International Journal of Modern Physics C Vol. 20, No. 6 (2009) 941–952 c  World Scientific Publishing Company THE EFFECTS OF BUS STOP ON TRAFFIC FLOW TIE-QIAO TANG ∗,†,‡ , YAN LI ∗ and HAI-JUN HUANG † ∗ School of Transportation, Science and Engineering Beijing University of Aeronautics and Astronautics Beijing 100191, P. R. China † School of Economics and Management Beijing University of Aeronautics and Astronautics Beijing 100191, P. R. China ‡ tieqiaotang@buaa.edu.cn Received 27 October 2008 Accepted 18 February 2009 In this paper, we use the traffic flow model proposed by Tang et al. [Physica A 387, 6845 (2008)] to study the effects of bus stop on traffic flow. Our numerical tests show that bus stop will have great effects on the stability of traffic flow and that the effects are related to the initial density and the number of bus stops. The numerical results are accordant with the real traffic, which shows that the model proposed by Tang et al. can describe some complex traffic phenomena resulted by bus stop. Keywords : Traffic flow; bus stop; traffic interruption; stability. PACS Nos.: 89.40-a, -45.70.vn, -05.70.Fh. 1. Introduction Traffic problems have become very serious in some cities and attracted many schol- ars to develop various models to describe complex traffic phenomena. 1 Among the existing traffic flow models, macro models are relatively simple, so they have been used to study shock, rarefaction wave, and small perturbation. 2–10 But scholars assumed that the perturbation is very small when studying the evolution of per- turbation. In fact, large perturbation (lane-changing, overtaking, tolling station, accident, pedestrian, bus stop, signal light, and other traffic interruptions) often appears in traffic system and it will have great effects on the stability of traffic flow. Tang et al. 11 studied the inner relationship between various perturbations and the stability of traffic flow and found that the effects of any perturbation on traffic flow are related to the initial conditions. However, the above models 2–11 cannot be used to directly study bus stop, since bus stop is not explicitly considered. Since bus stop is common in urban traffic sys- tem, some scholars recently presented some models to study bus stop and obtained 941