentile .................................................................. 113

Definition and application of procedures to forecast urban travel time Ernesto Cipriani, Roberto Gigli, Livia Mannini ............................................. 122

Methodologies for building transport models for routing applications from standard data sources: estimating road operative speeds Giuseppe Cantisani, Michele Di Vito, Guido Gentile, Lorenzo Meschini......... 129

Contents

vii

Mobility Management at manager and employer level through a web-based system and its application Benedetto Barabino , Sara Salis, Giovanni Corona........................................ 133

ITS projects in Italy developed by the National Operative Programme for Transport 2000-2006 P. Baratono, G. Di Muro, V. Galdi, C. Ricciolio, G. Aresu............................. 139

Part III Advanced Driver Assistance Systems and Road Safety.............................................................................................145

Car-driver cooperation in future vehicles Alberto Broggi, Luca Mazzei, Pier Paolo Porta ............................................. 146

Development and testing of a fully adaptive cruise control system Gennaro Nicola Bifulco, Luigi Pariota, Fulvio Simonelli, Roberta Di Pace ............................................................................................................. 152

Reasons and estimation of IVC outcomes on secondary accident Bruno Dalla Chiara, Francesco Deflorio....................................................... 156

Stability phase diagram of adaptive cruise control traffic flow Dong Ngoduy................................................................................................ 160

A two-stage safety control model for highway traffic: current findings Hilmi Berk Celikoglu, Gurkan Emre Gurcanli, Ozge Celikoglu ...................... 165

SAFETY: management and reduction of accident – the help of mathematical models and ITS systems Eugenio Morello, Silvana Toffolo .................................................................. 171

Safety evaluation methodology of ITS for riders Annie Pauzié, Christhard Gelau, Samuel Aupetit ........................................... 178

Extended Cooperative Automatic Incident Detection: an innovative algorithm for incident detection in cooperative environments Stefano Marco, Eugenio Morello................................................................... 184

Advanced methods for improvement of driver resistance to attention decreases M. Novák, Z. Votruba.................................................................................... 191

Contents

viiiviii

Investigation of visual stimuli recognition as causes of driving accidents M. Novák, Z. Votruba, S. Novotný, R. Piekník ................................................ 197

A clustering of range sensory data by integrating stereovision information for tracking objects in urban environment Pawe Kmiotek, Cyril Meurie, Frederick Zann, Yassine Ruichek .................... 204

Part IV Advanced Railway Traffic Control and Management Systems ......................................................................................... 211

Optimization and coordination in real-time railway traffic management F. Corman, A. D’Ariano, D. Pacciarelli, M. Pranzo....................................... 212

Railway timetable perturbations: analysis, forecasting and reduction through a Petri Nets based decision support tool Antonio Tieri, Stefano Ricci........................................................................... 216

Running map for railway platform schedule Roberto Marmo............................................................................................. 220

Flexibility, modularity and interactivity. A new working strategy on railway line simulators J.M. Mera, E. Castellote, M.A. Pérez, Manuel Soler....................................... 227

Use of Formal Languages to represent the ERTMS/ETCS System Requirements Specifications of the Interconnection L0/L2 A. Piccolo, F. Senesi, V. Galdi, R. Malangone................................................ 236

Design of the driver assistance system for train control in case of signaling system ERTMS dysfunction Saïd Hayat, Sabrine Dhahbi, Abdeljalil Abbas Turki...................................... 242

Safety-related Fault States in Railway Operation Andreas Schöbel, Thomas Maly ..................................................................... 248

Lock Management System – Emerging Technology For Waterborne ITS Natalija Joli , Zvonko Kavran, Damir Obad .................................................. 252

A track segment-based simulation approach for management of railway traffic in real-time Jose Luis Espinosa, Ricardo García .............................................................. 257

Contents

ix

Concept for Wayside Train Monitoring at Serbian Railways Aleksandar Radosavljevic, Andreas Schöbel, Simo Mirkovic .......................... 262

An incremental heuristic for the train routing and scheduling problem Joaquin Rodriguez, Grégory Marlière, Sonia Sobieraj................................... 268

