In this work we generalize the concept of activity of continuous time signals. We define the activity of order n of a signal and show that it allows us to estimate the number of sections of polynomials up to order n which are needed to represent that signal with a certain accuracy. Then we apply this concept to obtain a lower bound for the number of steps performed by quantization-based integration algorithms in the simulation of ordinary differential equations.
We perform an exhaustive analysis over two examples, computing the activity of order n and comparing it with the number of steps performed by different integration methods. This analysis corroborates the theoretical predictions and also allows us to measure the suitability of the different algorithms depending on how close to the theoretical lower bound they perform.
JammalamadakaR. Activity characterization of spatial models: Application to discrete event solution of partial differential equations. Master’s Thesis, The University of Arizona, AZ, 2003.
2.
KofmanEJuncoS. Quantized state systems: A DEVS approach for continuous system simulation. Sim: Trans Soc Model Sim Int2001; 18(3): 123–132.
3.
MigoniGKofmanECellierF. Quantization-based new integration methods for stiff ODEs. Sim: Trans Soc Model Sim Int2012; 88(4): 387–407.
4.
MigoniGBortolottoMKofmanE. Linearly implicit quantization-based integration methods for stiff ordinary differential equations. Sim Modell Prac Theor2013; 35: 118–136.
5.
KofmanE. A second order approximation for DEVS simulation of continuous systems. Sim: Trans Soc Model Sim Int2002; 78(2): 76–89.
6.
LacknerMR. Toward a general simulation capability. In: Proceedings of the spring joint computer conference, San Francisco, CA, 1962, pp. 1–14.
7.
LacknerMR. Digital simulation and system theory. Santa Monica, CA: System Development Corp., 1964.
8.
KiviatPJ. Digital computer simulation: Modeling concepts. Santa Monica, CA: RAND Corporation, 1967.
9.
KiviatPJ. Digital computer simulation: Computer programming languages. Santa Monica, CA: RAND Corporation, 1969.
10.
FishmanGS. Concepts and methods in discrete event digital simulation. New York, NY: John Wiley and Sons, 1973.
11.
BalciO. The implementation of four conceptual frameworks for simulation modeling in high-level languages. In: Proceedings of the 20th conference on winter simulation, 1988, pp. 287–295.
MuzyAZeiglerBP. Introduction to the activity tracking paradigm in component-based simulation. Open Cyber System J2008; 2: 30–38.
14.
ZeiglerBPKimTGPraehoferH. Theory of modeling and simulation. 2nd edn.New York, NY: Academic Press, 2000.
15.
ZeiglerBPJammalamadakaRAkerkarSR. Continuity and change (activity) are fundamentally related in DEVS simulation of continuous systems. In: KimT (ed.) Artificial intelligence and simulation (Lecture Notes in Computer Science, vol. 3397). Berlin/Heidelberg: Springer, 2005, p. 1–13.
16.
JainSCreaseyRRHimmelspachJ. What is new with the activity world view in modeling and simulation? Using activity as a unifying guide for modeling and simulation. In: Proceedings of the 2011 winter simulation conference (WSC), 2011, pp. 2882–2894.
17.
MuzyAJammalamadakaRZeiglerBP. The Activity tracking paradigm in discrete-event modeling and simulation: The case of spatially continuous distributed systems. Sim: Trans Soc Model Sim Int2011; 87(5): 449–464.
18.
HuXZeiglerBP. Linking information and energy – activity-based energy-aware information processing. Sim: Trans Soc Model Sim Int2013; 89(4): 435–450.
19.
SantucciJFCapocchiL. Implementation and analysis of DEVS activity-tracking with DEVSimPy. In: ITM web of conferences, 2013.
20.
MuzyAVarenneFZeiglerBP. Refounding of the activity concept? Towards a federative paradigm for modeling and simulation. Sim2013; 89(2): 156–177.
21.
CellierFEKofmanE. Continuous system simulation. New York, NY: Springer, 2006.
22.
KofmanE. A third order discrete event simulation method for continuous system simulation. Lat Am Appl Res2006; 36(2): 101–108.
23.
ZeiglerBLeeJS. Theory of quantized systems: Formal basis for DEVS/HLA distributed simulation environment. In: SPIE proceedings, 1998, pp. 49–58.
