Modeling Intra-object Parallelism in Parallel Discrete Event Simulation

In parallel discrete event simulation, a run in which events are executed at each object according to their timestamp is a correct run (i.e., it satisses causal-ity). In such a run, the execution order of events at any object corresponds to the total order imposed on them by timestamps. In this paper we introduce the notion of weak causality between simulation events. Such a relation deenes a partial order on the events occurring at an object based on both timestamp values and a notion of events' connict here introduced. Weak causality models the intra-object parallelism and allows to deene the largest set of runs of a simulation that are equivalent to the timestamp ordered run. More technically, all runs in which the execution order of events at each object is a linear extension of the partial order imposed by weak causality are shown to be equivalent to the timestamp ordered run. Finally , we describe an application of weak causality to optimistic synchronization (Time Warp) by introducing a synchronization protocol, namely weak causality based Time Warp, that allows out of timestamp order executions of events which are not weakly causally related. Compared to classical Time Warp synchronization , the introduced protocol has the potential to reduce the number of rollbacks and their extent. Finally, our analysis shows some similarity with the database se-rializability theory.