1 Proceedings of the 9 th International Symposium on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS 2001), Cincinnati, Ohio, IEEE Computer Society Press, 15-18 August 2001. Effect of Event Orderings on Memory Requirement in Parallel Simulation Y.M. Teo, B.S.S. Onggo and S.C. Tay Department of Computer Science National University of Singapore 3 Science Drive 2 Singapore 117543 email: teoym@comp.nus.edu.sg Abstract A new formal approach based on partial order set (poset) theory is proposed to analyze the space requirement of discrete-event parallel simulation. We divide the memory required by a simulation problem into memory to model the states of the real-world system, memory to maintain a list of future event occurrences, and memory required to implement the event synchronization protocol. We establish the relationship between poset theory and event orderings in simulation. Based on our framework, we analyze the space requirement using an open and a closed system as examples. Our analysis shows that apart from problem size and traffic intensity that affects the memory requirement, event ordering is an important factor that can be analyzed before implementation. In an open system, a weaker event ordered simulation requires more memory than strong ordering. However, the memory requirement is constant and independent of event ordering in closed systems. 1. Introduction Parallel simulation offers the potential to speedup simulations and to increase the size and complexity of models simulatable within a given time. However, additional memory is required by these event synchronization protocols that exploit parallelism. While much effort has been devoted to improve the runtime of parallel and distributed simulation, the amount of memory required for a simulation run is also an important issue to address. In conservative protocols [3,5], events are executed in the correct event time order. To prevent deadlock, null messages are introduced and it has been shown that the memory overhead for null messages can grow at an exponential rate [18]. On the other hand, the optimistic approach [12] executes simulation events without the consideration for event ordering and a rollback mechanism is used to correct out-of-order event execution. Additional memory is required to store the simulation states in anticipation of rollbacks. There have been many studies on the space aspect of parallel simulation but most of them concentrate on managing the memory required to implement various synchronization protocols. In particular, conservative approach focuses on reducing the number of null messages, for example, the carrier-null mechanism [4] demand-driven method [1], and flushing method [18]. For optimistic approach, the focus is on delimiting the optimism thus constraining the memory consumption, and to reclaim memory before a simulator runs out of storage, for example, the use of event horizon in Breathing Time Bucket [17], the adaptive Time Warp [2], message send- back [11,13], the artificial rollback [15], adaptive memory management [6]. There are few publications on space analysis using analytical methods [13,22], and they concentrated on the CMB protocol only. Since each execution platform contains a fixed amount of memory, a performance model that analyzes the memory requirement of a simulation problem is necessary in understanding the potentials and limits of exploiting parallelism. This paper proposes a methodology to study the memory required to implement a simulation model of a real-world problem based on event ordering. Poset theory is used to formalize event ordering in simulation. The analysis in this paper is independent of the synchronization protocol used, and we study the effect of different event orderings on memory requirements. The rest of this paper is organized as follows. Section 2 presents an overview of simulation modeling process. Section 3 defines our memory analysis framework. Section 4 introduces the poset theory and its relationship to event orderings in simulation. We formalize the three event orderings using poset theory and derive their