In this paper, we analyze the stochastic characteristics of the measured video telephony service traffic and propose a mathematical model of the video telephony service traffic based on the analyzed stochastic characterisitics. From our analysis, a voice traffic can be modelled by a renewal process with deterministic inter-arrival times and fixed packet size. On the other hand, a video traffic is modelled by an on and off source, where on and off periods are according to gamma distributions with respective parameters. Using the mathematical model, we estimate the required bandwidth to satisfy a given Quality of Service (QoS) requirement for the video telephony service traffic. To show the validity of our analysis, numerical studies with the NS-2 simulator are provided.