### Quality Properties of Connected Flow Model and Application for Traffic

Alexander Pavlovich Buslaev, M.G. Gorodnichev, A.V. Provorov, M.V. Yashina
1.360 265

#### Abstract

Sequential moving of particles in one direction is considered. Model of totally-connected  flow is introduced in [1] -[4] and concerned to the type of follow-the-leader in traffic flow theory.

Properties of traffic flow are significantly determinate by state-function. For describing of non connected  flow  we introduce new model when acceleration of particles takes into consideration the dynamics of neighborhoods particles.For a chain of particles the model is describing by differential equations of second degree. The function of communication for this model is defined. Inpartial  case the sufficient conditions for convergence of solution the model to totally-connected state are obtained.

In the case of leader-follower pair of particles with linear state and communication functionsthe statements of belonging of solutions to some Sobolev classes of function are proved.

#### Keywords

follow-the-leader model, totally-connected flow, dynamical dimension|, communication function, Sobolev classes of function

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