Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
Volume 19, Issue 8, Pages 1163-1173Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129183108012868
Keywords
traffic flow; lattice model; relative current; numerical simulation
Funding
- Ministry of Science and Technology, China [2005DFA10100]
- National Basic Research Program of China [2006CB705500]
- National Natural Science Foundation of China [10532060]
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In this paper, the lattice model which depends not only on the difference of the optimal current and the local current but also on the relative current is presented and analyzed in detail. We derive the stability condition of the extended model by considering a small perturbation around the homogeneous flow solution with finding that the improvement in the stability of the traffic flow is obtained by taking into account the relative current, which is also confirmed by direct simulations. Moreover , from the nonlinear analysis to the extended models, the relative current dependence of the propagating kink solutions for traffic jam is obtained by deriving the modified KdV equation near the critical point by using the reductive perturbation method.
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