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Best-choice problems with disorder

Evgeny Ivashkoivashko@krc.karelia.ru

Science advisor:Prof. Vladimir Mazalov

Institute of Applied Mathematical ResearchKarelian Research Centre

Russian Academy of Sciences

22Karelian Research Center of the RAS, Institute of Applied Mathematical Research

Best-choice problems with disorder: Background

1. A. N. Shiryaev, Statistical sequential analysis, Moscow, 1976, Russian: Disorder problem

2. V. Mazalov, P. Neumann, I. Falco. Game of optimal stopping observations with unknown values, Chita, 1998, Russian.

3. M. Sakaguchi. A best-choice problem for a production system which deteriorates at a disorder time. Scienticae Mathematicae Japonicae, Vol. 54, No 1

The problem of the fastest finding the moment of disorder (the moment of changing the probability distribution)

The best-choice full-information perfect problem with disorder

The best-choice game with partial information

33Karelian Research Center of the RAS, Institute of Applied Mathematical Research

Best-choice problems with disorder: Model

Production system (PS) sequentially generates independent identical distributed random variables X

1, X

2, ..., X

N

PS in a good state (Good): Xi uniform on [0,1]

PS in a bad state (Bad): Xi uniform on [0,b]

Observer aims to accept the largest value

Every value can be accepted or rejectedRecall is not allowed

44Karelian Research Center of the RAS, Institute of Applied Mathematical Research

Best-choice problems with disorder: Main Results

1. Full-information best-choice problem with disorder (maximizing

probability of success, one-threshold strategy): analitical formula of optimal

thresholds for various parameters (α, b) is found;

2. Multithresholds full-information best-choice problem with disorder

(maximizing expect value of accepting observation, multithresholds

strategies):

analitical formula of optimal thresholds for various parameters (α, b) is

found;

3. Considered applications of the best-choice problem with disorder to

management and defending against Denial-of-Service attacks.

55Karelian Research Center of the RAS, Institute of Applied Mathematical Research

Best-choice problems with disorder: Applications and Future plans

Applications: Security: detecting denial-of-service attacks

Management: house-selling problem at the «hot» market

Grid tasks management: optimal-time big tasks passing to the Grid

other...

Future plans: Imperfect best-choice game with disorder

Best-choice game with disorder and player's priorities

Law-linked multithreaded best-choice problem with disorder

Some application-specific articles

66Karelian Research Center of the RAS, Institute of Applied Mathematical Research

Best-choice problems with disorder: References

1. Vladimir V. Mazalov, Evgeny E. Ivashko Best-choice problem with disorder // Proceedings of Dynamic games and multicriteria Optimization (DGMO-2006), Petrozavodsk, September 2-7, 2006

2. Vladimir V. Mazalov, Evgeny E. Ivashko Best-choice problem with disorder // Proceedings of V Moscow International Conference on Operations Research (ORM2007), dedicated to the outstanding Russian scientists Nikita N. Moiseev 90th birthday, Moscow, April 10-14, 2007

3. Vladimir V. Mazalov, Evgeny E. Ivashko Full-information best-choice problem with disorder // Surveys in Applied and Industrial Mathematics, Vol 2, No 14, 2007, pp. 215-224

4. Evgeny E. Ivashko Multithreaded full-information best-choice problem with disorder // Proceedings of the Institute of Applied Mathematical Research, Vol 8, 2007, pp. 11-15