Mathematical foundations for time warp systems

Abstract

We develop a simple formal model of the Time Warp approach to distributed computation, prove several important properties of the model, and devise some extensions to Time Warp that provide improved termination behavior. Our model consists of processes that communicate solely via message passing. One of the basic process steps is a rollback operation that includes message retraction via transmission of antimessages. In the model, we consider three problems: safety, progress, and termination. By safety, we mean that for a given system of processes, if a run of the system terminates, then the final system state of the run is identical to the final system state of a rollback-free run. We give premises that imply safety, and a counterexample that shows how safety can fail. By progress, we mean that, as a run of a system proceeds, the minimum timestamp of an unprocessed message always eventually increases. We state three axioms that imply the progress property. By termination, we mean that, if all rollback-free runs of a system terminate, then all runs terminate. The termination property is generally false in existing implementations of Time Warp systems due to the possibility of Time Warp vortices. We define additional mechanisms that can guarantee the termination property for most Time Warp applications.