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Road Traffic Flow Considered as a Stochastic Process

Published online by Cambridge University Press:  24 October 2008

A. J. Miller
A. J. Miller
Affiliation:
University CollegeLondon
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Abstract

Equations are derived for the process of catching-up and overtaking which occurs in one lane of traffic for a model in which vehicles travel in random bunches and overtake at random times. The model allows vehicle velocities to be distributed and allows for several vehicles at a time to overtake. At first only stationary states are considered, that is states in which the rate of catching-up equals, on average, the rate of overtaking.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 312 - 325
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Bartlett, M. SSome problems associated with random velocity. Publ. Inst. Statist. Univ. Paris, 6 (1957), 261–270.Google Scholar
(2)Carleson, L.A mathematical model for highway traffic. Nordisk Mat. Tidskr. 5 (1957) (in Swedish).Google Scholar
(3)Chandler, R. E., Herman, R. and Montroll, E. WTraffic dynamics: studies in car following. Operations Res. 6 (1958), 165–184.CrossRefGoogle Scholar
(4)Gazis, D. C., Herman, R. and Potts, R. BCar following theory of steady state traffic flow. Operations Res. 7 (1959), 499–505.CrossRefGoogle Scholar
(5)Herman, R., Montroll, E. W., Potts, R. B and Rothery, R. WTraffic dynamics: analysis of stability in car-following. Operations Res. 7 (1959), 86–106.CrossRefGoogle Scholar
(6)Jackson, R. R. P.Queueing systems with phase type service. Operational Res. Quart. 5 (1954), 109–120.CrossRefGoogle Scholar
(7)Kometani, E.On the theoretical solution of highway traffic under mixed traffic. Mem. Fac. Engrg. Kyoto Univ. 17 (1955), 79–88.Google Scholar
(8)Kometani, E. and Sasaki, T. Dynamic behaviour of traffic with a non-linear spacingspeed relationship. Publ. Fac. Engrg. Kyoto Univ. (1959).Google Scholar
(9)Lighthill, M. J and Whitham, G. BOn kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London. Ser. A. 229 (1955), 317–345.Google Scholar
(10)Miller, A. J Ph.D. thesis, Manchester (1960).Google Scholar
(11)Miller, A. J Road traffic flow treated as a stochastic process. (Symposium on Theory of Traffic Flow, Detroit (1959); Elsevier, Amsterdam 1961).Google Scholar
(12)Miller, A. JA queueing model for road traffic flow. J. Roy. Statist. Soc. Ser. B, 23 (1961), 64–75.Google Scholar
(13)Newell, G. FMathematical models for freely flowing highway traffic. Operations Res. 3 (1955), 176–186.Google Scholar
(14)Newell, G. F and Bick, J. HA continuum model for traffic flow on an undivided highway. (Publ. Div. Appl. Math., Brown Univ. 1958).Google Scholar
(15)Prigogine, I. A Boltzmann-like approach for traffic flow. (Symposium on Theory of Traffic Flow, Detroit (1959); Elsevier, Amsterdam 1961).Google Scholar
(16)Reuschel, A.Fahrzeugbewegungen in der Kolonne. Österreichisches Ing. Arch. 4 (1950), 193–213.Google Scholar
(17)Tanner, J. CAn improved model for delays on a two lane road. J. Roy. Statist. Soc. Ser. B, 23 (1961), 38–63.Google Scholar