# Modeling Complex Living SystemsMathematical Modeling

Modeling Complex Living Systems: Mathematical Modeling of Vehicular Traﬃc Flow Phenomena 6.1 Introduction The modeling of systems treated in Chapter 5 refers to the case of spatial homogeneity (being well mixed), and also to a number of interacting active particles that are constant, or known, in time. This chapter deals with systems with a somewhat diﬀerent structure: the number of active particles is still constant in time, but the particles are heterogeneously distributed in space. Speciﬁcally, the modeling refers to the mathematical description of traﬃc ﬂow phenomena for vehicles in one- or multi-lane roads. If the inlet and outlet of vehicles are given, the number of vehicles included in the road can be regarded as a known function of time. Vehicles should be modeled as active particles because their mechani- cal properties need to be integrated by considering the role of the driver, which diﬀers from vehicle to vehicle. Drivers may be experienced or inex- perienced, timid or aggressive, and so on. Even the properties of vehicles diﬀer from case to case, and consequently their speciﬁc characteristics can- not be considered constant parameters of the system. Possibly, one may deal with them by using random variables. The above reasoning suggests that we include, in the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Modeling Complex Living SystemsMathematical Modeling

38 pages

/lp/springer-journals/modeling-complex-living-systems-mathematical-modeling-D2TUMrKbKS
Publisher
Birkhäuser Boston
© Birkhäuser Boston 2008
ISBN
978-0-8176-4510-6
Pages
109 –146
DOI
10.1007/978-0-8176-4600-4_6
Publisher site
See Chapter on Publisher Site

### Abstract

of Vehicular Traﬃc Flow Phenomena 6.1 Introduction The modeling of systems treated in Chapter 5 refers to the case of spatial homogeneity (being well mixed), and also to a number of interacting active particles that are constant, or known, in time. This chapter deals with systems with a somewhat diﬀerent structure: the number of active particles is still constant in time, but the particles are heterogeneously distributed in space. Speciﬁcally, the modeling refers to the mathematical description of traﬃc ﬂow phenomena for vehicles in one- or multi-lane roads. If the inlet and outlet of vehicles are given, the number of vehicles included in the road can be regarded as a known function of time. Vehicles should be modeled as active particles because their mechani- cal properties need to be integrated by considering the role of the driver, which diﬀers from vehicle to vehicle. Drivers may be experienced or inex- perienced, timid or aggressive, and so on. Even the properties of vehicles diﬀer from case to case, and consequently their speciﬁc characteristics can- not be considered constant parameters of the system. Possibly, one may deal with them by using random variables. The above reasoning suggests that we include, in the

Published: Jan 1, 2008

Keywords: Kinetic Theory; Active Particle; Test Vehicle; Discrete Velocity; Microscopic State

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