Open AccessA car-following model with stochastically considering the relative velocity in a traffic flow
Author(s) -
Xue Yu
Publication year - 2003
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.52.2750
Subject(s) - jamming , physics , flow (mathematics) , instability , relative velocity , traffic flow (computer networking) , perturbation (astronomy) , flow velocity , diagram , mechanics , statistical physics , mathematics , statistics , computer science , classical mechanics , thermodynamics , computer security , quantum mechanics
In this paper, the car-following model with stochastically considering the relative velocity in a traffic flow is presented through investigating the vehicle a cceleration process with uncertainty. The stability criterion superior to the Ba ndo's model is derived by the linear stability analysis. The density wave is inv estigated analytically with the perturbation method. The results show that the o ccurrence of traffic jamming transitions can be described by the kink solution o f the modified Korteweg-de Vries equation. The effects of stochastic relative ve locity on the traffic flow are simulated and analyzed. It is shown that the chan ge rate of velocity in the new model is smaller than that of the Bando's model u nder the same condition and depends on the probability p. As the probability p i ncreases, a small initial disturbance does not magnify and influence on the traf fic flow, but fades away for a long time. The stable region in the new model is larger than in the Bando's model in the phase diagram. The existent initial hyst eresis in the new model will approach to a small region with the increase of tim e in the headway-velocity plot, which is exactly different from that in the Band o's model.In contrast,the hysteresis region in Bando's model will be continuousl y extended to cause traffic flow instability.