We have developed a Generalized Timed Petri Net (GTPN) model for evaluating the performance of computer systems. Our model is a generalization of the TPN model proposed by Zuberek [1] and extended by Razouk and Phelps [2]. In this paper, we define the GTPN model and present how performance estimates are obtained from the GTPN. We demonstrate the use of our automated GTPN analysis techniques on the dining philosophers example. This example violates restrictions made in the earlier TPN models. Finally, we compare the GTPN to the stochastic Petri net (SPN) models. We show that the GTPN model has capabilities for modeling and analyzing parallel systems lacking in existing SPN models. The GTPN provides an efficient, easily used method of obtaining accurate performance estimates for models of computer systems which include both deterministic and geometric holding times.