Accelerating Petri-Net simulations using NVIDIA Graphics Processing Units

Stochastic Petri-Nets (PNs) are combined with General-Purpose Graphics Processing Unit (GPGPUs) to develop a fast and low cost framework for PN modelling. GPGPUs are composed of many smaller, parallel compute units which has made them ideally suited to highly parallelised computing tasks. Monte Carlo (MC) simulation is used to evaluate the probabilistic performance of the system. The high computational cost of this approach is mitigated through parallelisation. The efficiency of different approaches to parallelisation of the problem is evaluated. The developed framework is then used on a PN model example which supports decision-making in the field of infrastructure asset management. The model incorporates deterioration, inspection and maintenance into a complete decision-support tool. The results obtained show that this method allows the combination of complex PN modelling with rapid computation in a desktop computer.

[1]  Mike Wright,et al.  Petri net-based modelling of workflow systems: An overview , 2001, Eur. J. Oper. Res..

[2]  Bryant Le,et al.  Modelling wind turbine degradation and maintenance , 2016 .

[3]  Stanimire Tomov,et al.  Benchmarking and implementation of probability-based simulations on programmable graphics cards , 2003, Comput. Graph..

[4]  Paul van Beek,et al.  Modelling and simulating multi-echelon food systems , 2000, Eur. J. Oper. Res..

[5]  Robert Geist,et al.  Systems modeling with xpetri , 1994, Proceedings of Winter Simulation Conference.

[6]  R. Schaller,et al.  Moore's law: past, present and future , 1997 .

[7]  John Andrews,et al.  A modelling approach to railway track asset management , 2013 .

[8]  John Andrews,et al.  A reliability analysis of railway switches , 2013 .

[9]  Wolfgang Paul,et al.  GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model , 2009, J. Comput. Phys..

[10]  Davide Aloini,et al.  Modelling and assessing ERP project risks: A Petri Net approach , 2012, Eur. J. Oper. Res..

[11]  Kevin Skadron,et al.  Pannotia: Understanding irregular GPGPU graph applications , 2013, 2013 IEEE International Symposium on Workload Characterization (IISWC).

[12]  Changwoo Lee,et al.  Task net: Transactional workflow model based on colored Petri net , 2002, Eur. J. Oper. Res..

[13]  Robert Geist,et al.  Parallel simulation of Petri nets on desktop PC hardware , 2005, Proceedings of the Winter Simulation Conference, 2005..

[14]  Armin Zimmermann,et al.  Modelling and evaluation of time aspects in business processes , 2002, J. Oper. Res. Soc..

[15]  Lars Michael Kristensen,et al.  Coloured Petri Nets - Modelling and Validation of Concurrent Systems , 2009 .

[16]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[17]  Doug Hunt,et al.  Advanced performance features of the 64-bit PA-8000 , 1995, Digest of Papers. COMPCON'95. Technologies for the Information Superhighway.

[18]  Jie Cheng,et al.  CUDA by Example: An Introduction to General-Purpose GPU Programming , 2010, Scalable Comput. Pract. Exp..

[19]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[20]  Masao Nagasaki,et al.  High Performance Hybrid Functional Petri Net Simulations of Biological Pathway Models on CUDA , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[21]  L. Dagum,et al.  OpenMP: an industry standard API for shared-memory programming , 1998 .

[22]  Pradeep Dubey,et al.  Debunking the 100X GPU vs. CPU myth: an evaluation of throughput computing on CPU and GPU , 2010, ISCA.

[23]  Brian A. Barsky,et al.  Advanced Renderman: Creating CGI for Motion Pictures , 1999 .

[24]  R. B. Randall,et al.  A hybrid maintenance model with imperfect inspection for a system with deterioration and Poisson failure , 1999, J. Oper. Res. Soc..

[25]  A. Arnold,et al.  Harvesting graphics power for MD simulations , 2007, 0709.3225.

[26]  Luís C. Neves,et al.  A Petri-Net-based modelling approach to railway bridge asset management , 2017 .

[27]  Jason Wittenberg,et al.  Clarify: Software for Interpreting and Presenting Statistical Results , 2003 .

[28]  Kishor S. Trivedi,et al.  SPNP: Stochastic Petri Nets. Version 6.0 , 2000, Computer Performance Evaluation / TOOLS.

[29]  Francesco Archetti,et al.  Computation of the makespan in a transfer line with station breakdowns using stochastic petri nets , 1987, Comput. Oper. Res..

[30]  Alistair P. Rendell,et al.  High-Performance Pseudo-Random Number Generation on Graphics Processing Units , 2011, PPAM.

[31]  Yunfei Chen,et al.  GPU accelerated molecular dynamics simulation of thermal conductivities , 2007, J. Comput. Phys..

[32]  Nukala Viswanadham,et al.  Performance analysis and design of supply chains: a Petri net approach , 2000, J. Oper. Res. Soc..