On Parallel Stochastic Simulation of Diffusive Systems

The parallel simulation of biochemical reactions is a very interesting problem: biochemical systems are inherently parallel, yet the majority of the algorithms to simulate them, including the well-known and widespread Gillespie SSA, are strictly sequential. Here we investigate, in a general way, how to characterize the simulation of biochemical systems in terms of Discrete Event Simulation. We dissect their inherent parallelism in order both to exploit the work done in this area and to speed-up their simulation. We study the peculiar characteristics of discrete biological simulations in order to select the parallelization technique which provides the greater benefits, as well as to touch its limits. We then focus on reaction-diffusion systems: we design and implement an efficient parallel algorithm for simulating such systems that include both reactions between entities and movements throughout the space.

[1]  Victor Yau,et al.  Automating parallel simulation using parallel time streams , 1999, TOMC.

[2]  Philip Heidelberger,et al.  Experiments with initial transient deletion for parallel, replicated steady-state simulations , 1992 .

[3]  Stephen Gilmore,et al.  Evaluating the Performance of Skeleton-Based High Level Parallel Programs , 2004, International Conference on Computational Science.

[4]  D. Bray,et al.  Stochastic simulation of chemical reactions with spatial resolution and single molecule detail , 2004, Physical biology.

[5]  Philip Heidelberger,et al.  Analysis of parallel replicated simulations under a completion time constraint , 1991, TOMC.

[6]  Satish K. Tripathi,et al.  Parallel and distributed simulation of discrete event systems , 1994 .

[7]  Luciano Bononi,et al.  Concurrent replication of parallel and distributed simulations , 2005, Workshop on Principles of Advanced and Distributed Simulation (PADS'05).

[8]  K. Mani Chandy,et al.  Asynchronous distributed simulation via a sequence of parallel computations , 1981, CACM.

[9]  Gerard T. Barkema,et al.  Monte Carlo Methods in Statistical Physics , 1999 .

[10]  David R. Jefferson,et al.  Virtual time , 1985, ICPP.

[11]  Atul Prakash,et al.  Hierarchical distributed simulations , 1988, [1988] Proceedings. The 8th International Conference on Distributed.

[12]  Philip Heidelberger,et al.  Analysis of Initial Transient Deletion for Parallel Steady-State Simulations , 1992, SIAM J. Sci. Comput..

[13]  Stephen J. Turner,et al.  A generalized carrier-null method for conservative parallel simulation , 1994, PADS '94.

[14]  Richard M. Fujimoto,et al.  Cloning parallel simulations , 2001, TOMC.

[15]  Arun Krishnan,et al.  A Parallel Implementation of Gillespie's Direct Method , 2004, International Conference on Computational Science.

[16]  Nicholas A. Hamilton,et al.  Computer-intensive simulations for cellular models , 2006 .

[17]  Adelinde M. Uhrmacher,et al.  Parallel and Distributed Spatial Simulation of Chemical Reactions , 2008, 2008 22nd Workshop on Principles of Advanced and Distributed Simulation.

[18]  Rinaldo B. Schinazi,et al.  Predator-prey and host-parasite spatial stochastic models , 1997 .

[19]  Michael A. Gibson,et al.  Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels , 2000 .

[20]  Richard C. Holt,et al.  Some deadlock properties of computer systems , 1971, SOSP '71.

[21]  Richard M. Fujimoto,et al.  Pre-sampling as an approach for exploiting temporal uncertainty , 2000, Proceedings Fourteenth Workshop on Parallel and Distributed Simulation.

[22]  K. Mani Chandy,et al.  Distributed Simulation: A Case Study in Design and Verification of Distributed Programs , 1979, IEEE Transactions on Software Engineering.

[23]  David M. Nicol,et al.  Parallel discrete-event simulation of FCFS stochastic queueing networks , 1988, PPEALS '88.

[24]  J. Elf,et al.  Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. , 2004, Systems biology.

[25]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[26]  Marta Rukoz.  Hierarchical deablock detection for nested transactions , 2005, Distributed Computing.

[27]  Simon Streltsov,et al.  Parallel replicated simulation of Markov chains: implementation and variance reduction , 1993, WSC '93.

[28]  Tianhai Tian,et al.  Parallel implementation of stochastic simulation for large-scale cellular processes , 2005, Eighth International Conference on High-Performance Computing in Asia-Pacific Region (HPCASIA'05).

[29]  Yi-Bing Lin,et al.  Parallel Independent Replicated Simulation on a Network of Workstations , 1994, PADS '94.

[30]  R. M. Fujimoto,et al.  Parallel discrete event simulation , 1989, WSC '89.

[31]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .