Abstract
Amdahl’s Law states that execution speedup S is nonlinearly proportional to the percentage of parallelizable code P and the number N of processors. Additional terms must be added to Amdahl’s Law when applied to agent-based simulations, depending on how synchronization is implemented. Since P is continuous but N is discrete, traditional multivariate operators based on nabla or del ∇ are applicable only for P, not for N, regardless of synchronization architecture (linear, logarithmic, constant, among other). Moreover, relatively low values of N (bound by Miller’s number 7 ±2) are common in some cases. Here I apply a novel and exact operator, called “nabladot” and denoted by the symbol “nabladot”, that is defined for hybrid function such as Amdahl’s Law. The main results show how exact solutions using nabladot differ from traditional approximations, particularly in the logarithmic case that is characteristic of hierarchical synchronization. Improvements in precision are inversely proportional to P and N, converging to 0.8 as N → 2.
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Amdahl, G.: Validity of the Single Processor Approach to Achieving Large-Scale Computing Capabilities. AFIPS Conference Proceedings 30, 483–485 (1967)
Cioffi-Revilla, C.: The Nabladot Operator for Hybrid Concrete Functions in Complex Systems. Presented at the Monday Seminar, Krasnow Institute for Advanced Study, George Mason University, Fairfax (2013)
Cioffi-Revilla, C.: Introduction to Computational Social Science: Principles and Applications. Heidelberg, Springer (2014a)
Cioffi-Revilla, C.: The Nabladot Operator for Hybrid Concrete Functions in Complex Systems. In: Proceedings of the Second World Conference on Complex Systems (WCCS 2014), Agadir, Morocco (2014b)
Eyerman, S., Eeckhout, L.: Modeling Critical Sections in Amdahls Law and its Implications for Multicore Design. In: ISCA 2010, Saint-Malo, France, June 19–23 (2010)
Grady, L.J., Polimeni, J.R.: Discrete Calculus: Applied Analysis on Graphs for Computational Science. Heidelberg, Springer (2010)
Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics: A Foundation for Computer Science, 2nd edn. Addison-Wesley, Reading (1994)
Gustafson, J.L.: Reevaluating Amdahl’s Law. Comm. ACM, 532–533 (May 1988)
Hill, M.D., Marty, M.R.: Amdahl’s Law in the Multicore Era, pp. 33–38. Computer - IEEE Computer Society (July 2008)
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Cioffi-Revilla, C. (2014). Theoretical Nabladot Analysis of Amdahl’s Law for Agent-Based Simulations. In: Lopes, L., et al. Euro-Par 2014: Parallel Processing Workshops. Euro-Par 2014. Lecture Notes in Computer Science, vol 8805. Springer, Cham. https://doi.org/10.1007/978-3-319-14325-5_38
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DOI: https://doi.org/10.1007/978-3-319-14325-5_38
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