David M. Nicol
ABSTRACT
This paper describes a method for simulating a large class of queueing network models with Markovian phase-type distributions on parallel architectures. The method, which is based on uniformization, exploits Markovian properties that permit one to first build schedules of simulation times at which processors ought to synchronize, and then simulate a mathematically correct sample path through the pre-chosen schedule. While the technique eliminates many of the overheads incurred by other synchronization methods, it may suffer when the maximum rate (in simulation time) at which one processor might possibly ever send jobs to another is much larger than the average rate at which it actually does. We show how to reduce these overheads, sometimes doubling the execution rate as a result. We discuss experiments performed on the Intel iPSC/2 and Touchstone Delta architectures, where speedups in excess of 155 are observed on 256 processors.
- 1.M. Abrams and P.F. Reynolds (eds.) 6th Workshop on Parallel and Distributed Simulation (PADS92). Simulation Series vol. 24, no. 3. The Society for Computer Simulation International, San Diego, CA, 1992.Google Scholar
- 2.L. Bomans and D. Roose, "Benchmarking the iPSC/2 Hypercube Multiprocessor," Concurrency: Practice and Experience, vol. 1, no. 1, pp. 3-18, 1989.Google ScholarCross Ref
- 3.J.P. Buzen, "Computational Algorithms for Closed Queueing Networks with Exponential Servers," Commun. A CM, vol. 16, no. 9, pp. 527-531, September 1973. Google ScholarDigital Library
- 4.R.M. Fujimoto, "Parallel Discrete Event Simulation," Commun. A CM, vol. 33, no. 10, pp. 31- 53,October 1990. Google ScholarDigital Library
- 5.R.M. Fujimoto, J.-J. Tsai and G.C. Gopalakrishnan, "Design and Evaluation of the Rollback Chip: Special Purpose Hardware for Time Warp," IEEE Trans. Comput., vol. 41, no. 1, pp. 68-82, January 1992. Google ScholarDigital Library
- 6.A. Goyal and S.S. Lavenberg. "Modeling and Analysis of Computer System Availability," IBM Journal of Research and Development, vol. 31, no. 6, pp. 651-664, November 1987. Google ScholarDigital Library
- 7.K.J. Gordon, R.F. Gordon, J.F. Kurose and E.A. MacNair. "An Extensible Visual Environment for Construction and Analysis of Hierarchically- Structured Models of Resource Contention Systems," Management Science, vol. 37, no. 6, pp. 714-732, June 1991. Google ScholarDigital Library
- 8.D. Gross and D.R. Miller, "The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes," Operations Research, vol. 32, no. 2, pp. 343-361, March-April 1984.Google ScholarDigital Library
- 9.P. Heidetberger and D.M. Ni~ol, "Conservative Parallel Simulation of Continuous Time Markov Chains Using Uniformization," IBM Research Report RC 16780~ Yorktown Heights, New York, 1991. To appear in IEEE Transactions on Parallel and Distributed Systems. Google ScholarDigital Library
- 10.D. R. Jefferson, "Virtual Time," A CM Trans. on Programming Languages and Systems, vol. 7, no. 3, pp. 404- 425, July 1985. Google ScholarDigital Library
- 11.A. Jensen, "Markoff Chains as an Aid in the Study of Markoff Processes," Skand. Aktuarietidskr., vol. 36, pp. 87-91, 1953.Google Scholar
- 12.P.A.W. Lewis and G.S. Shedler, "Simulation of Nonhomogeneous Poisson Processes by Thinning," Naval Research Logistics Quarterly, vol. 26, no. 3, pp. 403-413, September 1979.Google ScholarCross Ref
- 13.S.L. Lillevik, "The Touchstone 30 Gigaflop Delta Prototype", Proceedings of the 1991 Distributed Memory Computer Conference, IEEE Press, pp. 671-677, April 1991.Google ScholarCross Ref
- 14.B.D. Lubachevsky, "Simulating Colliding Rigid Disks in Parallel Using Bounded Lag Without Time Warp", Distributed Simulation, 1990, Simulation Series vol. 22, no. 2., pp. 194-204, January 1990.Google Scholar
- 15.D.M. Nicol and P. Heidelberger, "Optimistic Parallel Simulation of Continuous Time Markov Chains Using Uniformization," IBM Research Report RC 17932, Yorktown Heights, New York, 1992. To appear in journal of Parallel and Distributed Computing. Google ScholarDigital Library
- 16.R. Righter and J.V. Walrand, "Distributed Simulation of Discrete Event Systems," Proceedings of the IEEE, vol. 77, no. 1, pp. 99-113, January 1989.Google ScholarCross Ref
- 17.S. Ross, Stochastic Processes, John Wiley and Sons, New York, 1983.Google Scholar
- 18.J.G. Shanthikumar, "Uniformization and Hybrid Simulation/Analytic Models of Renewal Processes," Operations Research, vol. 34, no. 4, pp. 573-580, july-August 1986. Google ScholarDigital Library
Index Terms
- Parallel simulation of Markovian queueing networks using adaptive uniformization
Recommendations
Parallel simulation of Markovian queueing networks using adaptive uniformization
This paper describes a method for simulating a large class of queueing network models with Markovian phase-type distributions on parallel architectures. The method, which is based on uniformization, exploits Markovian properties that permit one to first ...
Optimistic Parallel Simulation of Continuous Time Markov Chains Using Uniformization
Special issue on parallel and discrete event simulationIn an earlier paper we described how uniformization can be used as the basis of a conservative parallel simulation algorithm for simulating a continuous time Markov chain (CTMC). The fundamental notion is that uniformization permits the calculation (in ...
Parallel discrete-event simulation of FCFS stochastic queueing networks
PPEALS '88: Proceedings of the ACM/SIGPLAN conference on Parallel programming: experience with applications, languages and systemsPhysical systems are inherently parallel; intuition suggests that simulations of these systems may be amenable to parallel execution. The parallel execution of a discrete-event simulation requires careful synchronization of processes in order to ensure ...
Comments