DISTRIBUTION OF GAPS AND BLOCKS IN A TRAFFIC STREAM

Abstract

Some theoretical questions of large openings or gaps in a single stream of traffic are studied. A gap is defined as a headway between vehicles greater than or equal to some minimum size -say x. Several authors have studied the probability distribution of the wait which a randomly located observer must endure before he finds a gap. This paper, while briefly reviewing the solutions of this well known problem, is primarily concerned with expressions for: (1) the distribution of gap sizes; (2) the distribution of spacings between vehicles and gaps; (3) the mean and variance of inter-vehicle and inter-gap spacings; (4) the stationary flow rates of gaps; and (5) the distribution of blocked and unblocked periods. It is assumed that the origin of measurements may be located (1) with the passing of a vehicle, (2) at the beginning of a gap, or (3) at random. It is also assumed that the distribution of inter-vehicle spacings are independently, but identically, distributed random variables.

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Document Details

Document Type
Technical Report
Publication Date
Jul 25, 1961
Accession Number
AD0267586

Entities

People

  • Robert M. Oliver

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Aircrafts
  • Automobiles
  • Convolution
  • Crossings
  • Equations
  • Flow
  • Flow Rate
  • Government Procurement
  • Observers
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Stationary
  • Statistics
  • United States
  • Vehicles

Readers

  • Aviation Safety and Air Traffic Management
  • Educational Psychology
  • Regression Analysis.

Technology Areas

  • Space