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.

On constructing optimistic simulation algorithms for the discrete event system specification

“…The liveness proof is taken, with minor adaptations, from Leivent and Watro [1993], where it was shown that if certain progress axioms hold, then global virtual time always eventually increases.…”

“…To prove this assumption, it is sufficient show that the progress axioms stated by Leivent and Watro [1993] hold. The progress axioms are:…”

A formal specification and verification framework for Time Warp-based parallel simulation

“…In addition, before the execution of the simulation object, every object receives messages The specification is sufficient to provide complete coverage of the time warp protocol and can be extended to show correctness of various optimizations. The framework can also be refined to model a more realistic distributed system behavior such that a proof of correctness similar to Leivent and Watro's [18] may be attempted. However, this specification is designed to be sufficient for proving correctness of optimizations to the algorithm and helps in providing a better understanding of the time warp protocol.…”

“…These efforts primarily focused on specific aspects of a parallel and distributed simulation system. Leivent and Watro [18] were the first to suggest a mathematical foundation for a time warp-based system. They developed a simple formal model of the the time warp approach to distributed computation and proven several important properties of the model.…”

“…The formal specification framework presented here is similar to the mathematical framework suggested by Leivent and Watro [18] in that it also models a complete time warp system. The distinction between Leivent and Watro and this work is the use of a software specification language rather than a purely mathematical model.…”