A shared buffer ATM switch loaded with bursty input traffic is modeled by a discrete-time queueing system. Also, the unbalanced and correlated routing traffic patterns are considered. An approximation method to analyze the queueing system under consideration is developed. To overcome the problem regarding the size of state space to be dealt with, the entire switching system is decomposed into several subsystems, and then each subsystem is analyzed in isolation. We first propose an efficient algorithm for superposing all the individual bursty cell arrival processes to the switch. And then, the maximum entropy method is applied to obtain the steady-state probability distribution of the queueing system. From the obtained steady-state probabilities, we can derive some performance measures such as cell loss probability and average delay. Numerical examples of the proposed approximation method are given, which are compared with simulation results.