Bandwidth Maximization Using Vehicle Arrival Functions

We revisit the offset optimization problem for maximization of two-way progression bands. A new formulation is proposed relying on the concepts of relative offset and vehicle arrival functions. Vehicle arrival functions represent the probability that a vehicle reaches a given intersection at a given time. Relative offsets are the displacement of the arrival functions with respect to a moving coordinate frame. An explicit formula for the bandwidth is derived based on these two quantities. The bandwidth maximization problem is then formulated as an unconstrained nonlinear program. The cases of pulse and Gaussian arrivals are considered in detail. Numerical techniques are proposed for both that return globally optimal solutions with small computational cost.

[1]  Henry X. Liu,et al.  SMART-Signal Phase II: Arterial Offset Optimization Using Archived High-Resolution Traffic Signal Data , 2013 .

[2]  Bart De Schutter,et al.  IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS Editor-In-Chief , 2005 .

[3]  Liang-Tay Lin,et al.  Synchronized Signal Control Model for Maximizing Progression along an Arterial , 2010 .

[4]  Renfrey B. Potts,et al.  A Theory of the Diffusion of Traffic Platoons , 1964 .

[5]  Ajay K. Rathi,et al.  A restricted branch-and-bound approach for generating maximum bandwidth signal timing plans for traffic networks , 1998 .

[6]  Thomas Urbanik,et al.  Traffic Signal Optimization Program for Oversaturated Conditions: Genetic Algorithm Approach , 1999 .

[7]  N. Gartner,et al.  Arterial-based control of traffic flow in urban grid networks , 2002 .

[8]  H Tsay,et al.  New algorithm for solving the maximum progression bandwidth , 1988 .

[9]  Alexander Skabardonis,et al.  COMPARATIVE ANALYSIS OF COMPUTER MODELS FOR ARTERIAL SIGNAL TIMING , 1985 .

[10]  Darcy M. Bullock,et al.  Dataset for Investigating Computational Efficiency of Alternative Arterial Offset Optimization Algorithms , 2010 .

[11]  John D. C. Little,et al.  The Synchronization of Traffic Signals by Mixed-Integer Linear Programming , 2011, Oper. Res..

[12]  Robert L Bleyl.  A PRACTICAL COMPUTER PROGRAM FOR DESIGNING TRAFFIC-SIGNAL- SYSTEM TIMING PLANS , 1967 .

[13]  Miguel Á. Carreira-Perpiñán,et al.  Mode-Finding for Mixtures of Gaussian Distributions , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Darcy M. Bullock,et al.  Computational Efficiency of Alternative Algorithms for Arterial Offset Optimization , 2011 .

[15]  Gaetano Fusco,et al.  Maximal bandwidth problems: a new algorithm based on the properties of periodicity of the system , 1998 .

[16]  John D. C. Little,et al.  Simultaneous optimization of offsets, splits, and cycle time , 1976 .

[17]  Nathan H. Gartner,et al.  A multi-band approach to arterial traffic signal optimization , 1991 .

[18]  Robert H Whitson,et al.  A VARIABLE-SEQUENCE MULTIPHASE PROGRESSION OPTIMIZATION PROGRAM , 1973 .

[19]  John D. C. Little,et al.  SYNCHRONIZING TRAFFIC SIGNALS FOR MAXIMAL BANDWIDTH , 1964 .

[20]  John D. C. Little,et al.  MAXBAND: A PROGRAM FOR SETTING SIGNALS ON ARTERIES AND TRIANGULAR NETWORKS , 1981 .

[21]  Nathan H. Gartner,et al.  MULTIBAND-96: A Program for Variable-Bandwidth Progression Optimization of Multiarterial Traffic Networks , 1996 .

[22]  Darcy M. Bullock,et al.  Data-Driven Algorithms for Real-Time Adaptive Tuning of Offsets in Coordinated Traffic Signal Systems , 2007 .

[23]  Darcy M. Bullock,et al.  Real-Time Offset Transitioning Algorithm for Coordinating Traffic Signals , 2001 .