In this paper, we propose a new traffic model (with correlation in interarrivals) for composite arrival process of packets in broadband networks and individual source modeling. The traffic model involves a generalization of Poisson process which is referred to as correlated interarrival time Poisson process (CIPP). The CIPP, a stationary counting process, is parametrized by a correlation parameter ρ which represents the degree of correlation in adjacent interarrivals in addition to λ, the intensity of the process. It is shown by simulations that this arrival process models well the real-time traffic source, in particular the video source. The burstiness measure corresponding to this process is evaluated as defined in Saito et al. It turns out that although CIPP is not strictly a self-similar model, it does exhibit self-similar behaviour over a range of time scales. We explore, by simulations, the relation between the positive correlation in interarrivals and the estimated local Hurst parameter.