Advanced Search
MyIDEAS: Login to save this paper or follow this series

Space-time modeling of traffic flow

Contents:

Author Info

  • Kamarianakis, Yiannis

    ()

  • Prastacos, Poulicos

    ()

Abstract

A key concern in transportation planning and traffic management is the ability to forecast traffic flows on a street network. Traffic flows forecasts can be transformed to obtain travel time estimates and then use these as input to travel demand models, dynamic route guidance and congestion management procedures. A variety of mathematical techniques have been proposed for modeling traffic flow on a street network. Briefly, the most widely used theories are: -Kinetic models based on partial differential equations that describe waves of different traffic densities, -deterministic models that use nonlinear equations for the estimation of different car routes, -large scale simulation models such as cellular automata and, -stochastic modeling of traffic density at distinct points in space. One problem with these approaches is that the traffic flow process is characterized by nonstationarities that cannot be taken into account by the vast majority of modeling strategies. However, recent advances in statistical modeling in fields such as econometrics or environmetrics enable us to overcome this problem. The aim of this work is to present how two statistical techniques, namely, vector autoregressive modeling and dynamic space-time modeling can be used to develop efficient and reliable forecasts of traffic flow. The former approach is encountered in the econometrics literature, whereas the later is mostly used in environmetrics. Recent advances in statistical methodology provide powerful tools for traffic flow description and forecasting. For a purely statistical approach to travel time prediction one may consult Rice and van Zwet (2002). In this work, the authors employ a time varying coefficients regression technique that can be easily implemented computationally, but is sensitive to nonstationarities and does not take into account traffic flow information from neighboring points in the network that can significantly improve forecasts. According to our approach, traffic flow measurements, that is count of vehicles and road occupancy obtained at constants time intervals through loop detectors located at various distinct points of a road network, form a multiple time series set. This set can be described by a vector autoregressive process that models each series as a linear combination of past observations of some (optimally selected) components of the vector; in our case the vector is comprised by the different measurement points of traffic flow. For a thorough technical discussion on vector autoregressive processes we refer to Lutkerpohl (1987), whereas a number of applications can be found in Ooms (1994). Nowadays, these models are easily implemented in commercial software like SAS or MATLAB; see for example LeSage (1999). The spatial distribution of the measurement locations and their neighboring relations cannot be incorporated in a vector autoregressive model. However, accounting for this information may optimize model fitting and provide insight into spatial correlation structures that evolve through time. This can be accomplished by applying space-time modeling techniques. The main difference of space-time models encountered in literature with the vector autoregressive ones lies in the inclusion of a weight matrix that defines the neighboring relations and places the appropriate restrictions. For some early references on space-time models, one could consult Pfeifer and Deutsch (1980 a,b); for a Bayesian approach, insensitive to nonstationarities we refer to Wikle, Berliner and Cressie (1998). In this work, we discuss how the space-time methodology can be implemented to traffic flow modeling. The aforementioned modeling strategies are applied in a subset of traffic flow measurements collected every 15 minutes through loop detectors at 74 locations in the city of Athens. A comparative study in terms of model fitting and forecasting accuracy is performed. Univariate time series models are also fitted in each measurement location in order to investigate the relation between a model's dimension and performance. References: LeSage J. P. (1999). Applied Econometrics using MATLAB. Manuscript, Dept. of Economics, University of Toronto Lutkerpohl H. (1987). Forecasting Aggregated Vector ARMA Processes. Lecture Notes in Economics and Mathematical Systems. Springer Verlag Berlin Heidelberg Ooms M. (1994). Empirical Vector Autoregressive Modeling. Springer Verlag Berlin Heidelberg Pfeifer P. E., and Deutsch S. J. (1980a). A three-stage iterative procedure for Space-Time Modeling. Technometrics, 22, 35-47 Pfeifer P. E., and Deutsch S. J. (1980b). Identification and Interpretation of First-Order Space-Time ARMA models. Technometrics, 22, 397-408 Rice J., and van Zwet E. (2002). A simple and effective method for predicting travel times on freeways. Manuscript, Dept. of Statistics, University of California at Berkeley Wikle C. K., Berliner L. M. and Cressie N. (1998). Hierarchical Bayesian space-time models. Environmental and Ecological Statistics, 5, 117-154

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www-sre.wu-wien.ac.at/ersa/ersaconfs/ersa02/cd-rom/papers/141.pdf
Download Restriction: no

Bibliographic Info

Paper provided by European Regional Science Association in its series ERSA conference papers with number ersa02p141.

as in new window
Length:
Date of creation: Aug 2002
Date of revision:
Handle: RePEc:wiw:wiwrsa:ersa02p141

Contact details of provider:
Postal: Welthandelsplatz 1, 1020 Vienna, Austria
Web page: http://www.ersa.org

Related research

Keywords:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Raffaella Giacomini & Clive W.J. Granger, 2002. "Aggregation of Space-Time Processes," Boston College Working Papers in Economics 582, Boston College Department of Economics.
  2. Elhorst, J.P., 2000. "Dynamic models in space and time," Research Report 00C16, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  3. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
  4. Whittaker, Joe & Garside, Simon & Lindveld, Karel, 1997. "Tracking and predicting a network traffic process," International Journal of Forecasting, Elsevier, vol. 13(1), pages 51-61, March.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Yiannis Kamarianakis, 2006. "Hierarchical Bayesian Modeling For Spatial Time Series: An Alternative Approach To Spatial Sur," Working Papers 0605, University of Crete, Department of Economics.
  2. Yiannis Kamarianakis & Poulicos Prastacos, 2006. "Spatial Time-Series Modeling: A review of the proposed methodologies," Working Papers 0604, University of Crete, Department of Economics.
  3. Tao Cheng & James Haworth & Jiaqiu Wang, 2012. "Spatio-temporal autocorrelation of road network data," Journal of Geographical Systems, Springer, vol. 14(4), pages 389-413, October.
  4. Shanjiang Zhu & David Levinson, 2011. "A Portfolio Theory of Route Choice," Working Papers 000096, University of Minnesota: Nexus Research Group.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:wiw:wiwrsa:ersa02p141. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Gunther Maier).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.