Abstract
The theory of input flows was developed in the works of A.K. Erlang, A.Ya. Hinchin, C. Palm, B.V. Gnedenko, and other authors. The theory assumed independence of the intervals between successive moments of receiving similar arrivals. In this paper, we propose a nonstandard way of describing and studying the incoming flows of moving nonhomogeneous arrivals. Moreover, we consider the flows of a complex probabilistic structure with the intervals between successive arrivals to be dependent random variables and have different distributions. Methods and results of studies of the properties of flows are substantially based on laws of flows of nonhomogeneous claims, both in space and in time. In general, this allows one to determine the nonlocal description of the spatial and time characteristic of flow even if they are statistically dependent. For the first time a method of approximation of the flow of complex probabilistic structure with nonordinary Poisson flow of a certain class is proposed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fedotkin, M.A., Nonlocal method of determination of regulated random processes, in Sb. nauchnykh rabot. “Matematicheskie voprosy kibernetiki” (Mathematical Questions of Cybernetics. Collection of Papers), Moscow: Nauka-Fizmatlit, 1998, No. 7, pp. 333–344.
Fedotkin, M.A. and Fedotkin, A.M., Analysis and optimization of output processes of conflicting Gnedenko-Kovalenko traffic flows under cyclic control, Autom. Remote Control 2009, vol.70, pp. 2024–2038.
Jagerman, D.L., Melamed, B., and Willinger, W., Stochastic modeling of traffic processes, in Frontiers in Queueing: Models and Applications in Science and Engineering, Dshalalov, J.H., ed., CRC, 1997, pp. 271–320.
Clegg, R.G., Landa, R., and Rio, M., Criticisms of modelling packet traffic using long-range dependence, J. Comput. System Sci., 2011, vol. 77, pp. 861–868.
Haight, F.A., Mathematical Theories of Traffic Flow, New York: Academic, 1963.
Fedotkin, M.A., Modeli v teorii veroyatnostei (Models in Probability Theory), Moscow: FIZMATLIT, 2012.
Saaty, T.L., Elements of Queuing Theory with Applications, New York: McGraw Hill, 1961.
Fedotkin, M.A., About mechanism of street traffic control at a crossroad with an exponential service law, Radiophys. Quant. Electr. 1967, vol. 10, pp. 505–512.
Fedotkin, M.A., Algebraic properties of distributions for Chung functionals in homogeneous Markov chains with enumerable set of states, Doklady Akademii Nauk SSSR 1976, vol. 227, no. 1, pp. 43–46.
Gnedenko, B.V. and Kovalenko, I.N., Vvedenie v teoriyu massovogo obsluzhivaniya (Introduction into Queueing Theory), Moscow: Nauka, 1987.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.A. Fedotkin, A.M. Fedotkin, E.V. Kudryavtsev, 2014, published in Avtomatika i Vychislitel’naya Tekhnika, 2014, No. 6, pp. 62–74.
About this article
Cite this article
Fedotkin, M.A., Fedotkin, A.M. & Kudryavtsev, E.V. Construction and analysis of a mathematical model of spatial and temporal characteristics of traffic flows. Aut. Control Comp. Sci. 48, 358–367 (2014). https://doi.org/10.3103/S0146411614060030
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0146411614060030