Traffic Grammar and Algorithmic Complexity in Urban Freeway Flow Patterns

This paper uses techniques from formal language theory to describe the linear spatial patterns in urban freeway traffic flows in order to understand and analyze “hidden order” in such high volume systems. A method for measuring randomness based on algorithmic entropy is introduced and developed. These concepts are operationalized using Pincus’ approximate entropy formulation in an appropriate illustration. These measures, which may be viewed as counterintuitive, are believed to offer robust and rigorous guidance to enhance the overall understanding of efficiency in urban freeway traffic systems. Utilization of such measures should be facilitated by information generated by real time intelligent transportation systems (ITS) technologies and may prove helpful in real time traffic flow management.

[1]  R E Kalman,et al.  Not all (possibly) "random" sequences are created equal. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[2]  S H Evans,et al.  Redundancy as a variable in pattern perception. , 1967, Psychological bulletin.

[3]  Asa Kasher,et al.  MEASURES OF SYNTACTIC COMPLEXITY , 1963 .

[4]  Claude E. Shannon,et al.  The Mathematical Theory of Communication , 1950 .

[5]  B. Kerner.  THE PHYSICS OF TRAFFIC , 1999 .

[6]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[7]  Michael F. Dacey,et al.  The syntax of a triangle and some other figures , 1970, Pattern Recognit..

[8]  Jim Woodcock,et al.  Software engineering mathematics , 1988 .

[9]  Edward J. Rzempoluck,et al.  Neural Network Data Analysis Using Simulnet™ , 1997, Springer New York.

[10]  Noam Chomsky,et al.  The Logical Structure of Linguistic Theory , 1975 .

[11]  Zurek,et al.  Algorithmic randomness and physical entropy. , 1989, Physical review. A, General physics.

[12]  P. Gordon,et al.  CONGESTION TRENDS IN METROPOLITAN AREAS , 1994 .

[13]  G. Chaitin.  Randomness and Mathematical Proof , 1975 .

[14]  Michael A. Harrison,et al.  Introduction to formal language theory , 1978 .

[15]  John H. Holland,et al.  Hidden Order: How Adaptation Builds Complexity , 1995 .

[16]  Mark Newson,et al.  乔姆斯基的普遍语法教程 = Chomsky's universal grammar : an introduction : , 1988 .

[17]  B. Hillier,et al.  The Social Logic of Space , 1984 .

[18]  Fred Phillips,et al.  The entropies: Some roots of ambiguity , 1980 .

[19]  S. Pincus,et al.  A recipe for randomness. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[20]  John F. Betak,et al.  Measuring two-dimensional complexity: A conceptual structure , 1972, Pattern Recognit..

[21]  Ralph Grishman,et al.  Computational linguistics : an introduction , 1986 .

[22]  K. Harris,et al.  Losing symmetry by design , 1989, Nature.

[23]  W. H. Zurek,et al.  Thermodynamic cost of computation, algorithmic complexity and the information metric , 1989, Nature.

[24]  M. Meyer.  ALTERNATIVE METHODS FOR MEASURING CONGESTION LEVELS , 1994 .

[25]  S M Pincus,et al.  Approximate entropy as a measure of system complexity. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Andrei N. Kolmogorov,et al.  Logical basis for information theory and probability theory , 1968, IEEE Trans. Inf. Theory.

[27]  G. A. Miller,et al.  Statistical behavioristics and sequences of responses. , 1949, Psychological review.

[28]  Steven M. Pincus,et al.  Approximate entropy: Statistical properties and applications , 1992 .

[29]  J. Betak.  Information Theory as a Basis for Studying Environmental Complexity: Some Limitations , 1974 .

[30]  S. Pincus,et al.  Randomness and degrees of irregularity. , 1996, Proceedings of the National Academy of Sciences of the United States of America.