G. Korniss
ABSTRACT
We investigate the universal characteristics of the simulated time horizon of the basic conservative parallel algorithm when implemented on regular lattices. This technique [1, 2] is generically applicable to various physical, biological, or chemical systems where the underlying dynamics is asynchronous. Employing direct simulations, and using standard tools and the concept of dynamic scaling from non-equilibrium surface/interface physics, we identify the universality class of the time horizon and determine its implications for the asymptotic scalability of the basic conservative scheme. Our main finding is that while the simulation converges to an asymptotic nonzero rate of progress, the statistical width of the time horizon diverges with the number of PEs in a power law fashion. This is in contrast with the findings of Ref. [3]. This information can be very useful, e.g., we utilize it to understand optimizing the size of a moving "time window" to enforce memory constraints.
- B. D. Lubachevsky. Efficient Parallel Simulations of Asynchronous Cellular Arrays. Complex Systems 1, 1099-1123 (1987).Google Scholar
- B. D. Lubachevsky. Efficient Parallel Simulations of Dynamic Ising Spin Systems. J. Comput. Phys.75, 103-122 (1988). Google ScholarDigital Library
- A. G. Greenberg, S. Shenker, and A. L. Stolyar. Asynchronous Updates in Large Parallel Systems. Proc. ACM SIGMETRICS, Performance Eval. Rev.24, 91-103 (1996). Google ScholarDigital Library
- R. Fujimoto. Parallel Discrete Event Simulation. Commun. of the ACM33, 30-53 (1990). Google ScholarDigital Library
- D. M. Nicol and R. M. Fujimoto. Parallel Simulation Today. Annals of Operations Research53 249-285 (1994).Google Scholar
- K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics. an Introduction, 3rd ed. (Springer, Berlin, 1997).Google Scholar
- K. M. Chandy and J. Misra. Distributed Simulation: a Case Study in Design and Verification of Distributed Programs. IEEE Trans. on Softw. Eng.SE-5, 440-452 (1979).Google Scholar
- K. M. Chandy and J. Misra. Asynchronous Distributed Simulation via a Sequence of Parallel Computations. Commun. ACM24, 198-205 (1981). Google ScholarDigital Library
- R. J. Glauber. Time-Dependent Statistics of the Ising Model. J. Math. Phys.4, 294 (1963).Google Scholar
- G. Korniss, M. A. Novotny, and P. A. Rikvold. Parallelization of a Dynamic Monte Carlo Algorithm: a Partially Rejection-Free Conservative Approach. J. Comput. Phys.153, 488-508 (1999). Google ScholarDigital Library
- G. Korniss, C. J. White, P. A. Rikvold, and M. A. Novotny. "Dynamic Phase Transition, Universality, and Finite-Size Scaling in the Two-Dimensional Kinetic Ising Model in an Oscillating. Phys. Rev. E63, 016120 (2001).Google Scholar
- A.-L. Barabási and H. E. Stanley. Fractal Concepts in Surface Growth. (Cambridge University Press, Cambridge, 1995)Google Scholar
- Timothy Halpin-Healy and Yi-Cheng Zhang. Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics. Phys. Rep.254 215-414 (1995).Google Scholar
- J. Krug. Origins of scale invariance in growth processes. Adv. Phys.46, 139-282 (1997).Google Scholar
- B. J. Overeinder. Distributed Event-driven Simulation: Scheduling Stategies and Resource Management. Ph.D. thesis, Universiteit van Amsterdam, 2000.Google Scholar
- B. J. Overeinder, A. Schoneveld, and P. M. A. Sloot. Self-organized Criticality in Optimistic Simulation of Correlated Systems. J. Parallel and Distributed Computing, submitted.Google Scholar
- B. J. Overeinder, A. Schoneveld, and P. M. A. Sloot. Spatio-temporal correlations and rollback distributions in optimistic simulations. Proceedings of the 15th Workshop on Parallel and Distributed Simulation (IEEE Comput. Soc., Los Alamitos, CA, 2001) p. 145-152. Google ScholarDigital Library
