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  • Print publication year: 2010
  • Online publication date: February 2010

5 - Performance analysis and optimization

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Summary

Many different mathematical tools have been used for modeling concurrent systems. One of the most common is Petri nets. This chapter focuses on their use in architectural performance analysis and the optimization of asynchronous pipelines. In later chapters we will discuss the more specific forms of Petri nets used in specifying asynchronous controllers for automated synthesis. In addition, we will also use Petri nets to describe the abstract behavior of various implementation templates. More extensive analyses of Petri nets can be found in references.

Petri nets

A Petri net is a four-tuple N = (P, T, F, m0), where P is a finite set of places pi and T is a finite set of transitions ti (see Figure 5.1); F ⊆ (P × T) ∪ (T × P) is a flow relation and m0 ∈ N|P| is the initial marking (see below), where N is the set of natural numbers. As can be seen in the figure, a Petri net is usually represented as a bipartite graph in which the pi and ti are the nodes. For any two nodes x and y, if (x, y) ∈ F then there is a directed arc from x to y. An arc runs between a place and a transition or between a transition and a place, but arcs do not run between two places or two transitions.

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References
Peterson, J. L., Petri Net Theory and the Modeling of Systems, Prentice-Hall, 1981.
Wang, J., Timed Petri Nets, Kluwer Academic, 1998.
Murata, T., “Petri nets: properties, analysis and application,”Proc. IEEE, vol. 77, no. 4, pp. 541–579, 1989.
Karp, R. M., “A characterization of the minimum cycle mean in a digraph,”Discrete Math., vol. 23, pp. 309–311, 1978.
Magott, J., “Performance evaluation of concurrent systems using Petri nets,”Information Proc. Lett., vol. 18, pp. 7–13, January 1984.
, C. V.Ramamoorthy, and Ho, G. S., “Performance evaluation of asynchronous concurrent systems using Petri nets,”IEEE Trans. Software Eng., vol. SE-6, no. 5, pp. 440–449, 1980.
Campos, J., Chiola, G., Colom, J. M., Silva, M., “Properties and performance bounds for timed marked graphs,”IEEE Trans. Circuits and Systems I: Fundamental Theory and Applications, vol. 39, no. 5, pp. 386–401, May 1992.
Silva, M. and Campos, J., “Structural performance analysis of stochastic Petri nets,” in Proc. IEEE Int. Computer Performance and Dependability Symp., 1995, pp. 61–70.
, A.Dasdan, , “Experimental analysis of the fastest optimum cycle ratio and mean algorithms,”ACM Trans. Design Automation of Electronic Systems, vol. 9, no. 4, pp. 385–418, October 2004.
Dasdan, A. and Gupta, R. K., “Faster maximum and minimum mean cycle algorithms for system-performance analysis,”IEEE Trans. CAD Integrated Circuits and Systems, vol. 17, no. 10, pp. 889–899, 1998.
Lines, A. M., “Pipelined asynchronous circuits,” Master's thesis, California Institute of Technology, June 1998.
Burns, S. M., “Performance analysis and optimization of asynchronous circuits,” Ph.D. thesis, California Institute of Technology, 1991.
Burns, S. M. and Martin, A. J., “Performance analysis and optimization of asynchronous circuits,” in Adv. Res. VLSI, MIT Press, 1991, pp. 71–86.
Varshavsky, V. I., Kishinevsky, M. A., Marakhovsky, V. B., et al., “Self-timed Control of Concurrent Processes, Kluwer Academic, 1990.
Cormen, T. H., Leiserson, C. E., and Rivest, R. L., Introduction to Algorithms, MIT Press, 1990.
Dantzig, G. B., Linear Programming and Extensions. Princeton University Press, 1963.
Papadimitriou, C. H. and Steiglitz, K., Combinational Optimization: Algorithms and Complexity, Dover, 1998.
GLPK: GNU linear programming kit package, http://www.gnu.org/software/glpk/ glpk.html.
Karp, R. M., “A characterization of the minimum cycle mean in a diagraph,”Discrete Math., vol. 23, pp. 309–311, 1978.
Manohar, R. and Martin, A. J., “Slack elasticity in concurrent computing,” in Proc. 4th Int. Conf. on the Mathematics of Program Construction, Lecture Notes in Computer Science vol. 1422, Springer-Verlag, 1998, pp. 272–285.
Beerel, P. A. and Xie, A., “Performance analysis of asynchronous circuits using Markov chains,” in Proc. Conf. on Concurrency and Hardware Design, 2002, pp. 313–344.
Xie, A. and Beerel, P. A., “Performance analysis of asynchronous circuits and systems using stochastic timed Petri nets,” in Proc. 2nd Workshop on Hardware Design and Petri Net (HWPN'99) of the 20th Int. Conf. on Application and Theory of Petri Nets (PN'99), 1999, pp. 35–62.
Xie, A., Kim, S., and Beerel, P. A., “Bounding average time separations of events in stochastic timed petri nets with choice,” in Proc. 5th IEEE Int. Symp. on Asynchronous Circuits and System (Async) 1999, p. 94.
Kim, S. and Beerel, P. A., “Pipeline optimization for asynchronous circuits: complexity analysis and an efficient optimal algorithm,”IEEE Trans. CAD Integrated Circuits and Systems, vol. 25, no. 3, pp. 389–402, 2006.
Beerel, P. A., Lines, A., Davies, M., and Kim, N., “Slack matching asynchronous designs,” in Proc. 12th IEEE Int. Symp. on Asynchronous Circuits and System (Async), March 2006, pp. 184–194.
Prakash, P. and Martin, A. J., “Slack matching quasi delay-insensitive circuits,” in Proc. 12th IEEE Int. Symp. on Asynchronous Circuits and System (Async), March 2006, pp. 195–204.
Venkataramani, G. and Goldstein, S. C., “Leveraging protocol knowledge in slack matching,” in Proc. ICCAD 2006, pp. 160–171.
Chakraborty, S. and Angrish, R., “Probabilistic timing analysis of asynchronous systems with moments of delays,” in Proc. 8th Int. Symp. on Asynchronous Circuits and Systems, April 2002, pp. 99–108.
McGee, P. B., Nowick, S. M., and Coffman, E. G., “Efficient performance analysis of asynchronous systems based on periodicity,” in Proc. 3rd IEEE/ACM/IFIP Int. Conf. on Hardware/Software Codesign and System Synthesis, September 2005, pp. 225–230.
Lines, A.. Private communication, 2006.