Despite their attractive properties, networked virtual environments (net-VEs) are notoriously difficult to design, implement, and test due to the concurrency, real-time and networking features in these systems. Net-VEs demand high quality-of-service (QoS) requirements on the network to maintain natural and real-time interactions among users. The current practice for net-VE design is basically trial and error, empirical, and totally lacks formal methods. This paper proposes to apply a Petri net formal modeling technique to a net-VE-NICE (narrative immersive constructionist/collaborative environment), predict the net-VE performance based on simulation, and improve the net-VE performance. NICE is essentially a network of collaborative virtual reality systems called the CAVE-(CAVE automatic virtual environment). First, we introduce extended fuzzy-timing Petri net (EFTN) modeling and analysis techniques. Then, we present EFTN models of the CAVE, NICE, and transport layer protocol used in NICE: transmission control protocol (TCP). We show the possibility analysis based on the EFTN model for the CAVE. Then, by using these models and design/CPN as the simulation tool, we conducted various simulations to study real-time behavior, network effects and performance (latencies and jitters) of NICE. Our simulation results are consistent with experimental data.