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LISPACK-A Methodology and Tool for the Performance Analysis of Parallel Systems and Algorithms
May 1993 (vol. 19 no. 5)
pp. 486-502

The performance analysis of parallel algorithms and systems is considered. For these, numerical solutions methods quickly show their limits because of the enormous state-space growth. The proposed methodology and software tool, list-manipulation parallel-modeling package (LISPACK) uses string manipulation, lumping, and recursive elimination to define the large Markovian process, its restructuring, and efficient solution. The analysis of a typical parallel system and algorithm model is developed as a case study, to discuss the features of the method. The paper has two contributions. The first is the symbolic-approach methodology proposed for the performance analysis of parallel algorithms and systems. The second is a tool that exploits the capabilities of the symbolic approach in the solution of parallel models, where the numerical techniques reveal their limits.

[1] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Menlo Park, CA: Addison-Wesley, 1974.
[2] A. Aho, J. Hopcroft, and J. Ullman,Data Structures and Algorithms. Reading, MA: Addison-Wesley, 1983.
[3] M. Ajmone Marsan, G. Balbo, G. Chiola, and G. Conte, "Modeling the software architecture of a prototype parallel machine," inProc. 1987 SIGMETRICS Conf., Alberta, Canada, May 1987.
[4] F. Baccelli and A.M. Makowski, "Asymptotic analysis of the fork join queue," inProc. Workshop on Computer Performance Evaluation, INRIA, Sophia Antipolis, France, 1986.
[5] M.A. Brun and G. Fayolle, "The distribution of the transaction processing time in a simple fork-join system," inComputer Performance and Reliability, G. Iazeolla, O. Boxma and P. J. Courtois, Eds. Amsterdam: North Holland, 1987.
[6] J.A. Carrasco and J. Figueras, "METFAC: Design and implementation of a software tool for modeling and evaluating complex fault tolerant computer systems," inProc. FTCS-16, 1986 IEEE Publications, pp. 424-429.
[7] G. Chiola and G. Franceschinis, "Colored GSPN models and automatic symmetry detection," inProc. 3rd Int. Workshop Petri Nets and Perform. Models, Kyoto, Japan, IEEE Computer Society Press, Dec. 1989.
[8] P.J. Courtois,Decomposability, Queueing and Computer System Applications. New York: Academic, 1977.
[9] P.J. Courtois and P. Semal, "Bounds for the positive eigenvectors of nonnegative matrices and their approximations by decomposition,"J. ACM, vol. 31, no. 4, 1984, pp. 804-825.
[10] M. Colajanni and S. Tucci, "soluzione Approssimata di un Modello Fork-Join,"Atti Congresso AICA, Cagliari 28 Sett., 1988.
[11] V. De Nitto Personé,et al., "Performance analysis of the basic parallel system and algorithm," RI.91.07,Ricerche di Informatica, University of Rome II, Nov. 1991.
[12] A. Douda, "Approximate performance analysis of parallel systems," inComputer Performance and Reliability, G. Iazeolla, O. Boxma and P.J. Courtois, Eds. Amsterdam: North Holland, 1987.
[13] C. Dutheillet and S. Haddad, "Aggregation of states in colored stochastic Petri nets: application to a multiprocessor architecture," inProc. 3rd Int. Workshop on Petri Nets and Performance Models(Kyoto, Japan), Dec. 1989, pp. 40-49.
[14] L. Flatto and S. Hahn, "Two parallel queues created by arrivals with two demands,"SIAM J. Appl. Math., vol. 44, pp. 1041-1053, Oct. 1984.
[15] J. Foderaro, Guest Editor, "Special Section LISP" (and related papers),Commu. ACM, vol. 34, no. 9, pp. 28-63, Sept. 1991.
[16] E. Gelenbe, "On the loop-free decomposition of stochastic finite-state systems,"Information and Control, vol. 17, pp. 464-484, 1970.
[17] E. Gelenbe and I. Mitrani,Analysis and Synthesis of Computer Systems. London: Academic, 1980.
