The city traffic system and average arrival time with traffic jams problems considered. Study of influence of various routing algorithms and average arrival time in case of city transport system is the main purpose of the paper. During the study authors suggested to use mathematical model of city routing system which presented as compositions of oriented roads graph with weights of each of its edges and two city population density matrixes which represents density of working and living city population. Also authors used cars representations in the mathematical model which are using one or the other routing algorithm to reach the destination point. Suggested mathematical model includes some restrictions which goes from real city cars limitations. In the paper authors used suggested mathematical model to show examples of calculations some simple traffic routes situations and offered some optimizations of the situations. At the last part of the paper authors wrote about simulation modeling software AnyLogic and how this product can help with simulate the whole city road graph. In conclusion the authors says that the paper might be starting point of further solutions for city traffic routing problems.

Keywords: automobile traffic, routes, road graph, smart city, graph, simulation, traffic flow, travel time, throughput, optimization