# Michael FlorianUniversité de Montréal | UdeM · Department of Computer Science and Operations Research

Michael Florian

Dr. Eng. Sc.

## About

153

Publications

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7,312

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Introduction

Michael Florian is Professor Emeritus at the Department of Computer Science and Operations Research, Université de Montréal and CIRRELT.

## Publications

Publications (153)

A path-based algorithm is developed for the static traffic assignment problem (TAP). In each iteration, it decomposes the problem into origin-destination (OD) pairs and solves each subproblem separately using the Wolfe reduced gradient (RG) method. This method reduces the dimensions of each single-OD subproblem by selecting a basic path between the...

In this chapter, the different basic assumptions for the development of assignment models to transit networks (frequency-based, schedule-based) are presented together with the possible approaches to the simulation of the dynamic system (steady state, macroscopic flows, agent-based). The main functional components of uncongested assignment and user...

Toll road operators and other toll facility stakeholders require analysis
tools to estimate the ridership and projected income for an increasing variety of
tolling schemes. Some tolling schemes commonly considered include link-based
tolls as well as derived schemes, such as charging both a minimum and a maximum
toll (or cap) for the use of the faci...

This chapter presents four categories of optimization models: spatial interaction models, network balancing models and multimodal multiproduct goods transport network planning models. Spatial interaction models are used to establish origin–destination demand matrices. Network balancing models are used to model the route choice on congested networks...

Since it was first developed [see Spiess and Florian, Transp Res 23:83–102 (1989)], the strategy-based transit assignment has been extensively used and its properties are well understood now. The computation of an optimal strategy is relatively fast and is comparable to the computation of a shortest path tree for one destination. However, since it...

The temporal demand matrix is an essential input to both on-line and off-line applications of dynamic traffic assignment (DTA). This paper presents a new method to solve the simultaneous adjustment of a dynamic traffic demand matrix, searching for a reliable solution with acceptable computational times for off-line applications and using as an inpu...

Dynameq is a simulation-based dynamic traffic assignment
(DTA
) model. This model employs an iterative solution
method to find the user-optimal assignment of time-varying origin–destination demands to paths through a road network where the path travel times – which depend on the assigned path flows – are time-varying and determined using a detailed...

The mainstay method of equilibrium assignment methods is based on adaptation of the linear approximation algorithm. Practically all commercial software packages for transportation planning offer a version of this algorithm. In the early days of personal computing, when random-access memory (RAM) was limited, this method was the most appropriate one...

A new adaptation of Rosen's projected gradient algorithm for solving fixed-demand equilibrium traffic assignments is developed. It is based on a Gauss-Seidel decomposition scheme in which origin-destination pairs are considered sequentially. The method operates in the space of path flows and shares this approach with earlier work on adapting the gr...

The analysis of transportation phenomena by quantitative approaches naturally gives rise to network models that represent
the spatial characteristics of the transport infrastructure. This paper surveys the nonlinear cost models that arise in transportation
analysis and points out the principal methods used for their solution in practice. We discuss...

In this paper, the gradient method for adjusting a single class origin-destination matrix by using observed flows is extended to consider a reference matrix and to adjust simultaneously the O-D matrices for several classes of traffic. The importance of using a reference matrix is demonstrated with computational results that are carried out with two...

This paper focuses on the analysis and planning of multimodal, multiproduct transportation systems at the international, national, and regional levels, where the movements of several commodities through the transportation networks and services of several carriers are considered simultaneously. The main questions relate to the evolution of a given t...

The aim of this article is to give a semi-technical and somewhat journalistic account of the contributions to the methods used for quantitative transportation planning by professors, researchers and graduate students who have been active at the Centre for Research on Transportation (CRT) of the University of Montreal since its inception.

The formulation of static assignment models, with variable and fixed demand, based on Wardrop's first principle, are presented
for deterministic and stochastic models. The main algorithms used to obtain solutions for these network equilibrium models
are given for each class of assignment problems. Calibration and validation issues are considered.

In this paper, the gradient method for adjusting a single class origin-destination matrix by using observed flows (see Spiess, 1990) is extended to adjusting simultaneously the origin-destination matrices of several classes of traffic. The algorithm is developed in detail and computational tests demonstrate the efficiency of the method. A compariso...

This paper presents a spatial price equilibrium model in an oligopoly market for refined oil products. Till 1997 the Brazilian oil market was characterized by the state monopoly of Petrobras, which up to 2001 remained the only firm authorized to import oil derivatives. With several agents operating in the primary oil supply market, the government s...

A computational procedure, that takes into account climatic data and produces
hourly mobile emissions of pollutants on a fine grid for the Montréal
Metropolitan area has been developed for the use of Environment Canada. The
procedure computes HC, CO, NOx, CO2, SO2 and NH3 mobile emissions, as well
as 2.5- and 10-µm particles. The mobile emissions a...