Part V Models and Technologies for Intelligent Logistic Systems..........................................................................................275

A reference architecture for freight transport management systems Silvio Di Re, Andrea Campagna, Umberto Nanni .......................................... 276

Random and Fuzzy Utility Route Choice Models for Road Freight Transport at National Level Agata Quattrone, Antonino Vitetta................................................................. 282

Pickup and Delivery problem Jan Pelikán................................................................................................... 286

A Heuristic Algorithm and a Software Program for Dynamic Management of a Urban Logistic Center Gaetano Fusco, Maria Pia Valentini, Chiara Colombaroni, Valentina Conti ............................................................................................................ 290

A secure and efficient emergency management system for disasters Eren Erman Özgüven, Kaan Özbay ............................................................... 298

Incorporating System Variability into Emergency Planning Jian Li, Kaan Özbay, Bekir Bartin................................................................. 306

Preventive and adaptive security of freight transport using RFID system Stefano Carrese, Marialisa Nigro, Stefano Saracchi ...................................... 311

Assessing the value of information for retail distribution of perishable goods Marta Flamini, Marialisa Nigro, Dario Pacciarelli ....................................... 314

Optimization of Baggage Handling System using tracking technologies Stefano Carrese, Marialisa Nigro, Stefano Saracchi ...................................... 320

Contents

xx

Part VI Advanced Bus Transit and Parking Management Systems ......................................................................................... 325

Intelligent Car Park Routeing for Road Traffic Victoria J. Hodge, Mike Smith, Jim Austin ..................................................... 326

Dynamic Hyperpaths: the STOP Model Valentina Trozzi, Solmaz Haji Hosseinloo, Guido Gentile, Michael G H Bell ............................................................................................................... 334

Optimising Activation of Bus Pre-signals Victoria J. Hodge, Tom Jackson, Jim Austin .................................................. 344

A Model and an Algorithm for Signal Synchronization and Bus Priority on Urban Arteries Chiara Colombaroni, Gaetano Fusco, Andrea Gemma .................................. 354

Schedule and headway based control of transit lines Giuseppe Bellei, Konstantinos Gkoumas ........................................................ 361

Improving service reliability in urban transit networks Shahram Tahmasseby, Rob van Nes............................................................... 365

Optimization Algorithms for On-Line Dial-a-Ride Systems Alberto Bosio, Giovanni Righini, Matteo Salani ............................................. 370

Traffic flow assignment models for Personal Rapid Transit networks Emiliano Traversi, Alberto Caprara, Joerg Schweizer ........................................... 375

Contents

Part I Theory and models for ITS deployment

Effects of ITS on surplus day-to-day dynamics in transportation networks

Giulio E. Cantarella1

Abstract The general problem of transportation supply design with demand assignment

provides a powerful framework to address Design of Intelligent Transportation Sys-tems, such as Advanced Traveller Information Systems (ATIS) or Advanced Driver Advanced Driver Assistance Systems (ADAS). All existing approaches are based on equilibrium assignment; still optimization of transportation supply under equilibrium assumptions may not guarantee that an effective solution is obtained, because the system may not evolve towards it. This paper reports some results of an undergoing research project on transportation supply design with dynamic process assignment. More specifically an existing deterministic model w.r.t. to (arc or path) flows and costs is extended to include one more variable modelling user surplus. A very simple way is proposed to apply the resulting model for analyzing ATIS or ADAS.

1. Introduction

Modifications of existing transportation facilities and/or services or the introduction of new ones affect traveller behaviour, concerning path choice at least. The general problem of transportation supply design (TSD) with demand assignment provides a powerful framework to address this issue. It includes discrete Network Design Problem (dNDP), for instance directions in an urban network, and continuous Network Design Problem (cNDP), for instance street width in a urban network, as well as Signal Setting. Design of Intelligent Transportation Systems (ITS) too, such as Advanced Traveller In-formation Systems (ATIS) or Advanced Driver Advanced Driver Assistance Systems (ADAS), can be casted within this general framework. All existing approaches are based on equilibrium assignment (a review and references on these topics may be found in chapter 9 in Cascetta, 2001, 2009).

