Correlated Interarrival time Process (CIPP) has been proposed in [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 undertake the performance modeling of more realistic finite buffered statistical multiplexer with smoothed VBR video traffic input using CIPP/M/1/K queue. Queueing performance measures considered here are, packet loss probability and conditional packet loss probability. The buffer occupancy distribution in a queue with real-world MPEG-1 VBR video traffic is compared with that of its `best fit' CIPP/M/1/K. The above simulation results show that, the correlation in interarrivals degrades the queueing performance in the finite capacity queue case also. (In [2], we have shown analytically that the (positive) correlation in interarrivals in a CIPP/M/1 queue degrades the queueing performance). Finally, we consider the fluid-flow approximation of queues with CIPP arrivals to study the behavior of statistical multiplexer with VBR video traffic input. Comparisons with other models like, Markov chain, histogram model are also undertaken.