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Recently, urbanization has been expanded rapidly in the world and a number of metropolitan areas have been appeared with a population of more than 10 million people. Because of dense population in metropolitan and consequently increasing the delivery of goods and services, there has been a lot of problems including traffic congestion, air pollution, accidents and high energy consumption. This made some complexities in distribution of urban goods; Therefore, it is essential to provide creative solutions to overcome these complexities. City logistics models can be effective in solving these complexities. In this paper, concepts and definitions related to city logistics are explained to provide a mathematical model in order to design city logistics distribution network aim at minimizing response times. This objective is effective for goods and emergency services, especially in times of crisis and also for goods that are delivered as soon as possible. This is a three-level network and has been used in modeling of queuing theory. To validate the model, a numerical example has been established and results of the model have been explained using BARON solver in Gams software. Finally, conclusions and recommendations for future research are presented.