1 Dept of Civil Engineering, Univer. of Salerno, Via Ponte Don Melillo 1 - 84084, Fisciano (SA) – Italy. g.cantarella@unisa.it .

Effects of ITS on surplus day-to-day dynamics in transport networks 3

This paper reports some results of an undergoing research project on transportation supply design with dynamic process assignment. Dynamic process assignment seems relevant since optimization of transportation sup-ply under equilibrium assumptions may not guarantee that an effective solu-tion is obtained, because the system may not evolve over time towards it.

The main aim of the paper is showing that a correct design ITS, such as ATIS or ADAS based on the effects on surplus requires a day-to-day dy-namic analysis. More specifically an existing deterministic model w.r.t. to (arc or path) flows and costs is extended to include one more variable model-ling user surplus. Results for a toy networks are also presented, supporting major findings and suggesting research perspectives.

2. Basic Definitions, Equations, Notations

In this section basic definitions, notations and equations are briefly re-viewed. For simplicity’s sake demand flows are assumed constant and one mode is considered, hence path choice is the only user choice behaviour af-fected by network performances, or more properly by congestion. User trav-elling between the same origin-destination pair with common behavioural features are grouped into a user class i. A six equation assignment modelling (SEAM) approach is followed below. Let

Ki be the (non-empty and finite) set of available paths for user class i;di 0 be the demand flow for user class i;pi 0 be the path choice probabilities for user class i, with 1T pi = 1; hi be the path flows for user class i;vi be path systematic utilities for user class i;wi be the path costs for user class i;c be the vector of arc costs; Bi be the arc-path incidence matrix for user class i, with entries bak = 1 if arc

a belongs to path k, bak = 0 otherwise; f be the vector of arc flows.

Demand conservation for user class i can be expressed by the following equation regarding path flows:

hi = di pi . (2.1)

Path choice behaviour can be modelled through random utility theory (as introduced by Domencich and McFadden, 1975; for details see Ben Akiva

Giulio Erberto Cantarella 4

and Lerman, 1995; chapters 3 and 4 in Cascetta, 2001, 2009). According to this theory a user gives each path a perceived utility, modelled by a random variable (due to several sources of uncertainty); hence the probability that a user of class i chooses path k is the probability that path k is the highest util-ity path. The perceived utility of path k, Uk, is expressed by the sum of its expected value or the systematic utility, vk = E[Uk], and a random residual,

k = Uk E[Uk]; thus, the probability to choose path k depends on path sys-tematic utility. When the perceived utility variance matrix is non singular probabilistic path choice function for user class i is obtained:

pi = pi(vi) . (2.2)

Systematic utility depends on path cost through the path utility function,generally specified by an affine transformation. Below, for notation simplic-ity a simple linear transformation is used for each user class i:

vi = wi . (2.3)

A (within-day static) transportation system is usually modelled through a network with a transportation cost and a flow associated to each arc. (Node costs can be considered by duly modifying the graph). Thus, path costs can be obtained from arc costs through a linear transformation expressing the arc path costs consistency (non-additive and/or specific path costs are omitted for notation simplicity):

wi = BiT c i . (2.4)

Congestion is generally simulated assuming that arc costs depend on arc flows (and other supply features) through the arc cost function:

c = c(f) . (2.5)

Arc flows can be obtained from path flows through a linear transforma-tion expressing the arc path flows consistency:

f = i Bi hi . (2.6)

Besides the above six basic equations, another relation is introduced ex-pressing the total user surplus S w.r.t. systematic utilities and demand flows:

S(v) = i di si(vi) . (2.7)

where si is the unitary surplus, assumed modelled by the satisfaction function,

si(vi), consistent the path choice function (2.2).

