Most work to date in parallel and distributed discrete event simulation is based on assigning precise time stamps to events, and time stamp order event processing. An alternative approach is examined where modelers use time intervals rather than precise time stamps to specify uncertainty as to when events occur. Partial orderings called approximate time (AT) and approximate time causal (ATC) order are proposed and synchronization algorithms developed that exploit these specifications to yield more efficient execution on parallel and distributed computers. Performance measurements of the AT-ordering mechanism on a cluster of workstations demonstrate as much as twenty-fold performance improvement compared to time stamp ordering with negligible impact on the results computed by the simulation. The context for much of this work is federated simulation systems that provided the initial motivation for this work. These results demonstrate that exploiting temporal uncertainty inherent in the ...