Multiple Gateways (GWs) provide network connectivity to Internet of Things (IoT) sensors in a Wide Area Network (WAN). The End Nodes (ENs) can connect to any GW by discovering and acquiring its periodic beacons. This provides GW diversity and hence improves coverage. If the GWs are within vicinity to each other, and they keep sending periodic beacons to be discovered, the result is interference and collisions. In this study, the impact of such intra-network interference is analyzed to determine the maximum number of GWs that can co-exist within a given urban neighborhood. The paper shows the relationship between beacon collisions and the resulting packet loss rates in a given urban environment. The expected collision rates are calculated for the Medium Access Control (MAC) layer. The eventual packet loss rates are calculated with the MAC and Physical (PHY) layers combined. For this purpose, a new co-channel interference model is presented. The model calculates the average Carrier to Interference ratio (C/I) averaged across all the colliding events. It takes into account the partial overlap durations and the relative power of each colliding signal. The model shows that a collision does not always cause a packet loss. Packet losses occur if there is a collision and if the C/I is below a threshold. The performance evaluation is presented using a combination of analytical and simulation methods. The analytical methods provide the theoretical foundation, and have been used to validate the simulation results. Furthermore, the system models are developed from experimental data obtained from measurements with real hardware. Numerical results are provided with a low bit rate Gaussian Frequency Shift Keying (GFSK) modulation at the PHY layer, which is derived from the IEEE 802.15.4 standard specification. This paper provides guidance on selecting the right GFSK modulation parameters for such low bit-rate and narrow bandwidth IoT applications. The analysis and simulation results show that larger beacon intervals help in reducing beacon loss rates, at the cost of larger beacon acquisition latency. On the flip side, the gateway discovery latency reduces with increasing GW density thanks to abundance of beacons.