Effects of ITS on surplus day-to-day dynamics in transport networks 5

3. Modelling Day-to-day Dynamics

In this section an existing deterministic process model is extended to in-clude total user surplus. Several deterministic process models have been proposed for demand assignment (since the seminal paper by Horowitz, 1984; a general framework in Cantarella and Cascetta, 1995; more recently Watling, 1999; Hazelton, 2002; Watling and Hazelton, 2003; Cantarella and Velonà, 2003; Lo and Bie, 2006; Nakayama, 2006; Bie and Lo, 2008). An effective model based on exponential smoothing is briefly resumed below. Let

xt be the path costs forecasted by users at day t;]0,1] be the weight given by users in their forecasting to yesterday costs;

yt be the path flows occurring at day t; ]0,1] be the fraction of users who reconsider previous day choice.

For notation simplification it is worth to introduce the path flow functionw.r.t. path costs for user class i obtained by combining equations (2.1, 2, 3):

hi = hi(wi) = di pi( wi) i

or h = h(w) . (2.8)

Moreover, the path cost function w.r.t. path flows for user class i is obtained by combining equations (2.4, 5, 6):

wi = BiT c( i Bi hi) i

or w = w(h) . (2.9)

User learning and forecasting is modelled through the cost update filter:

xt = w(yt-1) + (1 – ) xt-1 . (2.10)

User habit and inertia to change is modelled through the choice update filter:

yt = h(xt) + (1 – ) yt-1 . (2.11)

The two recursive equations (2.10, 11) describe a deterministic process model called DP(x, y) (Cantarella and Cascetta, 1995, Cantarella, 1997b).

Another recursive equation added to DP(x, y) leads to model DP(x, y, z), this equation expressing how total user surplus zt at day t is updated;

zt = S(xt) + (1 – ) zt-1 . (2.12)

Giulio Erberto Cantarella 6

Effects of ITS may be modelled through parameters of the arc cost func-tion, the path choice functions, as well as the dynamic parameters and .More specifically, it may be assumed that ATIS mainly affect user habit and inertia to change and user memory, as well as user behaviour dispersion (pa-rameters of choice functions). On the other hand, ADAS mainly affect arc capacity and reaction to congestion (parameters of arc cost function).

Fixed-point states of DP(x, y, z) are defined by conditions:

xt = xt-1, yt = yt-1, zt = zt-1

which combined with equations (2.10-11) give:

x* = w(y*) , (2.13)

y* = h(x*) , (2.14)

z* = S(x*) . (2.15)

Fixed-point states of DP(x, y) are given by equations (2.13) and (2.14); it can be easily recognized that they are equivalent to stochastic user equilib-rium (SUE)1. Existence of at least one fixed-point is granted by continuous arc cost function and path choice functions (and connected graph).

According to most adopted sufficient conditions for uniqueness if the path choice functions are monotone increasing2, as for invariant probabilistic path choice functions, and the arc cost function is monotone strictly increas-ing uniqueness is granted. Condition on arc cost function can be weakened to monotone increasing (but not necessarily strictly monotone) for invariant strictly positive probabilistic path choice functions, as it occurs for usually adopted probabilistic choice functions.3

It is worth noting that the definition of fixed-point states, as well as their existence and uniqueness do not depend on the value of parameters and .On the other hand all these features are greatly affected by demand flows, as well as parameters of the arc cost function, the path choice functions.

1 So called after Daganzo and Sheffi (1977), who introduced equilibrium assignment with probabilistic path choice functions. The user equilibrium approach to assign-ment was introduced by Wardrop in his seminal paper (1952). Fixed-point models for SUE have first been proposed by (Daganzo, 1983, Cantarella, 1997a). 2 As always the case for invariant probabilistic path choice functions, that is if pa-rameters of perceived utility distribution (but the mean) do not depend on path sys-tematic utility values. 3 A review including even weaker conditions in Cantarella and Velonà (2009).

