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On single-lane roads

Published online by Cambridge University Press:  01 July 2016

A. J. Koning
A. J. Koning*
Affiliation:
University of Limburg
*
∗Postal address: Department of Medical Informatics and Statistics, University of Limburg, P.O. Box 616, 6200 MD Maastricht, The Netherlands. Part of this research was performed at the Centre for Mathematics and Computer Science, Amsterdam.
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Abstract

A road which narrows at a bottleneck from an ∞-lane road to a one-lane road is studied with the aid of two stochastic processes. Special attention is given to headways and gaps. At the bottleneck an equilibrium headway can be viewed as the maximum of a shifted exponential random variable and a minimum headway. After the bottleneck the situation becomes far more complicated. However, limiting results are obtained for headways and gaps at a large distance from the bottleneck. The asymptotic behavior of headways and gaps is largely determined by the behavior of the desired speed distribution at the lower extreme of its support.

Keywords

TRAFFIC FLOWPOINT PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 1 , March 1989 , pp. 142 - 158
Copyright
Copyright © Applied Probability Trust 1989 

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References

Branston, D. (1976) Models of single lane time headway distributions. Trans. Sci. 10, 125–128.CrossRefGoogle Scholar
Breiman, L. (1963) The Poisson tendency in traffic distribution. Ann. Math. Statist. 34, 308–311.Google Scholar
Breiman, L. (1969) Data and models in homogeneous one-way traffic flow. Transpn Res. 3, 235–249.Google Scholar
Brill, E. A. (1971) Point processes arising in vehicular traffic flow. J. Appl. Prob. 8, 809–814.CrossRefGoogle Scholar
Buckley, D. J. (1968) A semi Poisson model of traffic flow. Trans. Sci. 2, 107–133.Google Scholar
Burke, P. J. (1956) The output of a queuing system. Operat. Res. 4, 699–704.CrossRefGoogle Scholar
Burke, P. J. (1972) Output processes and tandem queues. Proc. Symp. Computer Communications Networks and Teletraffic, Polytechnic Institute of Brooklyn Press, New York, 419–428.Google Scholar
Cohen, J. W. (1982) On the M/G/2 queueing model. Stoch. Proc. Appl. 12, 231–240.Google Scholar
Cooper, R. B. (1981) Introduction to Queueing Theory, 2nd edn. North-Holland, New York.Google Scholar
Cowan, R. J. (1971) A road with no overtaking. Austral. J. Statist. 13, 94–116.Google Scholar
Cowan, R. J. (1975) Useful headway models. Transpn Res. 9, 371–375.Google Scholar
Cowan, R. J. (1980) Further results on single-lane traffic flow. J. Appl. Prob. 17, 523–531.Google Scholar
Daley, D. J. (1976) Queueing output processes. Adv. Appl. Prob. 8, 395–415.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. 2 Wiley, New York.Google Scholar
Helland, I. S. and Nilsen, T. S. (1976) On a general random exchange model. J. Appl. Prob. 13, 781–790.Google Scholar
Hodgson, V. (1968) The time to drive through a no-passing zone. Trans. Sci. 2, 252–264.Google Scholar
Kallenberg, O. (1978) On the asymptotic behavior of line processes and systems of non-interacting particles. Z. Wahrscheinlichkeitsth. 43, 65–95.CrossRefGoogle Scholar
Kingman, J. F. C. (1965) The heavy traffic approximation in the theory of queues. Proc. Symp. Congestion Theory, ed. Smith, W. L., and Wilkinson, W. E.. University of North Carolina Press, Chapel Hill, N.C. Google Scholar
Kleinrock, L. (1975) Queueing Systems, Volume I: Theory. Wiley, New York.Google Scholar
Koning, A. J. (1985) On roads with no overtaking. Report MS-R8508, Centrum voor Wiskunde en Informatica, Amsterdam.Google Scholar
Köllerström, J. (1974) Heavy traffic theory for queues with several severs I. J. Appl. Prob. 11, 544–552.Google Scholar
Kühne, R. (1984) Fernstrassenverkehrsbeeinflussung und Physik der Phasenübergänge. Physik in unserer Zeit 15, 84–93.Google Scholar
Lánský, P. (1978) On a modification of Rényi’s traffic model. Apl. Mat. 23, 39–51.Google Scholar
Lighthill, M. H. and Whitham, G. B. (1955) On kinematic waves II, a theory of traffic flow on long crowded roads. Proc. R. Soc. London A229, 317–345.Google Scholar
Lindley, D. V. (1952) The theory of queues with a single server. Proc. Camb. Phil. Soc. 48, 277–289.CrossRefGoogle Scholar
Loynes, R. M. (1962) The stability of a queue with nonindependent interarrival and service times. Proc. Camb. Phil. Soc. 58, 497–520.CrossRefGoogle Scholar
Michalopoulos, P. G., Beskos, D. E. and Yamauchi, Y. (1984) Multilane traffic flow dynamics: some macroscopic considerations. Transpn Res.-B 18B, 377–395.Google Scholar
Miller, A. J. (1962) Road traffic flow considered as a stochastic process. Proc. Camb. Phil. Soc. 58, 312–325.Google Scholar
Miller, A. J. (1965) Queueing in rural traffic. Vehicular Traffic Science, Proc. 3rd Internat. Symp. Theory of Traffic Flow. American Elsevier, New York.Google Scholar
Morse, P. M. and Yaffe, H. J. (1971) A queueing model for car passing. Trans. Sci. 5, 48–63.CrossRefGoogle Scholar
Newell, G. F. (1966) Equilibrium probability distributions for low density highway traffic. J. Appl. Prob. 3, 247–260.Google Scholar
Paveri-Fontana, S. L. (1975) On Boltzmann-like treatments for the traffic flow: a critical review and an alternative proposal for dilute traffic analysis. Transpn Res. 9, 225–235.CrossRefGoogle Scholar
Payne, H. J. (1971) Models of freeway traffic and control. Proc. Math. Publ. Syst., Simul. Council, 1, 51–61.Google Scholar
Phillips, W. F. (1979) A kinematic model for traffic flow with continuum implications. Transportation Planning and Technology 5, 131–138.Google Scholar
Prigogine, I., Herman, R. (1971) Kinetic Theory of Vehicular Traffic. American Elsevier, New York.Google Scholar
Rényi, A. (1964) On two mathematical models of the traffic on a divided highway. J. Appl. Prob. 1, 311–320.Google Scholar
Rørbech, J. (1976) Multilane traffic flow process: evaluation of queueing and lane-changing patterns. Transpn Res. Rec. 596, 22–29.Google Scholar
Ryll-Nardzewski, C. (1954) Remarks on the Poisson stochastic process (III). Studia Math. 14, 314–318.Google Scholar
Tanner, J. C. (1961) Delays on a two-lane road. J. R. Statist. Soc. B 23, 64–75.Google Scholar
Thedéen, T. (1964) A note on the Poisson tendency in traffic distribution. Ann. Math. Statist. 35, 1823–1824.Google Scholar
Unkelbach, H. D. (1979) Convergence to equilibrium in a traffic model with restricted passing. J. Appl. Prob. 16, 881–889.Google Scholar
Zeephongsekul, P. (1981) Laplace functional approach to point processes occurring in a traffic model. Ann. Prob. 9, 1034–1040.CrossRefGoogle Scholar