IP networks were designed to support non-real time applications, such as file transfer or e-mail. These applications are characterised by their bursty traffic and high bandwidth demands at burst times, but they are not highly sensitive to delay or delay variation (jitter). On the other hand, the VoIP application requires timely packet delivery with low delay, jitter and packet loss values. Integration of voice and data onto a single network is becoming a priority for many network operators. To achieve that goal, IP networks must be enhanced with mechanisms that ensure the quality of service required to carry real-time traffic such as voice. Three parameters emerge as the primary factors affecting voice quality within networks that offer VoIP technologies: clarity, end-to-end delay and echo. To support interactive voice applications on an IP network, we must be able to control four QoS categories: bandwidth, delay (latency), jitter and packet loss. In this paper, we present the behaviour of packet transit times for a VoIP application that produces an 8 kbps data stream. We simulate a simple network with one upstream, one downstream and one backbone link. Two scheduling principles are configured in network nodes (routers): FIFO and priority queuing. We present probability distribution functions for packet delay of VoIP traffic at different network loads. We then compare the performance of VoIP applications on the network with priority queuing (voice having priority over data) and FIFO queuing.