Effects of ITS on surplus day-to-day dynamics in transport networks 7

DP(x, y, z) may evolve towards fixed-points as well as other kind of at-tractors, such periodic, quasi-periodic, and a-periodic (chaotic) attractors, as it can be observed by running DP(x, y, z) with different values of parameters (see examples in the next section). Conditions for fixed-point (local) stability can be used to forecast the evolution of the system without actually run it, through an analysis of the Jacobian matrix of DP(x, y, z). At this aim, let

n be the number of paths; J(xt, yt) be the (2n) 2n) Jacobian matrix of DP(x, y), recursive equations

(2.10, 11); J(xt, yt, zt) be the (2n+1 2n+1) Jacobian matrix of DP(x, y, z), recursive

equations (2.10, 11, 12); it shows a low triangular block structure:

J(xt, yt, zt) = J(xt, yt)S(v)T (1 )

After some algebra (expanding arguments in Cantarella and Cascetta, 1995), the determinant of the Jacobian of DP(x, y, z) at any point is:

J(xt, yt, zt) = (1 )n (1 )n (1 ) [0,1[

thus, the system is dissipative, that is converging anyway to an attractor. Stability of a fixed-point (x*, y*, z) is granted if all the eigenvalues of the

Jacobian J(x*, y*, z*) at the fixed-point are within the unitary circle on the complex plan. After some algebra (expanding arguments in Cantarella and Cascetta, 1995), the stability condition can be written down as:

k E( ) k = 1, …, n . (2.16)

where k is one of the n eigenvalues of matrix Jac[h(w)] Jac[h(w)], which does

not depend on parameters and .E( ) is the interior of an ellipse on the complex plan, with semi-axis on

the real axis eR = (1 + (1 ) (1 )) / ( ) 1, semi-axis on the imagi-nary axis eI = (1 (1 ) (1 )) / ( ) 1, centre at ((eR 1), 0) on the real or imaginary axis, respectively. Examples are given in Fig. 3.

Condition (2.16) allow us to clearly distinguish the role of updating pa-rameters and , which only affects the area of the ellipse, and that of other parameters, such demand flows, arc capacities, parameters of choice func-tions and cost function, which only affects the eigenvalues .

Giulio Erberto Cantarella 8

It is worth noting that the lower the values of parameters and are, the greater area of ellipse E( ) is; in addition, ellipse E( ) is always lo-cated on the left of the vertical line through point (1, 0). Thus, if all the ei-genvalues have real part less than one, Re( ) < 1, there always are values of updating parameters and small enough to ensure stability. On the other hand, the greater the parameters and are, the greater the rate of convergence (if the case) is, but the more likely instability may occur.

4. Examples

In this section results of section 3 are applied to a toy network (a simple representation of motorway connections from Napoli to Salerno). The graph (Fig. 1) has four nodes, {A, B, C, D}, five arcs, {1 = (A,C), 2 = (B,C), 3 = (B,D), 4 = (A,B), 5 = (C,D)}. One O-D pair (A-D) is consid-ered connected by three paths, {A-C-D, A-B-C-D, A-B-D}.

Davidson (hyperbolic) travel time function describes cost for each arc; since it shows a vertical asymptote at capacity, it has been approximated by its tangent at a ratio of flow over capacity . According to these assumptions the arc cost function is continuous and strictly monotone increasing.

Path choice behaviour is modelled by an invariant Logit choice model with dispersion parameter = 8 (corresponding to a standard deviation equal to one forth of the minimum cost path). According to these assumptions the path choice functions are (invariant,) continuous and strictly positive mono-tone increasing.

Sufficient conditions for existence and uniqueness of one fixed-point states are granted by above assumptions.

Figure 1. Graph use in the examples; thickness of arcs indicates capacities.

B

C

D

A

Effects of ITS on surplus day-to-day dynamics in transport networks 9

Figure 2 shows the evolutions over time of user surplus w.r.t. days from 61 to 90 obtained changing values of parameters and/or In each box re-sults are reported for demand flow equal to 3000 (top), 3600 (middle), 4200 (bottom), each value being less than 4800 user per hour which is the maxi-mum flow that may traverse the network without over-saturation. Dashed line indicate fixed-point states (it may be hidden by evolution over time).

Figure 2 (left, top) show the reference scenario with = 0.72, = 0.62, = 0.62; for values of demand flow greater than 3000 (still below maximum

flow) the system does not evolve toward the fixed-point indicated by the dashed line, but to a periodic attractor. Moreover, periodic oscillations occur around a value of surplus that is less than the value for fixed-point states.

