We investigate conservative parallel discrete event simulations for logical circuits on shared-memory multiprocessors. For a first estimation of the possible speedup, we extend the critical path analysis technique by partitioning strategies. To incorporate overhead due to the management of data structures, we use a simulation on an ideal parallel machine (PRAM). This simulation can be directly executed on the SB-PRAM prototype, yielding both an implementation and a basis for data structure optimizations. One of the major tools to achieve these optimizations is the SB-PRAM's hardware support for parallel prefix operations. Our reimplementation of the PTHOR program on the SB-PRAM yields substantially higher speedups than before.