Abstract
A probabilistic model for time characteristic of a traffic flow moving on a motorway is proposed and investigated in this paper. The time intervals between consecutive cars are supposed to be dependent and have different distribution. Cars with the slow and fast movement are distinguished in the traffic flow. The mathematical model of such traffic flow is represented as a control cybernetic system of a certain class. The methods to derive estimate for the parameters of the control cybernetic system are proposed in order to select the adequate traffic flow model in the form of batches flow. These methods are approved processing the statistical data of the Bartlett traffic flow. Effectiveness of suggested methods for the parameters estimation and algorithms for splitting a real traffic flow into the batches is demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Fedotkin, M.A.: Service processes and control systems. Math. Ques. Cybern. (collected articles) 6, 51–70 (1996). Science-Physmathlit, Moscow
Lyapunov, A.A., Yablonskiy, S.V.: Theoretical problems of cybernetics. Cybern. Probl. (collected scientific articles) 9, 5–22 (1963). Physmathgiz, Moscow
Fedotkin, M.A.: Optimal control for conflict flows and market point processes with selected discrete component. I. Lietuvos Matematikos Rinkinys 28(4), 783–794 (1988)
Fedotkin, M.A.: Optimal control for conflict flows and market point processes with selected discrete component. II. Lietuvos Matematikos Rinkinys 29(1), 148–159 (1989)
Fedotkin, M.A., Zorine, A.V.: Optimization of control of doubly stochastic nonordinary flows in time-sharing systems. Autom. Remote Control 66(7), 1115–1124 (2005)
Proidakova, E.V., Fedotkin, M.A.: Control of output flows in the system with cyclic servicing and readjustments. Autom. Remote Control 69(6), 993–1002 (2008)
Fedotkin, M.A., Fedotkin, A.M.: Analysis and optimization of output processes of conflicting Gnedenko-Kovalenko traffic streams under cyclic control. Autom. Remote Control 70(12), 2024–2038 (2009)
Haight, F.A.: Mathematical Theories of Traffic Flow. Academic Press, New York (1963)
Fedotkin, M.A.: Models in Theory of Probability. Physmathlit, Moscow (2011)
Saaty, T.L.: Elements of Queueing Theory with Applications. McGraw Hill Book Company Inc., New York (1961)
Fedotkin, M.A., Kudryavsev, E.V., Rachinskaya, M.A.: About correctness of probabilistic models for dynamics of the traffic flows on the motorway. In: Proceedings of the International Workshop on Distributed Computer and Communication Networks (DCCN-2010), 26–28 October 2010. R&D Company Information and Networking Technologies, Moscow, Russia (2010)
Gnedenko, B.V., Kovalenko, I.N.: Introduction in Queuing Theory. LKI, Moscow (2007)
Fedotkin, A.M., Fedotkin, M.A.: Model for refusals of elements of a controlling system. In: Materials of the First French–Russian Conference on Longevity, Aging and Degradation Models in Reliability, Public Health, Medicine and Biology (LAD 2004), vol. 2, pp. 136–151. St. Petersburg State Polytechnical University, St. Petersburg (2004)
Bartlett, M.S.: The spectral analysis of point processes. J. Roy. Stat. Soc. Ser. B. 25, 264–296 (1963)
Cox, D.R., Lewis, P.A.W.: The Statistical Analysis of Series of Events. Wiley, London (1966)
Sachs, L.: Statistische Auswertungsmethoden. Springer, Heidelberg (1972)
Cramer, H.: Mathematical Methods in Statistics. Mir, Moscow (1975)
Fedotkin, M.A., Rachinskaya, M.A.: Investigation of traffic flows characteristics in case of small density. queues: flows, systems, networks. In: Proceedings of the International Conference Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks, vol. 21, pp. 82–87. BSU-RIVH, Minsk (2011)
Fedotkin, M.A., Rachinskaya, M.A.: Investigation of mathematical model of traffic based on Lyapunov-Yablonskiy method. Problems of theoretical cybernetics . In: Proceedings of XVI International Conference, pp. 508–512, 20–25 June 2011. Izd-vo of State University of Nizhni Novgorod, Nizhni Novgorod (2011)
Fedotkin, M., Kudryavtcev, E., Rachinskaya, M.: Simulation and research of probabilistic regularities in motion of traffic flows. In: Proceedings of the International Workshop on Applied Methods of Statistical Analysis, Simulations and Statistical Inference (AMSA’2011), pp. 11–18, 20–22 September 2011. Publishing House of NSTU, Novosibirsk, Russia (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Fedotkin, M., Rachinskaya, M. (2014). Parameters Estimator of the Probabilistic Model of Moving Batches Traffic Flow. In: Vishnevsky, V., Kozyrev, D., Larionov, A. (eds) Distributed Computer and Communication Networks. DCCN 2013. Communications in Computer and Information Science, vol 279. Springer, Cham. https://doi.org/10.1007/978-3-319-05209-0_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-05209-0_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05208-3
Online ISBN: 978-3-319-05209-0
eBook Packages: Computer ScienceComputer Science (R0)