The universal mobile telecommunications system (UMTS) utilizes the discontinuous reception (DRX) mechanism to reduce the power consumption of mobile stations (MSs). DRX permits an idle MS to power off the radio receiver for a predefined sleep period and then wake up to receive the next paging message. The sleep/wake-up scheduling of each MS is determined by two DRX parameters: the inactivity timer threshold and the DRX cycle. In the literature, analytic and simulation models have been developed to study the DRX performance mainly for Poisson traffic. In this paper, we propose a novel semi-Markov process to model the UMTS DRX with bursty packet data traffic. The analytic results are validated against simulation experiments. We investigate the effects of the two DRX parameters on output measures including the power saving factor and the mean packet waiting time. Our study provides inactivity timer and DRX cycle value selection guidelines for various packet traffic patterns.