In this paper, we extend the toll pricing framework previously developed for vehicular traffic networks to ones with the potential to include many modes of transportation such as walking, driving, and using public conveyance (e.g., buses, subways, and trains). To determine tolls, we construct a user equilibrium and system optimal model. In both mod...

This paper presents the first application of Dynameq to a freeway reconstruction impact study in the United States. Dynameq is a simulation-based equilibrium dynamic traffic assignment modeling software. The equilibrium solution property and the close to microscopic simulation traffic fidelity level make it an excellent tool in the traffic impact s...

In this paper, we consider a multi-class network equilibrium model where several classes of traffic, with their own travel times, interact on the links of the network. The volume/delay functions depend on each class of vehicles. Hence, the resulting cost functions are nonlinear and asymmetric. The problem is formulated as a nonlinear variational in...

This paper concerns a frequency-based route choice model for congested transit networks, which takes into account the consequences of congestion on the predicted flows as well as on the expected waiting and travel times. The paper builds on the results presented in Correa [Correa, J., 1999. Asignacion de flujos de pasajeros en redes de transporte p...

In this paper, we present exact and approximate algorithms for the problem of optimal network design, which was first studied by Ridley [15], Stairs [17] and Scott [16], among others. Given a network, the problem consists in selecting a subset of links that minimizes the sum of shortest routes between all nodes subject to a budget constraint. Conge...

We present an adaptation of the dual simplex algorithm, for computing all shortest paths on a network. Given a shortest path arborescence rooted at node r, the change of root to a new origin s, renders the arborescence rooted at r dual feasible and primal infeasible for the new problem. The adaptation of the dual simplex algorithm to compute the sh...

We present a Gauss–Seidel type algorithm for the problem of adjusting an O–D matrix by using observed flows in congested networks. The problem is formulated as a bi-level optimization problem. Necessary conditions for some properties of the solution of the O–D matrix adjusting problem are derived and a coordinate descent method is developed. The al...

The spatial price equilibrium on a general network may be formulated as a nonlinear-cost mathematical programming problem with simple constraints, when the decision variables are the path flows. The solution of this problem is difficult due to the very large number of variables (paths) and the impracticality of generating all the paths from all the...

The construction of toll highways by concessions awarded to private companies leads to the need of forecasting their usage
in order to estimate the future stream of revenues. Two main modeling approaches for this problem that result in variants
of multiclass network equilibrium models, are presented and commented upon.

The analysis of mixed traffic, which includes both private and trucks has received more attention recently due to the rapid development of urban truck traffic in many cities and regions of the world. In this paper, we consider a multi-class network equilibrium model where several classes of traffic, with their own travel times, interact on the link...

The calibration and application of a simulation-based dynamic traffic assignment (DTA) model on a portion of the city of Calgary road network in Alberta, Canada, are discussed. The DTA model iteratively reassigns flow to paths by using the method of successive averages on the basis of travel times obtained with a traffic simulation model. The origi...

ITS technologies that provide information to drivers can be an effective means of using the existing transportation infrastructure more efficiently. Dynamic traffic assignment (DTA) models can play a critical role in the design of information provision systems by modeling how drivers react to information (descriptive use), and also in determining t...

The basic building block of a schedule-based transit assignment problem is to find an optimal path for a passenger, given an origin node, a destination node and departure or arrival preferences. The schedule-based shortest time-dependent transit shortest path does not minimize always the total time of a trip; rather, it uses weight factors and pref...

This paper addresses the problem of the frequency optimization of transit lines in a congested transit network. We consider the transit frequency optimization model proposed by Constantin and we modify it to consider vehicles capacity indirectly. The model is formulated as a two levels Min-Min optimization problem with the same objective fonction a...

This paper addresses the problem of the frequency optimization of transit lines in a congested transit network. We consider the transit frequency optimization model proposed by Constantin and we modify it to consider vehicles capacity indirectly. The model is formulated as a two levels Min-Min optimization problem with the same objective fonction a...

The purpose of this paper is to present two improved numerical algorithms for the continuous dynamic network loading problem. These methods, which may be considered to be event-based simulations, represent a major improvement over the functional equations approaches which was developed by Wu et al. [Transportation Research 32 (1998) 173] and the so...

The study of network equilibrium models, and related solution algorithms may be considered to have reached a mature stage.
A variety of models may be formulated and solved efficiently on contemporary computing platforms. Applications of network
equilibrium models are abundant and relatively common in the practice of transportation planning. However...

The evaluation of on-line intelligent transportation system (ITS) measures, such as adaptive route-guidance and traffic management systems, depends heavily on the use of faster than real time traffic simulation models. Off-line applications, such as the testing of ITS strategies and operational planning studies, are also best served by fast running...