- R. E. Felderman and L. Kleinrock. Bounds and Approximations for Self-Initiating Distributed Simulation without Lookahead. ACM Trans. Model. Comput. Simul. 1, 386 (1991). Google ScholarDigital Library
- D. M. Nicol. Parallel Self-Initiating Discrete-Event Simulations. ACM Trans. Model. Comput. Simul. 1, 24 (1991). Google ScholarDigital Library
- J. S. Steinman. Breathing Time Warp. in Proceedings of the 7th Workshop on Parallel and Distributed Simulation (PADS'93), Vol. 23, No. 1, edited by R. Bagrodia and D. Jefferson (Soc. Comput. Simul., San Diego, CA, 1993), p. 109-118. Google ScholarDigital Library
- J. S. Steinman. Discrete-Event Simulation and the Event Horizon. in Proceedings of the 8th Workshop on Parallel and Distributed Simulation (PADS'94), edited by D. K. Arvind, R. Bagrodia, and J. Y.-B. Lin (Soc. Comput. Simul., San Diego, CA, 1994), p. 39-49. Google ScholarDigital Library
- J. S. Steinman. Discrete-Event Simulation and the Event Horizon II: Event List Management. in Proceedings of the 9th Workshop on Parallel and Distributed Simulation (PADS'96), (IEEE Comput. Soc. Press, Los Alamitos, CA, 1996), p. 170-178. Google ScholarDigital Library
- F. Family and T. Vicsek. Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model. J. Phys. A 18, L75-81 (1985)Google ScholarCross Ref
- G. Korniss, Z. Toroczkai, M. A. Novotny, and P. A. Rikvold. From Massively Parallel Algorithms and Fluctuating Time Horizons to Non-equilibrium Surface Growth. Phys. Rev. Lett.84, 1351-1354 (2000).Google Scholar
- M. Kardar, G. Parisi, and Y.-C. Zhang. Dynamic Scaling of Growing Interfaces. Phys. Rev. Lett.56, 889-892 (1986).Google Scholar
- G. Korniss, M. A. Novotny, Z. Toroczkai, and P. A. Rikvold. Nonequilibrium Surface Growth and Scalability of Parallel Algorithms for Large Asynchronous Systems. in Computer Simulation Studies in Condensed Matter Physics XIII, Springer Proceedings in Physics, Vol. 86, editors D. P. Landau, S. P. Lewis, and H.-B. Schüttler (Springer-Verlag, Berlin, Heidelberg, 2001), p. 183-188.Google Scholar
- Z. Toroczkai, G. Korniss, S. Das Sarma, and R. K. P. Zia. Extremal Point Densities of Interface Fluctuations. Phys. Rev. E62, 276 (2000).Google Scholar
- J. Krug and P. Meakin. Universal Finite-Size Effects in the Rate of Growth Processes. J. Phys. A23, L987 (1990).Google Scholar
- S. Raychaudhuri, M. Cranston, C. Przybyla, and Y. Shapir. Maximal Height Scaling of Kinetically Growing Surfaces. Phys. Rev. Lett.87, 136101 (2001).Google Scholar
Index Terms
- Statistical properties of the simulated time horizon in conservative parallel discrete-event simulations
Recommendations
Time scale combining of conservative parallel discrete event simulations
IPPS '95: Proceedings of the 9th International Symposium on Parallel ProcessingVery often many parameterized trials of a simulation are required. Modifying parameters of a simulation will often only modify a fraction of the work. This paper proposes time scale combining (TSC) to combine multiple independent simulation trials by ...
Discrete-event simulation and the event horizon
PADS '94: Proceedings of the eighth workshop on Parallel and distributed simulationThe event horizon is a very important concept that is useful for both parallel and sequential discrete-event simulations. By exploiting the event horizon, parallel simulations can process events in a manner that is risk-free (i.e., no antimessages) in ...
Discrete-event simulation and the event horizon
The event horizon is a very important concept that is useful for both parallel and sequential discrete-event simulations. By exploiting the event horizon, parallel simulations can process events in a manner that is risk-free (i.e., no antimessages) in ...
Comments