In this paper, we propose a new traffic model (with correlations in interarrivals), herein referred to as Correlated Interarrival time Poisson Process (CIPP), for modeling the VBR video traffic. The CIPP - a generalization of the Poisson process with stationary increments - is parameterized by a correlation parameter `ρ' which represents the degree of correlation in adjacent interarrivals in addition to `λ' the intensity of the process. We present the theory for the CIPP/M/1 queue and derive the corresponding expressions for queueing performance measures of interest. We undertake the performance modeling of statistical multiplexer with VBR video traffic input using the CIPP/M/1 queue. The simulation results show that the CIPP/M/1 queue approximates well the queueing situation as encountered by the VBR traffic in broadband networks.