In response to the problem that the traditional logistics distribution operation process is cumbersome and vulnerable to human factors, the method of introducing drones into logistics for distribution is proposed. Firstly, the Petri net theory is used to model the traditional logistics and distribution system and the UAV logistics and distribution system respectively. Second, a Markov chain is constructed based on stochastic Petri nets, and the performance of the model is analyzed using the Markov chain; then the reduction rules of stochastic Petri nets are used to equivalently transform the two models and calculate the average operating time of one distribution business process. Finally, a comparative study is carried out on the analysis results. The research and comparison results show that, compared with traditional logistics distribution, the use of drones to re-plan logistics routes, while satisfying the rationalization of the entire route, improves the time-limited performance by 25.6%. It can be seen that the use of drones for logistics distribution can be significantly Shortening the delivery time and effectively improving the delivery efficiency has certain theoretical reference significance for actual logistics problems.