The creation of a communication between an artery and a vein (arteriovenous fistula or AVF), to speed up the blood purification during hemodialysis of patients with renal insufficiency, induces significant rheological and mechanical modifications of the vascular network. In this study, we investigated the impact of the creation of an AVF with a zero-dimensional network model of the vascular system of an upper limb and a one-dimensional model around the anastomosis. We compared the simulated distribution of flow rate in this vascular system with Doppler ultrasound measurements. We studied three configurations: before the creation of the AVF, after the creation of the AVF, and after a focal reduction due to a hyper flow rate. The 0D model predicted the bounds of the diameter of the superficial vein that respects the flow constraints, assuming a high capillary resistance. We indeed highlighted the importance of knowing the capillary resistance as it is a decisive parameter in the models. We also found that the model reproduced the Doppler measurements of flow rate in every configuration and predicted the distribution of flow in cases where the Doppler was not available. The 1D model allowed studying the impact of a venous constriction on the flow distribution, and the capillary resistance was still a crucial parameter.