The risk management we propose uses multi-robot patrols to maintain security, which we treat as equivalent to minimizing observational uncertainty of a place – we call this place checkpoint i (i = 1,2, . . . ,n). We therefore formulate the uncertainty by entropy in information theory. Robots patrol and observe the checkpoint’s condition and update the patrol schedule based on the estimated uncertainty of checkpoints in real time. To relieve uncertainty, we propose Earliest Deadline First scheduling with adaptive Risk Estimation (EDFRE), then compare EDFRE with simple EDF scheduling and evaluate EDFRE adaptability to changes under different initial conditions. Results demonstrated EDFRE’s effectiveness in dynamic situations.

1. [1] R. E. Barlow and F. Proschan, “Mathematical Theory of Reliability,” Society for Industrial Mathematics, 1987.
2. [2] H. Pham and X. Zhang, “An NHPP Software Reliability Model and Its Comparison,” Int. J. of Reliability, Quality and Safety Engineering (IJRQSE), Vol.4, Issue 3, pp. 269-282, 1997.
3. [3] N. Ravishanker, Z. Liu, and B. K. Ray, “NHPP models with Markov switching for software reliability,” Computational Statistics and Data Analysis, Vol.52, Issue 8, pp. 3988-3999, 2008.
4. [4] T. Bektas, “The multiple traveling salesman problem: an overview of formulations and solution procedures,” Omega, Vol.34, pp. 209-219, 2006.
5. [5] J. Stankovic, M. Spuri, K. Ramamritham, and G. Buttazzo, “Deadline Scheduling for Real-time Systems: EDF and Related Algorithms,” Kluwer Academic Publishers, Boston, 1998.
6. [6] O. Braysy, “Vehicle Routing Problem with Time Windows, Part I: Route Construction and Local Search Algorithms,” Transportation Science, Vol.39, No.1, pp. 104-118, 2005.
7. [7] O. Braysy, “Vehicle Routing Problem with Time Windows, Part II: Metaheuristics,” Transportation Science, Vol.39, No.1, pp. 119-139, 2005.
8. [8] A. Srinivasan and J. H. Anderson, “Fair scheduling of dynamic task systems on multiprocessors,” J. of Systems and Software, Vol.77, Issue 1, pp. 67-80, 2005.
9. [9] H. Lia, K. Ramamritham, P. Shenoy, R. A. Grupen, and J. D. Sweeney, “Resource management for real-time tasks in mobile robotics,” J. of Systems and Software, Vol.80, No.7, pp. 962-971, 2007.
10. [10] J. Lehoczky, L. Sha, and Y. Ding, “The Rate monotonic scheduling algorithm: exact characterization and average case behavior”, IEEE Real-Time Systems Symposium, pp. 166-171, December 1989.
11. [11] C. L. Liu and J. W. Layland, “Scheduling Algorithm for Multiprogramming in a Hard Real-Time Environment,” J. of ACM, Vol.20, No.1, pp. 40-61, 1973.
12. [12] J. Goossens and P. Richard, “Overview of real-time scheduling problems,” ninth Int. workshop on project management and Scheduling, pp. 13-22, 2004.
13. [13] E. M. Atkins, T. F. Abdelzaher, K. G. Shin and E. H. Durfee, “Planning and Resource Allocation for Hard Real-time, Fault-Tolerant Plan Execution,” Autonomous Agents and Multi-Agent Systems, Vol.4, No.1-2, pp. 57-78, 2001.
14. [14] S. Carpin, “Fast and accurate map merging for multi-robot systems,” Autonomous Robots, Vol.25, No.3, pp. 305-316, 2008.
15. [15] S. Bermana, E. Schechtmana, and Y. Edan, “Evaluation of automatic guided vehicle systems,” Robotics and Computer-Integrated Manufacturing, Vol.25, Issue 3, pp. 522-528, 2009.
16. [16] H. V. D. Parunak and S. Brueckner, “Entropy and Self-Organization in Multi-Agent Systems,” Proc. of the Fifth Int. Conf. on Autonomous Agents, pp. 124-130, 2001.
17. [17] S. Guerin and D. Kunkle, “Emergence of Constraint in Self-Organizing Systems,” J. of Nonlinear Dynamics in Psychology and Life Sciences, Vol.8, No.2, pp. 131-146, 2004.
18. [18] N. Ueda, “Bayesian Learning [2]: Introduction to Bayesian Learning,” The J. of the Institute of Electronics, Information, and Communication Engineers, Vol.85, No.6, pp. 421-426, 2002. (in Japanese)
19. [19] J. M. Bernardo and A. F. M. Smith, “Bayesian Theory (Wiley Series in Probability and Statistics),” Wiley, 2001.
20. [20] P. M. Lee, “Bayesian Statistics: An Introduction (Arnold Publication),” Wiley, 2009.