Theoretical investigation of synchronous totally asymmetric simple exclusion process on lattices with two consecutive junctions in multiple-input-multiple-output traffic system
Xiao Song(肖松)a)†,Cai Jiu-Ju(蔡九菊) a), Wang Rui-Li(王瑞利)b), Liu Ming-Zhe(刘明哲)b), and Liu Fei(刘飞) a)
a SEPA Key Laboratory on Eco-Industry, Northeastern University, Shenyang 110004, China; b School of Engineering and Advanced Technology, Massey University, Palmerston North, New Zealand
Abstract In this paper, we study the dynamics of the synchronous totally asymmetric simple exclusion process (TASEP) on lattices with two consecutive junctions in a multiple-input-multiple-output (MIMO) traffic system, which consists of m sub-chains for the input and the output, respectively. In the middle of the system, there are $n (n < m)$ sub-chains via two consecutive junctions linking m sub-chains of input and m sub-chains of output, respectively. This configuration is a type of complex geometry that is relevant to many biological processes as well as to vehicular traffic flow. We use a mean-field approach to calculate this typical geometry and obtain the theoretical results for stationary particle currents, density profiles, and a phase diagram. With the values of m and n synchronously increasing, the vertical phase boundary moves toward the right and the horizontal phase boundary moves toward the upside in the phase diagram. The boundary conditions of the system as well as the numbers of input and output determine the no- quilibrium stationary states, stationary-states phases, and phase boundaries. We use the results to compare with computer simulations and find that they are in very good agreement with each other.
Received: 16 March 2009
Revised: 05 June 2009
Accepted manuscript online:
PACS:
45.70.Vn
(Granular models of complex systems; traffic flow)
Fund: Project supported by the State Key
Program for Basic Research of China (Grant No 2005CB724206).
Cite this article:
Xiao Song(肖松),Cai Jiu-Ju(蔡九菊), Wang Rui-Li(王瑞利), Liu Ming-Zhe(刘明哲), and Liu Fei(刘飞) Theoretical investigation of synchronous totally asymmetric simple exclusion process on lattices with two consecutive junctions in multiple-input-multiple-output traffic system 2009 Chin. Phys. B 18 5103
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