OPTIMAL TRAFFIC SIGNAL SETTINGS. II. A REFINEMENT OF WEBSTER'S METHOD

This paper deals with an optimal signal setting of a fixed-cycle traffic signal based upon the criterion of minimum overall delay. Webster's method which is an approximation method for the optimal signal setting is theoretically elucidated. Furthermore, approximation algorithms which are a refinement of Webster's method and are applicable to all traffic signals are presented. The algorithms are a combination of linear programming or mixed-integer programming and one-dimensional minimization technique.

[1]  E. M. L. Beale,et al.  Nonlinear and Dynamic Programming , 1965 .

[2]  J. Darroch.  On the Traffic-light Queue , 1964 .

[3]  G. F. Newell.  Approximation Methods for Queues with Application to the Fixed-Cycle Traffic Light , 1965 .

[4]  M. J. D. Powell,et al.  An efficient method for finding the minimum of a function of several variables without calculating derivatives , 1964, Comput. J..

[5]  R. Rangarajan,et al.  Allocations of Servicing Periods That Minimize Average Delay for N Time-Shared Traffic Streams , 1967, Transp. Sci..

[6]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[7]  Gordon F. Newell,et al.  Queues for a Fixed-Cycle Traffic Light , 1960 .

[8]  F. Webster.  TRAFFIC SIGNAL SETTINGS , 1958 .

[9]  Richard E. Allsop.  A diagram showing practicable settings for a fixed-time traffic signal and their effect on delay , 1971 .

[10]  J. B. Rosen.  The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints , 1960 .

[11]  Alan J. Miller.  Settings for Fixed-Cycle Traffic Signals , 1963 .

[12]  D. J. Buckley,et al.  Some Results for Fixed-time Traffic Signals , 1964 .

[13]  R. Allsop.  Delay-minimizing Settings for Fixed-time Traffic Signals at a Single Road Junction , 1971 .

[14]  Donald R. McNeil,et al.  A solution to the fixed-cycle traffic light problem for compound Poisson arrivals , 1968 .

[15]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

[16]  G. Zoutendijk,et al.  Methods of Feasible Directions , 1962, The Mathematical Gazette.

[17]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[18]  Stuart E. Dreyfus,et al.  Applied Dynamic Programming , 1965 .

[19]  Katsuhisa Ohno,et al.  Optimal traffic signal settings—I. Criterion for undersaturation of a signalized intersection and optimal signal setting , 1973 .