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Origin-destination matrix estimation from traffic counts
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
2003 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

For most kind of analyses in the field of traffic modeling, there is a need for origin-destination (OD) matrices, which specify the travel demands between the origin and destination nodes in the network. The process of obtaining OD-matrices is long, complicated and expensive. The counting of traffic, which provides link flow observations, therefore is an opportune possibility for easily up-dating the information on the travel demand. This thesis concerns the estimation of OD-matrices from traffic counts. 

We will consider the problem to estimate OD-matrices for both time-indepenent and time-dependent models. Many models have been suggested for the time-independent case, where the quantities represent and average situation. If a user equilibrium is assumed for the link flows in the network, a bilevel problem structure is recognized, where the link flows are implicitly expressed as a traffic assignment of the present OD-matrix. A descent heuristic, which is an adaptation of the well-known projected gradient method, is proposed. Special attention is given to the problem of approximating the Jacobian matrix, which expresses the change of a certain link flow with respect to a unit change of the travel demand in a certain pair of origin and destination.

When a time dimension is introduced, the estimation problem becomes more complex. Besides the problem of distributing the travel demand onto different routes, the flow propagation with respect to time must be handled. A general time-dependent extension of the estimation problem is given and the complications with dynamic traffic assignment are discussed. In a case study, the conventional solution technique is improved by introducing pre-adjustment schemes, which the structure of the information provided by the OD-matrix and the link flow observations.

Place, publisher, year, edition, pages
Linköpings Universitet: Linköpings universitet , 2003. , 4 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1057
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-38828Local ID: 45788ISBN: 91-7373-785-2 (print)OAI: oai:DiVA.org:liu-38828DiVA: diva2:259677
Presentation
2003-11-28, Sal TP45, Hus Täppan, Linköpings Universitet, Campus Norrköping, Linköping, 10:15 (Swedish)
Opponent
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-12-10
List of papers
1. Traffic Demand Modeling and Origin-Destination Matrix Estimation
Open this publication in new window or tab >>Traffic Demand Modeling and Origin-Destination Matrix Estimation
(English)Manuscript (preprint) (Other academic)
Abstract [en]

An origin-destination (OD) matrix describes the travel demand between all pairs of origins and destinations in a traffic network. OD-matrices are essential input for most types traffic models, both for long-term planning, where the actions are meant to be permanent, and for short-term planning, where the operational situation is managed. This paper is a literature overview of models and methods for obtaining reliable OD-matrices.

We present the Four-stage model which is commonly used for sequentially computing the number of trips starting and terminating at the centroid nodes, the distribution to travel demand between origins and destinations, the split onto different travel modes and the choice-based assignment of routes and links in the network. Further, we identify the information contained in traffic counts as an important source for adjusting the computed OD-matrix. The generic OD-matrix estimation problem from link flow observations is formulated and we discuss different solution techniques and how they relate to the assumptions used for the assignment of travel demand to routes and links.

Time-dependence is a fundamental difference between the model types. A time-independent (static) model describes a steady state, which represents and average situation. If the interaction between sequential time periods is to be analyzed, however, a dynamic model is required. The time dimension is a complicating factor, since not only the route choice, but also the flow propagation must be taken care of in the model. Especially those models where the OD-matrix is to be estimated in real-time, must be simplified as to the computational effort.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-102432 (URN)
Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2013-12-10
2. A Heuristic for the Bilevel Origin–Destination Matrix Estimation Problem
Open this publication in new window or tab >>A Heuristic for the Bilevel Origin–Destination Matrix Estimation Problem
2008 (English)In: Transportation Research Part B: Methodological, ISSN 0191-2615, E-ISSN 1879-2367, Vol. 42, no 4, 339-354 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we consider the estimation of an origin–destination (OD) matrix, given a target OD-matrix and traffic counts on a subset of the links in the network. We use a general nonlinear bilevel minimization formulation of the problem, where the lower level problem is to assign a given OD-matrix onto the network according to the user equilibrium principle. After reformulating the problem to a single level problem, the objective function includes implicitly given link flow variables, corresponding to the given OD-matrix. We propose a descent heuristic to solve the problem, which is an adaptation of the wellknown projected gradient method. In order to compute a search direction we have to approximate the Jacobian matrix representing the derivatives of the link flows with respect to a change in the OD-flows, and we propose to do this by solving a set of quadratic programs with linear constraints only. If the objective function is differentiable at the current point, the Jacobian is exact and we obtain a gradient. Numerical experiments are presented which indicate that the solution approach can be applied in practice to medium to large size networks.

Place, publisher, year, edition, pages
Institutionen för teknik och naturvetenskap, 2008
Keyword
Origin-Destination matrix; Sensitivity analysis; User-equilibrium
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-11461 (URN)10.1016/j.trb.2007.09.005 (DOI)
Note
Original publication: Jan T Lundgren and Anders Peterson, A Heuristic for the Bilevel Origin–Destination Matrix Estimation Problem, 2008, Transportation Research Part B: Methodological, (42), 4, 339-354. http://dx.doi.org/10.1016/j.trb.2007.09.005. Copyright: Elsevier B.V., http://www.elsevier.com/Available from: 2008-04-03 Created: 2008-04-03 Last updated: 2017-12-13
3. Methods for Pre-Adjusting Time-Dependent Origin–Destination Matrices: an Application to Gothenburg
Open this publication in new window or tab >>Methods for Pre-Adjusting Time-Dependent Origin–Destination Matrices: an Application to Gothenburg
2003 (English)In: Proceedings of the 10th World Congress and Exhibition on Intelligent Transport Systems and Services, Madrid, Spain, November 16–20, 2003, no 2436Conference paper, Published paper (Refereed)
Abstract [en]

We present a number of schemes for adjusting time-dependent travel demand information with respect to link flow observations. The aim is to utilize the structure of the given OD-matrix, which is compounded from different sources, for making simple overall adjustments. These pre-adjustments are then followed up with a complete OD-estimation procedure, such as that in Contram. Numerical results from the city of Gothenburg are presented.

National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-14467 (URN)
Conference
10th World Congress and Exhibition on Intelligent Transport Systems and Services, Madrid, Spain, November 16–20
Available from: 2007-06-04 Created: 2007-06-04 Last updated: 2013-12-10

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