Intelligent reflecting surface (IRS) has been regarded as an efficient technology to enhance the network performance. Since the IRS can assist transmitters to communicate in a directional reflection way, its deployment usually has a strong correlation with the locations of transmitters. In order to well capture the directional transmission and the spatial correlation while guaranteeing the analytical tractability, we propose an IRS-assisted network model based on a Gauss-Poisson process and a simple yet effective IRS reflected model. Under this setup, we derive the success probabilities for two association policies, namely the dedicated transmitter-receiver pairs with fixed-distance and the nearest associations. To highlight the impact of the IRS, we also derive the success probabilities of three special cases, i.e., without deploying IRSs, ignoring the IRS interference, and blocked direct link between transceivers. The results show that deploying IRS improves the success probability, especially in the cases of IRSs deployed near the transmitters and blocked direct link, and the IRS interference cannot be ignored which becomes the bottleneck factor in the case of transmitters equipped with massive antenna arrays. Owing to the proposed model, the impact of the correlation between IRSs and transmitters is well studied, which provides useful guidance for integrating IRSs into wireless networks.