Volume 11, no. 3Pages 72 - 84
Discrete Model of Paired Relay-RaceE.V. Larkin, A.V. Bogomolov, A.N. Privalov, N.N. Dobrovolsky
The case of the active and passive team relay-race, in which an active team operates in accordance with rigid schedule and a passive team overcome the stage of its distance at randomly selected alternative routs during occasional time intervals is considered. Due to high complexity of classical relay-race analysis, method of simulation, based on representation of time intervals densities of passing stages routs with discrete distributions is proposed. It is shown, that after transformation of time intervals densities into discrete distributions the problem of a relay race analysis reduces to the task of analysis of two-team system with rigid schedules. The method of sampling of densities composition with estimation a sampling error, and recursive procedure of rigid schedule relay-race analysis with calculation of forfeit are worked out. It is shown, that forfeit depends on the difference of stages, teams overcome at current time and a strategy, which active team realizes during relay-race. Full text
- relay race; semi-Markov process; distance; stage; route; sampling; schedule; distributed forfeit.
- 1. Valk R. Concurrency in Communicating Object Petri Nets. Concurrent Object-Oriented Programming and Petri Nets, 2001, pp. 164-195. DOI: 10.1007/3-540-45397-0_5
2. Chatterjee K., Jurdzi'nski M., Henzinger T. Simple Stochastic Parity Games. Lecture Notes in Computer Science, 2003, vol. 2803, pp. 100-113. DOI: 10.1007/978-3-540-45220-1_11
3. Eisentraut C., Hermanns H., Zhang L. Concurrency and Composition in a Stochastic World. CONCUR 2010-Concurrency Theory, 2010, pp. 21-39.
4. Wooldridge M. An Introduction to Multi-Agent Systems. Chichester, John Wiley and Sons, 2009.
5. Ivutin A.N, Larkin E.V. Simulation of Concurrent Games. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2015, vol. 8, no. 2, pp. 43-54. DOI: 10.14529/mmp150204
6. Larkin E.V., Ivutin A.N., Kotov V.V., Privalov A.N. Simulation of Relay-Races. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2016, vol. 9, no. 4, pp. 117-128. DOI: 10.14529/mmp160411
7. Jiang Q., Xi H.-S., Yin B.-Q. Event-Driven Semi-Markov Switching State-Space Control Processes. IET Control Theory and Applications, 2012, vol. 6, no. 12, pp. 1861-1869. DOI: 10.1049/iet-cta.2011.0174
8. Yang T., Zhang L., Yin X. Time-Varying Gain-Scheduling-Error Mean Square Stabilisation of Semi-Markov Jump Linear Systems. IET Control Theory and Applications, 2016, vol. 10, no. 11, pp. 1215-1223. DOI: 10.1049/iet-cta.2015.1327
9. Korolyuk V., Swishchuk A. Semi-Markov Random Evolutions. N.Y., Springer Science and Buseness Media, 1995. DOI: 10.1007/978-94-011-1010-5
10. Limnios N., Swishchuk A. Discrete-Time Semi-Markov Random Evolutions and Their Applications. Advances in Applied Probability, 2013, vol. 45, no. 1, pp. 214-240. DOI: 10.1239/aap/1363354109
11. Bauer H. Probability Theory. Berlin, N.Y., Walter de Gruyter, 1996. DOI: 10.1515/9783110814668
12. Shiryaev A.N. Probability. N.Y., Springer Science and Business Midia, 1996. DOI: 10.1007/978-1-4757-2539-1
13. Squillante M.S. Stochastic Analysis and Optimization of Multiserver Systems. Run-Time Models for Self-Managing Systems and Applications. Mathematic Subject Classification. Basel, Springer Basel, 2010, pp. 1-15. DOI: 10.1007/978-3-0346-0433-8_1
14. Pinedo M.L. Scheduling. Theory: Algorithms and Systems. N.Y., Springer Science and Business Media, 2016. DOI: 10.1007/978-1-4614-2361-4
15. Khodr Y.M. Scheduling Problems and Solutions. N.Y., Nova Science, 2012.
16. Drozdowski M. Scheduling for Parallel Processing. London, Springer, 2009. DOI: 10.1007/978-1-84882-310-5
17. Gawiejnowicz S. Time-Dependent Scheduling. Berlin, Springer, 2008. DOI: 10.1007/978-3-540-69446-5
18. Heymann M. Concurrency and Discrete Event Control. IEEE Control Systems Magazine, 1990, vol. 10, pp. 103-112. DOI: 10.1109/37.56284
19. Larkin E.V., Ivutin A.N. 'Concurrency' in M-L-Parallel Semi-Markov Process. 2017 International Conference on Mechanical, Aeronautical and Automotive Engineering (ICMAA 2017). MATEC Web of Conferences, 2017, vol. 108, no. 05003, 5 p.
20. Larkin E.V., Bogomolov A.V., Privalov A.N., Dobrovolsky N.N. Relay-Races Along Selectable Routes. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2015, vol. 11, no. 1, pp. 16-24.
21. Attar A., Campioni E., Piaser G. On Competing Mechanisms under Exclusive Competition. Games and Economic Behavior. Toulouse School of Economics, 2015, no. TS-609, 17 p.
22. Hokan T., Thomson W. Cooperative Game Theory. International Encyclopedia of Social and Behavioral Sciences, 2015, pp. 867-880.