Intra-Period (Within-Day) Dynamic Models

  • Ennio Cascetta
Part of the Applied Optimization book series (APOP, volume 49)


The mathematical models described in the previous chapters are based on the assumptions of intra-period stationariety. This is equivalent to assuming, as stated in Chapter 1, that all significant variables are constant, at least on average, over successive sub-intervals of a reference period long enough to allow the system to reach stationariety condition. This assumption, although acceptable for many applications, does not allow for the satisfactory simulation of some transportation systems such as heavily congested urban road networks or low frequency scheduled services. In the first case, some important phenomena cannot be reproduced by traditional intra-period static models, including demand peaks, temporary capacity variations, temporary over-saturation of supply elements, and formation and dispersion of queues. In the second case, low-frequency services (e.g. two flights per day) may call into question the assumption of intra-period uniform supply and mixed preventive-adaptive users’ choice behavior introduced in the previous chapters. To simulate these aspects, different intra-periodal or within-day dynamic models have recently been developed; these models are usually referred to in the literature as (within-day) Dynamic Traffic Assignment (DTA) models, implying that dynamic assignment models require within-day dynamic demand and supply models.


Travel Time Supply Model Link Flow Dynamic Traffic Assignment Travel Time Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference Notes

  1. [22]
    Ben Akiva M., M. Cyna, and A. de Palma (1984). Dynamic model of peak period congestion. Transportation Research 18B: 339–355.Google Scholar
  2. [188]
    Merchant D. K., and Nemhauser G.L. (1978). A model and an algorithm for the dynamic traffic assignment problem. Transportation Science 12: 183–199.Google Scholar
  3. [72]
    Cascetta E., and G.E. Cantarella (1991). A day-to-day and within-day dynamic stochastic assignment model Transportation Research 25A: 277–291Google Scholar
  4. [124]
    Friesz T.L., J. Luque, R.L. Tobin, and B.W. Wie (1989). Dynamic network traffic assignment considered as continuous time optimal control problem. Operations Research 37: 893–901.Google Scholar
  5. [84]
    Chabini I., and S. Kachani (1999). Analytical dynamic network loading models: analysis of a single link network Forthcoming in Transportation Research.Google Scholar
  6. [266]
    Wu.J. H., Y. Chen, and M. Florian (1995). The continuous dynamic network loading problem: a mathematical formulation and solution method. Transportation Research 32B: 173–187.Google Scholar
  7. [10]
    Astarita V. (1996). A continuous time link based model for dynamic network loading based on travel time function. Proceedings of the 13th International Symposium on Transportation and Traffic Theory. Lyon, France.Google Scholar
  8. [267]
    Xu Y., J. Wu, M. Florian, P. Marcotte, and D.L. Zhu (1994). New advances in the continuous dynamic network loading problem Forthcoming in Transportation Science.Google Scholar
  9. [152]
    Jayakarishnan R., H. Mahamassani, and T. Hu (1994). An evaluation tool for advanced traffic information and management system in urban networks. Transportation Research 2C: 129–147.Google Scholar
  10. [25]
    Ben-Akiva M., M. Bierlaire, J. Bottom, H. Koutsopoulos, and R. Mishalani (1997). Development of a route guidance generation system for real-time application. Proceedings of the 8th IFAC Symposium on Transportation Systems, Chania, Greece.Google Scholar
  11. [47]
    Cantarella G. E., E. Cascetta, V. Adamo, and V. Astarita (1999). A doubly dynamic traffic assignment model for planning applications. Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Jerusalem, Israel.Google Scholar
  12. [269]
    Yang Q., and H. Koutsopoulos (1996). A microscopic traffic simulator for evaluation of dynamic traffic management systems. Transportation Research 4C: 113–129.Google Scholar
  13. [2]
    Abkowitz M.D. (1981). An analysis of the commuter departure time decision. Transportation 10: 283–297.CrossRefGoogle Scholar