This paper describes the hydrodynamic model of traffic flow, which is used to derive the future density and flow along a roadway with known initial density. The complete model is a first-order partial differential equation, complemented by the entropy condition. The contributions from fluid dynamics and traffic flow theory are integrated. The entro...

The evaluation of on-line intelligent transportation system (ITS) measures, such as adaptive route-guidance and traffic management systems, depend heavily on the use of faster than real time traffic simulation models. Fast-running traffic models are needed off-line for use in iterative approaches that imitate drivers' adaptation to changes to the n...

The production of petroleum refined products in refineries results in the output of a main product and several byproducts. Conventional oligopoly models cannot be applied to analyze oligopolies in the petroleum industry because they do not consider interaction among products on the supply side. A spatial oligopoly equilibrium model is proposed to a...

The evaluation of on-line intelligent transportation system (ITS) measures, such as adaptive route-guidance and traffic management systems, depends heavily on the use of faster than real time traffic simulation models. Off-line applications, such as the testing of ITS strategies and planning studies, are also best served by fast-running traffic mod...

We consider a multi-class multi-mode variable demand network equilibrium model where the mode choice model is given by aggregate hierarchical logit structures and the destination choice is specified as a multi- proportional entropy type trip distribution model. The travel time of transit vehicles depends on the travel time of other vehicles using t...

Two issues are addressed in this paper: (1) How to reconstruct the product-specific path information based on the link and transfer flows that result from a nonlinear, multimodal, multiproduct network optimization formulation and (2) how to use this information efficiently for various path analyses for transportation planning purposes. The paper al...

The basic timetable based assignment problem is to find an optimal path for a passenger, given an origin node, a destination node, and departure or arrival time information. The deterministic transit assignment does not necessarily minimize the total elapsed travel time, but rather uses weight factors and non-time-based cost elements in determining...

We explore two types of parallel computing implementations for three algorithms for computing temporal shortest paths on transportation networks. One implementation is done on a distributed network of SUN SPARC workstations using PVM and the other on a shared memory computing platform, a SUN SPARC server equipped with eight processors, using thread...

Some of the new possibilities in monitoring traffic and in
deploying new control strategies with the use of mobile phone
localization data are discussed. The possibilities open to these new
applications are enormous given: (1) the extraordinary diffusion of
mobile phones; (2) the new technological developments in the field of
mobile phone data tran...

This paper investigates three methods for dynamic network loading that are considerably less detailed than microscopic modeling. Each of the three methods is based on a different approach to modeling traffic dynamics: link-based travel time functions, the cell-transmission model, and a link-based model derived from a simplified car-following relati...

The evaluation of ITS measures, such as advanced traveler
information systems and advanced traffic management systems depend
heavily on the use of faster than real time traffic simulation methods.
Although many micro-simulation traffic models have already been
developed, their execution times are still too slow for large-scale ITS
applications. Thi...

The analytical approaches to dynamic traffic assignment did not
consider until now the limited capacity of arcs. In this paper a model
and an algorithm are developed for this problem. The method was coded
and computational results were obtained

The work focuses on the analysis of mixed toll stations with
different toll collection systems. A new microscopic simulation model
for the analysis of vehicular flow at a toll plaza system is presented.
It is able to represent the traffic demand/supply interaction and the
effects on traffic induced by the geometric and functional
characteristics of...

The problem of adjusting freight demand matrices to observed flows for multimodal, multicommodity transportation planning is addressed. A model is introduced, and an algorithm is described to solve the corresponding bilevel optimization problem. The algorithm is efficiently implemented by using strategic transportation analysis, an interactive-grap...

Interest in temporal modeling of road traffic has increased over the past decade because of the need to model traffic dynamics for the purpose of evaluating a variety of intelligent transportation components, such as traffic control measures and route guidance. Several approaches are available, including macroscopic, mesoscopic, and microscopic tra...

The continuous dynamic network loading problem (CDNLP) consists in determining, on a congested network, time-dependent arc volumes, together with arc and path travel times, given the time-varying path flow departue rates over a finite time horizon. This problem constitutes an intrinsic part of the dynamic traffic assignment problem. In this paper,...

This paper provides a way to adjust some existing network models in order to take into account the spill-back of congestion. There are a number of models capable of performing Dynamic Network Loading (DNL), i.e., the reproduction of within-day variable link (or local) performances given the path flow rates, but none adequately address the problem o...

Short abstract: In this paper the problem of defining the analytical rules that govern flows at an intersection node is addressed. This problem pertains to flow based Dynamic Network Loading (DNL) models that consider the spill-back of queues. The limited resource of flow supply on the downstream links, of such a node, has to be distributed between...

