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

Mohammad Maghrour Zefreh,Adam Torok,David Baranyai,M Figueira,Z Guo

doi:10.1051/matecconf/20168104002

Mohammad Maghrour Zefreh, Adam Torok + Show 3 more

Open Access

https://doi.org/10.1051/matecconf/20168104002

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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.

Highlights

Flying birds, running water, electric current, internet packets, and moving vehicles can all be considered as flows, yet each exhibits distinct characteristics
The main contribution of this paper is to survey on the relation of speed-density parameters to see whether it is possible to derive speed parameter capable of presenting behaviour of traffic dynamics rather than presenting just the average speed of the entire traffic flow
Schematic fitting of the mentioned correlation in Fig. 4. by generally accepted deterministic speed-density models may imply the possibility of capturing the chance of presenting the semistochastic speed density model which deals with different traffic conditions rather than the average speed

Summary

Introduction

Flying birds, running water, electric current, internet packets, and moving vehicles can all be considered as flows, yet each exhibits distinct characteristics. Fundamental relations of traffic flow have historically been established either empirically or derived from carfollowing models. It can be used as a tool to study on moving objects (or particles) in many scientific areas: pedestrians [3, 4], conveyors, network information packages [5], crowd dynamics [6], molecular motors, and biological systems [7]. It has been almost 75 years since Greenshields’ seminal paper Study of Traffic Capacity in 1935 [8]. These efforts include singleregime models: Greenberg’s Model [9], the Underwood Model [10], Northwestern [11], Drew [12], and the PipesMunjal Generalized Model [13].There are multiregime models which include: two-regime models such as Edie Model [14], multi-regime model by cluster analysis [15], two-regime model [16], modified Greenberg, and three-regime models [16, 11]

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