  14. [237]
    Small K.A. (1982). The scheduling of commuter Activities: work trips The American Economic Review 72: 467–479.Google Scholar
  15. [62]
    Cascetta E., A. Nuzzolo, and L. Biggiero (1992). Analysis and modeling of commuters departure time and route choices in urban networks. Proceedings of the 2nd International Seminar on Urban Traffic Networks, Capri, Italy.Google Scholar
  16. [175]
    Mahamassani H., and Y. H. Liu (1999). Dynamics of commuting decision behaviour under Advanced Traveller Information Systems. Transportation Research 7C: 91–107.Google Scholar
  17. [41]
    Boyce D.E., B. Ran, and L. J. Le Blanc (1991). Dynamic user-optimal traffic assignment model: a new model and solution technique. Proceedings of the 151 TRISTAN, Montreal, Canada.Google Scholar
  18. [150]
    Janson B. N. (1989). Dynamic traffic assignment for urban road network. Transportation Research 25B: 143–161.Google Scholar
  19. [249]
    Vytoulkas P.K. (1990). A dynamic stochastic assignment model for the analysis of general networks Transportation Research 24B: 453–469.Google Scholar
  20. [122]
    Friesz T. L., D. Bernstein, T.E. Smith, R. L. Tobin, and B.W. Wie (1993). A variational inequality formulation of the dynamic network users equilibrium problem. Operations Research 41: 179–191.Google Scholar
  21. [257]
    Wie B. W., T. L. Friesz, and T. L. Tobin (1990). Dynamic user optimal traffic assignment on congested multi-destination networks. Transportation Research 24B: 431–442.Google Scholar
  22. [227]
    Ran B., and D. E. Boyce (1994). Dynamic urban transportation network models: theory and implications for Intelligent Vehicle-Highway Systems Springer-Verlag.Google Scholar
  23. [96]
    Daganzo C. (1983). Stochastic Network equilibrium problem with multiple vehicle types and asiymmetric, indefinite link cost jacobians Transportation Science 17: 282–300.Google Scholar
  24. [49]
    Cantarella G.E. (1997). A General Fixed-Point Approach to Multi-Mode Multi-User Equilibrium Assignment with Elastic Demand Transportation Science 31: 107–128.Google Scholar
  25. [73]
    Cascetta E., and Improta A.A. (1999). Estimation of travel demand using traffic counts and other data sources. Optimization Days 1999 ( Michael Florian’s special session) Montreal, Canada.Google Scholar
  26. [153]
    Jha M., S. Madanat, and S. Peeta (1998). Perception updating and day-to-day travel choice dynamics in traffic networks with information provision. Transportation Research 6C: 189–212.Google Scholar
  27. [65]
    Cascetta E., A. Nuzzolo, F. Russo, and A. Vitetta (1996). A new route choice logit model overcoming IIA problems: specification and some calibration results for interurban networks. Proceedings of the 13th International Symposium on Transportation and Traffic Theory ( Jean-Baptiste Lesort ed. ), Pergamon Press.Google Scholar
  28. [75]
    Cascetta E., L. Biggiero, A. Nuzzolo, and F. Russo (1996). A system of within-day dynamic demand and assignment models for scheduled inter-city services Proceedings of the 24th European Transportation Forum, London, Great Britain.Google Scholar
  29. [211]
    Nuzzolo A., U. Crisalli, and F. Gangemi (2000). A behavioural choice model for the evaluation of railway supply and pricing policies. Transportation Research 35A: 211–226.Google Scholar
  30. [139]
    Hickman M.D., and N.H.M. Wilson (1995). Passenger travel time and path choice implications of real-time transit information. Transportation Research 3C: 211–226.Google Scholar
  31. [138]
    Hickman M.D., and D.H. Bernstein (1997). Transit service and path choice models in stochastic and time-dependent networks. Transportation Science 31: 129–146.Google Scholar
  32. [210]
    Nuzzolo A., F. Russo, and U. Crisalli (1999). A doubly dynamic assignment model for congested urban transit networks. Proceedings of 27th European Transportation Forum, Cambridge, England, Seminar F: 185–196.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Ennio Cascetta
    • 1
  1. 1.Dipartimento di Ingegneria dei Trasporti “Luigi Tocchetti”Università degli Studi di Napoli “Federico II”NapoliItaly

Personalised recommendations