This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
The Circulating Processor Model of Parallel Systems
May 1997 (vol. 46 no. 5)
pp. 572-587

Abstract—This paper introduces the circulating processor model for parallel computer systems. Models of parallel systems tend to be computationally complex due to synchronization constraints such as task forking and joining. However, product form queuing network models remain computationally efficient as the size of the system grows by calculating only the mean performance metrics of the system. The circulating processor model is a product form queuing network model that differs from more traditional models in that the processors circulate among the parallel applications. In traditional models, the tasks of the parallel application circulate among the processors. Behaviors such as forking and joining of tasks and barrier synchronizations are better captured using this new approach. The circulating processor model may be load-dependent or load-independent. For systems that contain a single parallel application, the load-dependent circulating processor model is exact, while the load-independent model is not. In the latter case, an exact error can be calculated. For systems that contain multiple parallel applications, the load-dependent circulating processor model is a good approximation to the actual system, while the load-independent model is not. A case study using Parallel Virtual Machine (PVM) on a network of workstations illustrates the applicability of the circulating processor model.

[1] M. Ajmone Marsan, G. Balbo, and G. Conte, Performance Models of Multiprocessor Systems.Cambridge, Mass.: MIT Press, 1986.
[2] M. Reiser and S. Lavenberg, “Mean-Value Analysis of Closed Multichain Queueing Networks,” J. ACM, vol. 27, no. 2, pp. 313-322, 1980.
[3] P. Heidelberger and K.S. Trivedi, "Queueing Network Models for Parallel Processing with Asynchronous Tasks," IEEE Trans. Computers, vol. 31, no. 11, pp. 1,099-1,109, Nov. 1982.
[4] P. Heidelberger and K.S. Trivedi, "Analytic Queueing Models for Programs with Internal Concurrency," IEEE Trans. Computers, vol. 32, no 1, pp. 73-82, Jan. 1983.
[5] A. Thomasian and P.F. Bay, "Analytic Queueing Network Models for Parallel Processing of Task Systems," IEEE Trans. Computers, vol. 35, no. 12, pp. 1,045-1,054, Dec. 1986.
[6] R. Nelson, D. Towsley, and A. Tantawi, “Performance Analysis of Parallel Processing Systems,” IEEE Trans. Software Engineering, vol. 14, pp. 532–539, Apr. 1988.
[7] R.D. Nelson, “A Performance Evaluation of a General Parallel Processing Model,” Proc. ACM Sigmetrics Conf. Measurement and Modeling of Computer Systems, pp. 13–26, May 1990.
[8] M.K. Vernon, E.D. Lazowska, and J. Zahorjan, “An Accurate and Efficient Performance Analysis Technique for Multiprocessor Snooping Cache-Consistency Protocols,” Proc. 15th Ann. Int'l Symp. Computer Architecture, pp. 308–315, May 1988.
[9] K.C. Sevcik and S. Zhou, “Performance Benefits and Limitations of Large NUMA Multiprocessors,” Performance Evaluation 20, pp. 185-205, 1994.
[10] K. C. Sevcik,“Characterizations of parallelism in applications and their use in scheduling,”inProc. ACM Sigmetrics Conf., Berkeley, 1989, pp. 171–180.
[11] C.-S. Chang, R. Nelson, and D.D. Yao, "Optimal Task Scheduling on Distributed Parallel Processors," Performance '93, G. Iazeolla and S. Lavenberg, eds., pp. 205-219, 1993.
[12] J.D.C. Little, "A Proof of the Queueing Formula L =λW," Operations Research, vol. 9, pp. 383-387, 1961.
[13] G. Franceschinis and R.R. Muntz, "Bounds for Quasi-Lumpable Markov Chains," Performance '93, G. Iazeolla and S. Lavenberg, eds., pp. 220-244, 1993.
[14] Simulog Corp., QNAP2 Reference Manual, 1989.
[15] F. Baskett, K.M. Chandy, R.R. Muntz, and R. Palacios, “Open, Closed and Mixed Networks of Queues with Different Classes of Customers,” J. ACM, vol. 22, no. 2, pp. 248-260, 1975.
[16] V.S. Sunderam, "PVM: A Framework for Parallel Distributed Computing," technical report, Mathematical Sciences Section of Oak Ridge Nat'l Laboratory, 1991.

Index Terms:
Circulating processor model, load-dependent models, parallel systems, performance evaluation, product form queuing network models.
Citation:
Amy W. Apon, Larry W. Dowdy, "The Circulating Processor Model of Parallel Systems," IEEE Transactions on Computers, vol. 46, no. 5, pp. 572-587, May 1997, doi:10.1109/12.589223
Usage of this product signifies your acceptance of the Terms of Use.