Figure 2 (left, bottom) and figure 2 (right, top) show the evolution over time of user surplus with of the introduction of an ADAS, modelled by re-ducing effects of congestion, = 0.63, or an ATIS, modelled by enhancing user memory w.r.t. path costs occurred in previous days, = 0.42, respec-tively; in both cases only the larger value of demand flow (4200) still causes oscillations. Finally figure 2 (right, bottom) show that the combination of both ADAS, = 0.63, and ATIS, = 0.42, assures stability of fixed-points for any values of demand flow.

Figure 2. Evolution over time of user surplus (see text).

Giulio Erberto Cantarella 10

It is worth noting that the introduction of an ADAS, change from 0.72 to 0.63 (top to bottom), affects the fixed-point states, whilst the introduction of an ATIS, from 0.62 to 0.42 (left to right), does not affects the fixed-point states that do not depend on parameters and as it may be expected from consideration in section 3 above.

Since there are three paths, n = 3, 3 eigenvalues k, for each value of de-mand flow can be computed w.r.t. to the stability region. All the eigenvalues are real and less or equal to zero, even though matrix Jac[h(w)] Jac[h(w)] is neither symmetric nor semi-definite negative (a formal proof, not reported for brevity sake, can be obtained by expanding arguments in Cantarella and Cascetta, 1995).

Results of the stability analysis, according to equation (2.16), are shown in figure 3. One eigenvalue is always zero since path flows must comply with demand conservation equation, whichever is the value of demand flow. Another one is less than zero but very close to zero, so far the eigenvalues for the different values of demand flows {3000, 3600, 4200} are different, but can hardly be distinguished in the figure. The third eigenvalues can be more clearly singled out with a square for d = 3000, a circle for d = 3600, a diamond for d = 4200. Results are consistent with those in fig. 2: for evolu-tions over time towards a periodic attractor, at least one eigenvalue is outside the stability region. In particular figure 3 (right, bottom) shows that the com-bination of both ADAS and ATIS assures that all the eigenvalues are within the stability region for any value of demand flows, in other words fixed-points are stable for any values of demand flow.

Figure 3. Eigenvalues w.r.t. stability region (see text).

Effects of ITS on surplus day-to-day dynamics in transport networks 11

It is worth noting that after the change of from 0.72 to 0.63 (top to bot-tom), the stability region does not change since it only depends on parame-ters and (but the fixed-points and the eigenvalues do). On the other hand, the change of from 0.62 to 0.42 (left to right) affects the stability region but not the eigenvalues. Hence, the effects of the introduction of both ADAS and ATIS (right, bottom) can be anticipated by using the eigenvalues for ADAS and the stability region for ATIS, without an explicit analysis of their combination.

5. Conclusions

In this paper1 an existing deterministic process model has been extended to deal with user surplus, together with a method to assess fixed-point stabil-ity without running the model2. It turns out that stability analysis may play a relevant role in surplus estimation relevant for transportation supply design as well as transportation project assessment.

The proposed approach can be used to analyze the effects of the introduc-tion of ITS, such as ADAS and ATIS, on user surplus evolution over time. Other examples (not reported for brevity sake) regarding improving an arc may show that carefully designed ITS may better off facility improvements.

Some issues are still worth of further research work, such as the use of a matrix norm to approximate the eigenvalues, and the analysis of bifurca-tions and their relationships with weaker uniqueness conditions. All these is-sues will be addressed in future papers.

In all the examples reported in this paper, as well as those reported in lit-erature, it seems that fixed-point local stability also assures global stability, when existence and uniqueness are granted. However general conditions for global stability are still the main open issue of day-to-day dynamics in trans-portation networks (at least to author’s knowledge). Other research perspec-tives regard multi-user class assignment and more effective models of ITS3,as well as parameter calibration and large scale applications.

