In this paper, we model the background network traffic by CIPP in an ATM multiplexer while simulating the end-to-end transport of real world VBR traffic over ATM networks. CIPP has been proposed by Manivasakan et al. (1999) for modeling broadband teletraffic. It was shown that, an empirical relationship exists between the parameter rho/ of CIPP and estimated local Hurst parameter H. This feature is made use of to study the effect of degree of self-similarity of background network traffic on various performance measures. The modeling and simulation results show the effect of self-similarity of the background process (as measured by rho/ of CIPP) on various performance measures parameterised by ATM multiplexer buffer size and decoder buffer size. © 1999 IEEE.