Journal Article10.1017/S0001867800038209
Low density traffic streams
TL;DR: It is shown that if PI is the expected time for a vehicle to travel from A to B under the STOCHASTIC PROCESS GOVERNING the MOTION of VEHICLES, then a non-HOMOGENEOUS POISSON SPATIAL PROCESS with MEAN MEASURE PI is INVARIant.
read more
Abstract: LOW DENSITY TRAFFIC REFERS TO THE STUDY OF MACROSCOPIC PROPERTIES OF A TRAFFIC STREAM WHEN VEHICLES TRAVEL INDEPENDENTLY OF ONE ANOTHER. IT IS USUALLY ASSUMED THAT EACH VEHICLE TRAVELS AT A CONSTANT VELOCITY, THE VELOCITY VARYING FROM VEHICLE TO VEHICLE. VERY GENERAL VEHICULAR MOTIONS ARE PERMITTED TO STUDY VARIOUS ASPECTS OF THE TRAFFIC STREAMS. FOR EXAMPLE, IT IS SHOWN THAT IF PI(A,B) IS THE EXPECTED TIME FOR A VEHICLE TO TRAVEL FROM A TO B UNDER THE STOCHASTIC PROCESS GOVERNING THE MOTION OF VEHICLES, THEN A NON-HOMOGENEOUS POISSON SPATIAL PROCESS WITH MEAN MEASURE PI IS INVARIANT. /AUTHOR/
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Useful headway models
TL;DR: In this paper, four headway models of increasing generality are considered from three points of view: (i) the value of the models for use as arrival processes in stochastic model building, (ii) some traffic situations where it is known from theoretical considerations, that the models are appropriate, and (iii) empirical evidence to support the models.
355
Encountered data, statistical ecology, environmental statistics, and weighted distribution methods
TL;DR: Weighted distribution methods arise in the context of data gathering, modeling, inference, and computing, and help provide a unified approach in dealing with encountered data.
35
Estimation of the PDF and the CDF of exponentiated moment exponential distribution
TL;DR: This article addresses the different methods of estimation of the probability density function and the cumulative distribution function for the exponentiated moment exponential distribution and shows that the ML estimator performs better than others.
8
Mean Streets: The Median of a Size-Biased Sample and the Population Mean
Woollcott Smith,Milton Parnes +1 more
TL;DR: In this article, a consistent estimator of the population mean velocity is found that depends solely on counts of the number of cars the observer passes and the count of cars that pass the observer.
8
Statistical Inference of Exponentiated Moment Exponential Distribution Based on Lower Record Values
Devendra Kumar,Tanujit Dey,Sanku Dey +2 more
- 21 Jul 2017
TL;DR: In this article, the authors derived explicit expressions as well as recurrence relations for the single and product moments of record values and then used these results to compute the means, variances and coefficient of skewness and kurtosis of exponentiated moment exponential distribution (EMED).
8
References
An introduction to probability theory and its applications - 3/E. volume 3
William Feller
- 22 Mar 2002
Abstract: The classic text for understanding complex statistical probability An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivreLaplace theorem.
21.5K
•Book
Stochastic processes
J. L. Doob,Joseph L. Doob +1 more
- 01 Jan 1953
TL;DR: Stochastic processes are probabilistic models of data streams such as speech, audio and video signals, stock market prices, and measurements of physical phenomena by digital sensors such as medical instruments, GPS receivers, or seismographs that are essential for understanding phenomena and processing information.
10.6K
•Book
A first course in stochastic processes
Samuel Karlin,Howard M. Taylor +1 more
- 01 Jan 1966
TL;DR: In this paper, the Basic Limit Theorem of Markov Chains and its applications are discussed and examples of continuous time Markov chains are presented. But they do not cover the application of continuous-time Markov chain in matrix analysis.
4.4K
•Book
An Introduction to Probability Theory and Its Applications, Volume II
Frank E. Grubbs,William Feller +1 more
- 01 Jan 1971
1.4K