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Sample networks from Racine WI

Article on Core Concepts of QRS II’s Transit Assignment

This article, published over 30 years ago, describes the core concepts of QRS II’s stochastic transit assignment algorithm.  We have recently scanned this article because of an request for more information about the algorithm. 


Without NCHRP #187 there would not have been a QRS II. However, many of the innovative concepts in QRS II come from research on travel forecasting by Alan Horowitz. Here are a few articles that influenced the philosophy and structure of QRS II and GNE.

  1. Alan J. Horowitz and Sam Granato, “Practical Considerations in Implementing Travel Time Reliability in Regionwide Travel Forecasting”, Transportation Research Record, Journal of the Transportation Research Board, 2012 (in press).
  2. Alan J. Horowitz, Origin-Destination Table Disaggregation Using Biproportional Least Squares Estimation, Transportation, Vol. 37, pp. 689-703, 2010.
  3. Alan J. Horowitz and Layali Dajani, “Tests of Dynamic Extensions to a Family of Trip Table Refinements Methods”, Transportation Research Record, Journal of the Transportation Research Board, #2003, 2007, pp. 27-34.
  4. Alan J. Horowitz, “Tests of a Family of Trip Table Refinements for Quick Response Travel Forecasting”, Transportation Research Record, Journal of the Transportation Research Board, Number 1921, 2005, pp. 19-26.
  5. Alan J. Horowitz, “Lowry-Type Land Use Models”, Handbooks in Transportation Planning, No 5, Transport Geography and Spatial Systems, 2004, pp. 167-182.
  6. Alan J. Horowitz, “Internodal Delay Issues in Long-Range Adaptive Travel Forecasts”, Transportation Research Record Journal #1783, 2002, pp. 49-54.
  7. Alan J. Horowitz, “Computational Issues in Increasing the Spatial Precision of Traffic Assignments”, Transportation Research Record Journal, #1777, 2001, pp. 68-74.
  8. Alan J. Horowitz, “Integrating GIS Concepts into Transportation Network Data Structures, Transportation Planning and Technology, 1997, Vol 21, pp 139-153.
  9. Alan J. Horowitz, “Intersection Delay in Regionwide Traffic Assignment:  Implications of the 1994 Update of the Highway Capacity Manual”, Transportation Research Record 1572, 1997, pp 1-8.
  10. Alan J. Horowitz and Edward A. Beimborn, “Methods and Strategies for Transit Benefit Assessment”, Transportation Research Record, No. 1496, 1995, pp. 9-16.
  11. Alan J. Horowitz, “Assessing User Benefits of Transit System Improvements and Spatially Varying Demands”, Transportation Research Record, No. 1452, 1995, pp. 1-9.
  12. Alan J. Horowitz, “A Revised Queuing Model of Delay at All-Way Stop Controlled Intersections”, Transportation Research Record, No. 1398, 1993, pp. 49-53.
  13. Alan J. Horowitz, “Implementing Travel Forecasting with Traffic Operational Strategies”, Transportation Research Record, No. 1365, 1992, pp. 54-61.
  14. “Integrated Traffic Flow and Region-Wide Travel Forecasting”, paper presented at the 61st Annual Meeting of the Institute of Transportation Engineers, September 25, 1991. Paper published in conference proceedings.
  15. Alan J. Horowitz, “Convergence of Certain Traffic/Land-Use Equilibrium Assignment Models”, Environment and Planning A, Vol. 23, 1991, pp. 371-383.
  16. Alan J. Horowitz, “Subarea Focussing with Combined Models of Spatial Interaction and Equilibrium Assignment”, Transportation Research Record, No. 1285, 1990, pp. 1-8.
  17. Alan J. Horowitz, “Convergence Properties of Some Iterative Traffic Assignment Algorithms”, Transportation Research Record, No. 1220, 1989, pp. 21-27.
  18. Alan J. Horowitz, “Extensions of Stochastic Multipath Trip Assignment to Transit Networks,” Transportation Research Record, No. 1108, pp. 66-72, 1987.
  19. Alan J. Horowitz, “Applications of the General Network Editor”, in Microcomputer Applications in Transportation II, ed. Robert E. Stammer and Mark D. Abkowitz, American Society of Civil Engineers, New York, 1987.
  20. Alan J. Horowitz and Anand Pithavadian, “Generalized Computer-Aided Design of Transportation Networks”, Transportation Quarterly, Vol. 41, No. 3, July 1987, pp. 397-409.
  21. Alan J. Horowitz and Anand Pithavadian, “Towards a Data Structure for Computer-Aided Design of Transportation Networks”, Transportation Research B, Vol. 21B, No. 4, 1987, pp. 317-321.
  22. Alan J. Horowitz and Dennis Zlosel, “Transfer Penalties: Another Look at Transit Riders’ Reluctance to Transfer”, Transportation, Vol. 10, No. 3, September 1981, pp. 279-282.
  23. Alan J. Horowitz, “Subjective Value of Time in Bus Transit Travel”, Transportation, Vol. 10, No. 2, June 1981, pp. 149-164.
  24. Alan J. Horowitz, “The Subjective Value of Time Spent in Travel”, Transportation Research, Vol. 12, 1979, pp. 385-393.
  25. Alan J. Horowitz, “Developable Area and Trip Distribution in Residential Location: A Detroit Case Study”, Journal of Regional Science, Vol. 18, No. 3, December 1978, pp. 429-446.
  26. Alan J. Horowitz, “The Evaluation of Transportation Model Random Error in Social and Environmental Indices”, Environment and Planning A, Vol. 9, April, 1977, pp. 385-394.