[18] M. Ghodsi and K. Kant, "Performance analysis of parallel search algorithms on multiprocessor systems," inPERFORMANCE '90, Proc. 14th IFIP WG 7.3 Int. Symp. Computer Performance Modeling, Measurement and Evaluation, North Holland, Sept. 1990, pp. 407-421.
[19] A. Goyal and S. S. Lavenberg, "Modeling and analysis of computer system availability,"IBM J. Res. Develop., vol. 31, pp. 651-664, 1987.
[20] G. Golub and C. Van Loan,Matrix Computations. Baltimore, MD: The Johns Hopkins University Press, 1983.
[21] P. Heidelberger and K.S. Trivedi, "Analytic queueing models for programs with internal concurrency," IBM Res. Rep. RC9194, May 1982, pp. 1-22.
[22] G. Iazeolla, "The complexity of performance analysis of parallel algorithms and systems," inProc. IEEE Compeuro 91, A. Monaco, R. Negrini, Eds., May 1991, pp. 502-504.
[23] G. Iazeolla, "State space analysis and reduction techniques in the performance evaluation of parallel systems and algorithms,"Proc. 1991 SCSC, The Society for Computer Simulation, July 1991, pp. 282-286.
[24] G. Iazeolla and F. Marinuzzi, "Performance analysis of concurrent systems and parallel algorithms," RI.90.07,Ricerche di Informatica, pp. 1-22, Oct. 1990.
[25] J.G. Kemeny and J. L. Snell,Finite Markov Chains. Princeton: Van Nostrand-Reinhold, 1960, pp. 123 ff.
[26] Y.C. Liu and H.G. Perros, "Approximate analysis of closed fork/join models," TR.87.12, Department of EE&Comp. Eng.,&Dept. of Comp. Sci., North Carolina State Univ., Raleigh, 1987.
[27] R. Nelson, "A performance evaluation of a general parallel processing model,"Proc. 1990 ACM-Sigmetrics Conference, May 1990, pp. 13-26.
[28] R. Nelson and A. N. Tantawi, "Approximating task response in fork/join queues," IBM Res. Rep. RC13012, Yorktown Heights, NY, Aug. 1987, pp. 1-20.
[29] R. Nelson and A. N. Tantawi, "Approximate analysis of fork/join synchronization in parallel queues,"IEEE Trans. Comput., vol. 37, pp. 739-743, June 1988.
[30] R. Nelson and A. N. Tantawi, "Comparison of task response times in parallel systems," IBM Res. Rep., pp. 1-20, Oct. 1988.
[31] R. Nelsonet al., "Performance analysis of parallel processing systems,"IEEE Trans. Software. Eng., vol. 14, Apr. 1988.
[32] M. Neuts,Matrix-Geometric Solutions in Stochastic Models. Baltimore, MD: The Johns Hopkins University Press, 1981.
[33] P. J. Schweitzer, "Aggregation methods for large Markov chains," inMathematical Computer Performance and Reliability, P. J. Courtois, G. Iazeolla, and A. Hordijk, Eds. Amsterdam, The Netherlands: North Holland, 1984, pp. 275-285.
[34] muMATH 83 Reference Manual. Soft Warehouse Inc., Honolulu, HI.
[35] G.W. Stewart, "Computable error bounds for aggregated Markov chains,"J. ACM, pp. 271-285, 1983.
[36] G. Strang,Linear Algebra and its Applications. San Diego: Harcourt, 1988.
[37] K. Trivediet al., "Transient analysis of Markov and Markov reward models," inComputer Performance and Reliability, Proc. 2nd Int. MCPR Workshop, G. Iazeolla, P.J. Courtois, and O.J. Boxma, Eds. Amsterdam: North Holland, 1989.
[38] R. E. Tarjan, "Graph theory and gaussian elimination,"Sparse Matrix Computations. New York: Academic Press, 1976.
[39] C. Wooff and D. Hodgkinson,muMATH: A Microcomputer Algebra System, London: Academic, 1987.

Index Terms:
parallel algorithms; LISPACK; performance analysis; parallel systems; software tool; list-manipulation parallel-modeling package; string manipulation; lumping; recursive elimination; large Markovian process; symbolic-approach methodology; Markov processes; parallel algorithms; parallel processing; performance evaluation; software tools
G. Iazeolla, F. Marinuzzi, "LISPACK-A Methodology and Tool for the Performance Analysis of Parallel Systems and Algorithms," IEEE Transactions on Software Engineering, vol. 19, no. 5, pp. 486-502, May 1993, doi:10.1109/32.232014
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