The Synchronization of Traffic Signals by Mixed-integer Linear Programming
The Synchronization of Traffic Signals by Mixed-integer Linear Programming

Author: John D. C. Little

Publisher:

Published: 1966

Total Pages: 14

ISBN-13:

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Traffic signals can be synchronized so that a car, starting at one end of a main artery and traveling at preassigned speeds, can go to the other end without stopping for a red light. The portion of a signal cycle for which this is possible is called the bandwidth for that direction. Ordinarily the bandwidth in each direction is single. For this case we formulate the arterial problem as a mixed-integer linear program: Given (1) an arbitrary number of signals, (2) the fraction of the cycle that is red at each signal, (3) upper and lower limits on signal period, (4) upper and lower limits on speed each way between adjacent signals, (5) limits on change in speed, and (6) a constant of proportionality between the two bandwidths; find (1) a common signal period, (2) speeds between signals, and (3) the relative phasing of the signals so as to maximize the sum of the bandwidths. A branch and bound algorithm is developed for solving the given mixed-integer linear program by solving a sequence of ordinary linear programs. The problem of synchronizing a network of signals is also formulated. The resulting program consists of the arterial programs for the individual streets plus a set of further constraints that arise because the streets connect together to form closed loops.

Report No. FHWA-RD.
Report No. FHWA-RD.

Author: United States. Federal Highway Administration. Offices of Research and Development

Publisher:

Published: 1980

Total Pages: 262

ISBN-13:

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Integer Programming and Related Areas
Integer Programming and Related Areas

Author: C. Kastning

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 504

ISBN-13: 3662022842

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Integer Prograw~ing is one of the most fascinating and difficult areas in the field of Mathematical Optimization. Due to this fact notable research contributions to Integer Programming have been made in very different branches of mathematics and its applications. Since these publications are scattered over many journals, proceedings volumes, monographs, and working papers, a comprehensive bibliography of all these sources is a helpful tool even for specialists in this field. I initiated this compilation of literature in 1970 at the Institut fur ~konometrie und Operations Research, University of Bonn. Since then many collaborators have contributed to and worked on it. Among them Dipl.-Math. Claus Kastning has done the bulk of the work. With great perseverance and diligence he has gathered all the material and checked it with the original sources. The main aim was to incorporate rare and not easily accessible sources like Russian journals, preprints or unpublished papers. Without the invaluable and dedicated engagement of Claus Kastning the bibliography would never have reached this final version. For this reason he must be considered its responsible editor. As with any other collection this literature list has a subjective viewpoint and may be in some sense incomplete. We have however tried to be as complete as possible. The bibliography contains 4704 different publications by 6767 authors which were classified by 11839 descriptor entries.