Assessing the Possibility of Presenting a Semi-Stochastic Speed-Density Function

Abstract

Underlying a fundamental diagram is a relation between traffic speed and density which roughly corresponds to drivers’ speed choices under varying car-following distances. Stochastic and deterministic models are mainly two different categories of speed-density models. The advantages of deterministic models are their mathematical simplicity and analytical tractability though their results will show just the average parameters. Although the stochastic models may represent more accurate results taking uncertainty into account, they are often hard to use and analytically not tractable. The aim of this paper is to investigate the possibility of presenting a model which is neither completely deterministic nor completely stochastic but easy to use and understand which incorporates different traffic conditions and speed distributions. Monte Carlo Method has been used to generate different speed distributions based on different traffic conditions and consequently generating their relevant densities. Surveying the relation between the mentioned speed distributions and the obtained densities kept the chance of presenting a model which is neither completely deterministic nor completely stochastic but easy to use and understand which incorporates different traffic conditions and speed distributions.