THE HYPERLANG PROBABILITY DISTRIBUTION- A GENERALIZED TRAFFIC HEADWAY MODEL

THIS RESEARCH IS CONCERNED WITH THE DEVELOPMENT OF THE HYPERLANG PROBABILITY DISTRIBUTION AS A GENERALIZED TIME HEADWAY MODEL FOR SINGLE-LANE TRAFFIC FLOWS ON TWO-LANE, TWO-WAY ROADWAYS. THE STUDY METHODOLOGY INVOLVED A PROCESS THAT IS BEST DESCRIBED AS MODEL EVOLUTION, AND INCLUDED: (1) IDENTIFICATION OF SALIENT HEADWAY PROPERTIES, (2) CONSTRUCTION OF MATHEMATICAL MICRO-COMPONENTS TO SIMULATE ESSENTIAL HEADWAY PROPERTIES, (3) INTEGRATION OF THE MICRO- COMPONENTS INTO A GENERAL MATHEMATICAL HEADWAY MODEL, (4) NUMERICAL EVALUATION OF MODEL PARAMETERS, AND (5) STATISTICAL EVALUATION OF THE MODEL. THE PROPOSED HYPERLANG HEADWAY MODEL IS A LINEAR COMBINATION OF A TRANSLATED EXPONENTIAL FUNCTION AND A TRANSLATED ERLANG FUNCTION. THE EXPONENTIAL COMPONENT OF THE DISTRIBUTION DESCRIBES THE FREE (UNCONSTRAINED) HEADWAYS IN THE TRAFFIC STREAM, AND THE ERLANG COMPONENT DESCRIBES THE CONSTRAINED HEADWAYS. IT IS A VERY FLEXIBLE MODEL THAT CAN DECAY TO A SIMPLE EXPONENTIAL FUNCTION, TO AN ERLANG FUNCTION, OR TO A HYPER-EXPONENTIAL FUNCTION AS MIGHT BE REQUIRED BY THE TRAFFIC SITUATION. IT IS LIKELY, HOWEVER, THAT A TRAFFIC STREAM WILL ALWAYS CONTAIN BOTH FREE AND CONSTRAINED VEHICLES, AND THAT, THE GENERAL FORM OF THE HYPERLANG FUNCTION WILL BE REQUIRED IN ORDER TO EFFECT AN ADEQUATE DESCRIPTION OF THE COMPOSITE HEADWAYS. THE PARAMETERS OF THE HYPERLANG FUNCTION WERE EVALUATED FOR DATA SETS OBTAINED FROM THE 1965 HIGHWAY CAPACITY MANUAL AND FROM A 1967 PURDUE UNIVERSITY RESEARCH PROJECT. THE PROPOSED HYPERLANG MODEL PROVED TO BE A SOUND DESCRIPTOR OF THE REPORTED HEADWAYS FOR VOLUMES RANGING FROM ABOUT 150 VPH TO ABOUT 1050 VPH. HOWEVER, IT SHOULD BE SUBSTANTIATED AND EVALUATED FOR A WIDE RANGE OF TRAFFIC AND ROADWAY CONDITIONS. DURING THE CONDUCT OF ANY FUTURE RESEARCH, CAREFUL ATTENTION SHOULD BE GIVEN TO PROPER FLOW RATE MONITORING AND TO PROPER DATA STRATIFICATION TO REFLECT THE VARIATIONS IN HEADWAY CHARACTERISTICS THAT ARE CAUSED BY VARIATIONS IN TRAFFIC AND ROADWAY CONDITIONS. /AUTHOR/