We present a framework for descent algorithms that solve the monotone variational inequality problem VIPv
which consists in finding a solutionv
*∈Ω
v satisfyings(v
*)T(v−v
*)⩾0, for allv∈Ω
v. This unified framework includes, as special cases, some well known iterative methods and equivalent optimization formulations. A descent method is developed f...

The continuous dynamic network loading problem aims to find, on a congested network, temporal arc volumes, arc travel times, and path travel times given time-dependent path flow rates for a given time period. This problem may be considered as a subproblem of a temporal (dynamic) traffic assignment problem. In this paper, we study this problem and f...

Simulation is a process based on building a computer model that suitably represents a real or proposed system which enables to extract valid inferences on the behavior of the modeled system, from the outcomes of the computer experiments conducted on its model. Simulation has become in recent years one of the most used and powerful tools for systems...

The problem of adjusting (or estimating) an origin-destination matrix by using observed flows on the links of a congested traffic network, which we denote DAP, is considered. After reviewing the previous contributions made in stating models and development solution algorithms for this problem, a nonlinear bilevel programming formulation is proposed...

We present parallel computing implementations of the linear approximation method for solving the fixed demand network equilibrium problem. As the main computational task is that of computing shortest routes, the paper contains as well parallel computing implementations of a shortest routes algorithm. We used the PVM (Parallel Virtual Machine) envir...

STAN is an interactive-graphic multiproduct multimode method for national or regional strategic analysis and planning of freight transportation. We review the main features of the system and describe some of the most important recent developments and enhancements. A complete version of this paper, including numerical and graphical illustrations bas...

The adaptation of the primal simplex method for solving minimum linear cost network flow problems is well known. We present a new data structure for storing the tree associated with a basis and introduce a new adaptive heuristic method for the pivot choice. The pivot choice is modified dynamically during the application of the algorithm. The code w...

The problem of adjusting (or estimating) an origin-destination (O-D) matrix by using observed flows on the links of a congested traffic network, which we denote DAP, is considered in this paper. After reviewing the previous contributions made in stating models and development solution algorithms for this problem, a nonlinear bilevel programming for...

A truncated-Newton method is applied to the spatial price equilibrium problem and the method is compared with other specialized techniques that exploit the inherent network structure of the problem. Variants of the linear conjugate gradient algorithm for approximately solving the Newton equations are discussed. Numerical results for the truncated-N...

The issue of 'feedback' in the traditional four-step urban travel forecasting procedure (UTFP) has reemerged recently under the pressure of the Clean Air Act Amendments of 1990 and the Intermodal Surface Transportation Efficiency Act of 1991. FHWA now requires that metropolitan planning organizations implement feedback in the UTFP. The combined ori...

We consider the problem of optimizing the frequencies of transit lines in an urban transportation network. The problem is formulated first as a nonlinear nonconvex mixed integer programming problem and then it is converted into a bi-level Min-Min nonconvex optimization problem. This problem is solved by a projected (sub)gradient algorithm, where a...

In this paper, we study regularity and optimality conditions for the BLPP by using a marginal function formulation, where the marginal function is defined by the optimal value function of the lower problem. We address the regularity issue by exploring the structure of the tangent cones of the feasible set of the BLPP. These regularity results indic...

We propose a model for the transit equilibrium assignment problem (TEAP) and develop two algorithms for its solution. The behavior of the transit users is modeled by using the concept of hyperpaths (strategies) on an appropriate network (general network) which is obtained from the road network and the transit lines by a transformation which makes e...

Many trips in urban areas are taken by using more than one mode, such as the so called “kiss’n ride” or “park’n ride” trips; the first part of the trip is taken by the private care and then completed by taking one or more transit modes. We present in this paper several approaches to formulating network equilibrium models with combined modes. One of...

We consider the general spatial price equilibrium problem. In order to solve such problems, we develop a Newton type algorithm that is combined with an active constraints strategy to handle the nonnegativety constraints or upper bounds on the variables. At each iteration of the algorithm, the choice of the initial active set is based on the value o...

We report the parallel computing implementations of a primal projected gradient algorithm and the classical RAS dual algorithm for matrix balancing. The computing platform used is a network of Transputers which is suitable for coarse grained parallelization of sequential algorithms. We report computational results with dense matrices of dimension u...

A transit equilibrium assignment problem assigns the passenger flows on to a congested transit (public transportation) network with asymmetric cost functions and a fixed origin-destination matrix. This problem which may be formulated in the space of hyperpath flows, is transformed into an equivalent problem in the space of total arc flows and an au...

We consider a normative transshipment problem for freight flows over a multimodal network. In addition to computing the flows, which minimize a convex cost objective function, an origin/destination matrix which corresponds to the minimal cost flows must be computed as well. The supply is given as totals at origins and the demand as totals at destin...