Estimation of traffic platoon structure from headway statistics

This paper deals first with the modeling of urban traffic headway statistics. It is shown that a composite distribution based on the convex combination of a lognormal and a shifted exponential distribution gives a good fit to observed traffic data. This statistical model is then used to generate a model for the formation and passage of "platoons" of vehicles. It is shown that the problem of estimating the time at which a "platoon" passes a detector, as well as the number of vehicles in the "platoon", corresponds to the point process disorder problem. An optimal estimator for the platoon size and passage time, based on detector data, is then derived via known results for the point process disorder problem. It is shown that the computations required by this estimator can be performed in a microprocessor. Furthermore, the estimator is tested-against the UTCS-1 traffic simulator and performs very well. Parameter sensitivity analysis of the estimator is presented. Finally, the use of these results to improve the filter/predictor described in a companion paper, and vice versa, is explained.

[1]  John S. Baras,et al.  Discrete time point processes in urban traffic queue estimation , 1978 .

[2]  C. Wan,et al.  The general point process disorder problem (Corresp.) , 1977, IEEE Trans. Inf. Theory.

[3]  A. N. Sirjaev,et al.  Statistical Sequential Analysis , 1973 .

[4]  Donald L. Snyder,et al.  Random point processes , 1975 .

[5]  Alan J. Miller.  A Queueing Model for Road Traffic Flow , 1961 .

[6]  W. F. Adams.  Road Traffic Considered as a Random Series , 1950 .

[7]  Thomas Kailath,et al.  Nonlinear filtering with counting observations , 1975, IEEE Trans. Inf. Theory.

[8]  R. L. Lawrence,et al.  The statistical properties of freeway traffic , 1977 .

[9]  D J Buckley,et al.  Road traffic headway distributions , 1962 .

[10]  Mark H. A. Davis.  The Representation of Martingales of Jump Processes , 1976 .

[11]  R. L. Lawrence,et al.  A SIMPLE STOCHASTIC MODEL FOR FREEWAY TRAFFIC , 1977 .

[12]  D. Branston.  Models of Single Lane Time Headway Distributions , 1976 .

[13]  W F Adams,et al.  ROAD TRAFFIC CONSIDERED AS A RANDOM SERIES. (INCLUDES PLATES). , 1936 .

[14]  Mark H. A. Davis.  A note on the Poisson disorder problem , 1976 .

[15]  J. Baras,et al.  Discrete time point processes in urban traffic queue estimation , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[16]  A Daou.  On flow within platoons , 1966 .

[17]  P. Varaiya,et al.  Martingales on Jump Processes. I: Representation Results , 1975 .

[18]  P. Varaiya,et al.  Martingales on Jump Processes. II: Applications , 1975 .

[19]  B. L. Rozovskii,et al.  The “Disorder” Problem for a Poisson Process , 1971 .