Correlated Interarrival time Process (CIPP) has been proposed in Ref. 1, for modeling both the composite arrival process of packets in broadband networks and the individual source modeling. The CIPP - a generalization of the Poisson process - is a stationary counting process and 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. In this paper, we present the performance modeling of VBR video traffic in ATM networks, using CIPP/M/1 queue. We first give the expressions for stationary distributions for CIPP/M/1 queue. Then, we derive the queueing measures of interest. We simulate a queue with smoothed VBR video trace data as input (with exponential services) to compare with the theoretical measures derived above. Experimental results show that the CIPP/M/1 queue, models well the ATM multiplexer performance with the real world VBR video traffic input.