1 Author wishes to thank Gaetano Fusco who carefully edited the text and suggested some improvements (the author is the only responsible for any remaining errors). 2 Author wishes to thank Francesco Viti who underlined this issue during the discus-sion after the presentation. 3 Author wishes to thank Cino Bifulco who suggested the relevance of this issues during a private conversation after the presentation.

Giulio Erberto Cantarella 12

Acknowledgments Partially supported under National research grant n. 2007R9CSXY_004 fi-nancial year 2007, UNISA local grants n.ORSA082744 - 2008 and n. ORSA091208 - 2009.

References Ben Akiva M., Lerman S. R. Discrete Choice Analysis. MIT Press, Cambridge MA,

1985. Bie J., Lo H. K. A User Equilibrium in Day-to-Day Traffic Dynamics: Stability, At-

tainability and Attraction Domain, Proceeding of The International Symposium on Dynamic Traffic Assignment (DTA), 18-20 June 2008, Leuven, Belgium.

Cantarella G.E. A General Fixed-Point Approach to Multi-Mode Multi-User Equi-librium Assignment with Elastic Demand. Transpn Science, 31, 107-128, 1997a.

Cantarella G.E. Fixed-Point Stability and Bifurcations in Dynamic Processes for Traffic Assignment. In Advances in Intelligent Systems, F.C. Morabito (ed.), (Proceedings of International Symposium on Intelligent System. Reggio Cala-bria, Italy September, 1997), 254-261, 1997b.

Cantarella G.E., Cascetta E. Dynamic Process and Equilibrium in Transportation Networks: Towards a Unifying Theory. Transpn Science, 29, 305-329, 1995.

Cantarella G.E. and Velonà P. Stability analysis of equilibrium patterns in a trans-portation network In Proceedings of the European Transport Conference 2003.

Cantarella G.E. and Velonà P. SUE: conditions for solution uniqueness and MSA-based algorithm convergence. Proceedings of the EWGT, Padua, Italy, Septem-ber 2009.

Cascetta E. Transportation Systems Engineering: Theory and Methods. Kluwer Academic Publisher, 2001.

Cascetta E. Transportation Systems Analysis: Models and Applications. Springer, 2009.

Daganzo C.F., Sheffi Y. On Stochastic Models of Traffic Assignment. Transpn. Sci-ence, 11(3), 253-274, 1977.

Daganzo C.F. Stochastic Network Equilibrium with Multiple Vehicle Types and Asymmetric, Indefinite Link Cost Jacobians. Transpn. Science, 17, 282-300, 1983.

Domencich T. A., McFadden D. Urban Travel Demand: a Behavioral Analysis. North Holland, Amsterdam, 1975.

Gentile G. Sufficient conditions for the uniqueness of the solution to the Stochastic User Equilibrium problem. Preliminary accepted for publication in Transn Sci. Currently first version is available at http://w3.uniroma1.it/guido.gentile, 2003.

Hazelton M.L. Day-to-day variation in Markovian traffic assignment. Transpn. Res.I, 36B, 637-648, 2002.

Horowitz J.L. The Stability of Stochastic Equilibrium in a Two-link Transportation Network. Transpn. Res., 18B, 13-28, 1984

Lo H. K., Bie J. Stability domains of traffic equilibrium: directing traffic system evolution to equilibrium. Proceeding of The First International Symposium on Dynamic Traffic Assignment (DTA), 21-23 June 2006, Leeds, U.K.

Effects of ITS on surplus day-to-day dynamics in transport networks 13

Nakayama S. Stability of Network Flows with bounded rational route choice. Pro-ceeding of The First International Symposium on Dynamic Traffic Assignment (DTA), 21-23 June 2006, Leeds, U.K.

Wardop J.G. Some Theoretical Aspects of Road Traffic Research. Proc. Inst. Civ. Eng. 2(1), 325-378, 1952.

Watling D. Stability of the stochastic equilibrium assignment problem: a dynamical systems approch. Transpn. Res. 33B, 281-312, 1999.

Watling D., Hazelton M.L. The Dynamics and Equilibria of Day-to-Day Assignment Models. Network and Spatial Economics, 3, 349-370, 2003.