# A CAPACITY ANALYSIS TECHNIQUE FOR HIGHWAY JUNCTIONS

LINEAR PROGRAMMING IS A GENERAL FORM OF APPLIED MATHEMATICS IN WHICH A LINEAR FUNCTION (CALLED THE OBJECTIVE FUNCTION) OF A SET OF VARIABLES IS MAXIMIZED OR MINIMIZED, DEPENDING ON THE NATURE OF THE PROBLEM, SUBJECT TO A SET OF LINEAR CONSTRAINTS. THE STARTING POINT OF THE PRESENT ANALYSIS IS THE 1961 CAPACITY STUDY, BY CAPELLE AND PINNELL, OF SIGNALIZED DIAMOND INTERCHANGES. THE ANALYSIS BEGINS WITH A STATEMENT OF THE OBJECTIVE FUNCTION---WHICH IN THIS CASE IS TO BE MAZIMIZED---OF A FOUR-LEG INTERCHANGE AT WHICH ALL POSSIBLE MOVEMENTS ARE PERMITTED. THIS GIVES 12 MOVEMENTS, EACH OF WHICH DEFINES A SET OF VARIABLES FOR WHICH VALUES ARE SOUGHT; IN ADDITION, A THIRTEENTH VARIABLE, CRITICAL LANE VOLUMES, IS DEFINED. TWO SETS OF CONSTRAINTS ARE RECOGNIZED: FIRST, THE CAPACITY OF EACH OF THE INTERCHANGE ELEMENTS; SECOND, THE DISTRIBUTION OF MOVEMENTS THROUGH THE INTERCHANGE. A CONSTRAINT EQUATION IS DEVELOPED IN WHICH THE VOLUMES OF RELATED MOVEMENTS, SUCH AS CONFLICTS, ARE SUMMED TO DEFINE A SINGLE CONSTRAINT VARIABLE. THESE VARIABLES ARE FACTORED ACCORDING TO AN EMPIRICAL DISTRIBUTION TABLE AND THEN SUMMED TO BE EQUAL TO A GIVEN CRITICAL LANE VOLUME FOR A GIVEN SERVICE LEVEL AND TYPE OF FACILITY. WITH THIS THE MODEL IS COMPLETE, AND THE NEXT STEP IS SOLUTION OF THE PROBLEM. WHILE THE SIMPLEX METHOD IS OFTEN USED FOR THIS PURPOSE, THE AUTHORS HAVE EMPLOYED IBM'S MATHEMATICAL PROGRAMMING SYSTEM (MPS). IT IS NOTED IN CONCLUSION THAT ANY ONE OF THE 13 VARIABLES EMPLOYED IN THE SAMPLE EQUATION MAY BE CRITICAL, NOT ONLY THE CRITICAL LANE VOLUMES. THE MODEL IS APPLICABLE TO THE DESIGN OF INTERCHANGES FOR BOTH ADT AND PEAK-HOUR CONDITIONS.

• Record URL:
• Supplemental Notes:
• Sponsored by Committee on Highway Capacity and Quality of Service. Distribution, posting, or copying of this PDF is strictly prohibited without written permission of the Transportation Research Board of the National Academy of Sciences. Unless otherwise indicated, all materials in this PDF are copyrighted by the National Academy of Sciences. Copyright © National Academy of Sciences. All rights reserved.
• Authors:
• Wattleworth, Joseph A
• Ingram, Jerry W
• Conference:
• Publication Date: 1972

## Media Info

• Media Type: Print
• Features: Figures; References; Tables;
• Pagination: p. 31-36
• Monograph Title: Highway capacity and quality of service evaluation
• Serial:

## Filing Info

• Accession Number: 00228230
• Record Type: Publication
• Files: TRIS, TRB
• Created Date: Feb 23 1973 12:00AM