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100%<br />

1<br />

95%<br />

2<br />

14 15<br />

64%<br />

TAO 4<br />

64%<br />

62%<br />

5 6 7<br />

59%<br />

VI. CONCLUSIONS<br />

In this paper, we developed a methodology for extracting<br />

features by characterizing the time series’ <strong>and</strong> relating it to<br />

stress situations in distributed multiagent systems. One<br />

important aspect of our approach is that we identify the<br />

stress situations of the agents in the society by observing<br />

local behavior of one representative agent. This approach is<br />

motivated by the fact that a local time series can have the<br />

information of the dynamics of entire system in<br />

deterministic dynamic systems. It is important to identify the<br />

situations of other agents when agents are interdependent in<br />

networked systems.<br />

When we have a large society we will be able to predict<br />

the stress levels in some other agents in the society. This<br />

helps in invoking an appropriate control policy. For example<br />

by studying the local behavior of TAO during certain time,<br />

we may be able to estimate that agent 11’s OpTempo is high<br />

with 62% accuracy. This may need us to reduce the amount<br />

of tasks to the agent as high OpTempo requires more<br />

computational resource.<br />

To extract meaningful behavioral parameters we collected<br />

the time series data from a representative agent <strong>and</strong><br />

computed 38 statistical <strong>and</strong> deterministic parameters to<br />

represent its behavior. Discriminability Index defined by us<br />

in this paper as a measure of the discriminating power of the<br />

parameters seems to be a promising direction for agent<br />

behavior estimation. Using those selected parameters we<br />

validated our approach through identifying the stress<br />

situations using k-nearest neighbor algorithm with the index<br />

values as weights. Although our analysis showed that<br />

deterministic parameters don’t have significant ability to<br />

identify stress situations in our stress space, it is possible<br />

that they can be good indicators under other stress space<br />

such as security <strong>and</strong> robustness stresses.<br />

8<br />

9<br />

16 17<br />

52%<br />

10<br />

62%<br />

Fig. 5. Correct estimation with proportional weights to DI<br />

11<br />

12<br />

13<br />

[2] O. F. Rana <strong>and</strong> K. Stout, “What is scalability in multi-agent systems?”<br />

in Proc. 4th Int. Conf. Autonomous Agents, 2000, pp. 56–63.<br />

[3] N. H. Packard, J. P. Crutchfield, J. D. Farmer, <strong>and</strong> R. S. Shaw,<br />

“Geometry from a time series,” Physical Review Letters, vol. 45, pp.<br />

712–716, 1980.<br />

[4] F. Taken, “Detecting strange attractors in turbulence,” in Dynamical<br />

Systems <strong>and</strong> Turbulence, D. R<strong>and</strong> <strong>and</strong> L.-S. Young, Eds. Springer:<br />

Berlin, 1981, pp. 366–381.<br />

[5] A. P. Moore, R. J. Ellison, <strong>and</strong> R. C. Linger, “Attack modeling for<br />

information security <strong>and</strong> survivability,” Software Engineering<br />

Institute, Carnegie Mellon University, Pittsburg, PA, Tech. Note<br />

CMU/SEI-2001-TN-001, 2001.<br />

[6] F. Moberg, “Security analysis of an information system using an<br />

attack tree-based methodology,” M.S. thesis, Automation Engineering<br />

Program, Chalmers University of Technology, Sweden, 2000.<br />

[7] S. Jha <strong>and</strong> J. M. Wing, “Survivability analysis of networked systems,”<br />

in Proc. 23rd Int. Conf. Software engineering, 2001, pp. 307–317.<br />

[8] A. M. Fraser <strong>and</strong> H. Swinney, “Independent coordinates for strange<br />

attractors from mutual information,” Physical Review A, vol. 33, pp.<br />

1134–1140, 1986.<br />

[9] H. G. Schuster, Deterministic Chaos: An Introduction,<br />

Verlagsgesellshaft: Weinheim, 1989.<br />

[10] H. D. I. Abarbanel, M. E. Gilpin, <strong>and</strong> M. Rotenberg, Analysis of<br />

Observed Chaotic Data, Springer: New York, 1998.<br />

[11] P. Grassberger <strong>and</strong> I. Procaccia, “Characterization of strange<br />

attractors,” Physical Review Letters, vol. 50, pp. 346–349, 1983.<br />

[12] P. Grassberger <strong>and</strong> I. Procaccia, “Characterization of strange<br />

attractors,” Physica D, vol. 9, pp. 189–208, 1983.<br />

[13] A. Wolf, J. B. Swift, H. L. Swinney, <strong>and</strong> J. Vastano, “Determining<br />

Lyapunov exponents from a time series,” Physica D, vol. 16, pp. 285–<br />

317, 1985.<br />

[14] T. M. Mitchell, Machine Learning, MaGraw-Hill, pp. 230–236, 1997.<br />

REFERENCES<br />

[1] R. Ellison, D. Fisher, H. Lipson, T. Longstaff, <strong>and</strong> N. Mead,<br />

“Survivable network systems: An emerging discipline,” Software<br />

Engineering Institute, Carnegie Mellon University, Pittsburg, PA,<br />

Tech. Rep. CMU/SEI-97-153, 1997.

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