The stochastic Petri net (SPN) model is well suited to formal representation of concurrency, synchronization, and communication. In this paper we focus on discrete event simulation methods for SPN models with special structure and define a symmetric SPN. Exploiting properties of a symmetric SPN and underlying regenerative process structure, we establish steady state estimation procedures based on independent, nonidentically distributed blocks of the marking process. We also establish estimation procedures for passage times in the symmetric SPN setting. These results lead to efficient estimation procedures for delay/throughput characteristics of ring networks with identical ports.