Traffic accidents may pose a high risk with respect to human travel safety. In order to improve the safety of travelling, an insight into the traffic accidents is needed. This requires a practical and specifically approach when it comes to modelling for traffic accidents. This paper presents a traffic accident model based on self-exciting processes, which describes the specific phenomena and problems in traffic accidents. The research focuses on the stationary condition, reliability and safety analysis of the traffic network in a certain city or the traffic situation in a certain area. First, a traffic accident model based on self-exciting processes is developed, and secondly, the stationary condition of the model is studied, which is used to analyze the reliability and safety of the traffic network in a certain city or the traffic situation in a certain area. In addition, the probability and related characteristics for traffic process are evaluated by simulation methods. The traffic accident model is developed with the use of self-exciting processes. Maximum Likelihood Estimate (MLE) is used for the parameter estimations of the traffic accident model. Finally, a numerical example is presented, in which the traffic accident model developed is applied to the simulation data.
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