Abstract
Flows of transactions in digital control systems of robots are investigated. On the base of the fact, that uses the conception of Poisson character of transactions flow permits to simplify analytical simulation of robot control process, the problem of estimation the degree of approach of real flow to Poisson one is putted on. Proposed the criterion based on evaluation of expectation of waiting function. On the example of investigation of “competition” in the swarm of robots it is shown that flow of transactions, generated by swarm, when quantity of robots aspire to infinity approximately aspire to Poisson one.
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References
Tzafestas, S.G.: Introduction to Mobile Robot Control. Elsevier, Amsterdam (2014)
Kahar1, S., Sulaiman1, R., Prabuwono1, A.S., Akma, N., Ahmad, S.A., Abu Hassan, M.A.: A review of wireless technology usage for mobile robot controller. In: International Conference on System Engineering and Modeling (ICSEM 2012), International Proceedings of Computer Science and Information Technology IPCSIT, vol. 34, pp. 7–12 (2012)
Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. Intelligent Robotics and Autonomous Agents series. MIT Press, Cambridge (2005)
Ching, W.-K., Huang, X., Ng, M.K., Siu, T.K.: Markov Chains: Models, Algorithms and Applications. International Series in Operations Research & Management Science, vol. 189. Springer Science+Business Media New York, New York (2013)
Pang, G., Zhou, Y.: Two-parameter process limits for an infinite-server queue with arrival dependent service times. Stoch. Process. Appl. 127(5), 1375–1416 (2017)
Mathijsen, B., Zwart, B.: Transient error approximation in a Lévy queue. Queueing Syst. 85(3), 269–304 (2017)
Larkin, E.V., Ivutin, A.N., Kotov, V.V., Privalov, A.N.: Interactive generator of commands. In: Tan, Y., Shi, Y., Li, L. (eds.) ICSI 2016. LNCS, vol. 9713, pp. 601–609. Springer, Cham (2016). doi:10.1007/978-3-319-41009-8_65
Limnios, N., Swishchuk, A.: Discrete-time semi-Markov random evolutions and their applications. Adv. Appl. Probab. 45(1), 214–240 (2013)
Markov, A.A.: Extension of the law of large numbers to dependent quantities. Izvestiia Fiz.-Matem 2, 135–156 (1906)
Lu, H., Pang, G., Mandjes, M.: A functional central limit theorem for Markov additive arrival processes and its applications to queueing systems. Queueing Syst. 84(3), 381–406 (2016)
Bielecki, T.R., Jakubowski, J., Niewęgłowski, M.: Conditional Markov chains: properties, construction and structured dependence. Stoch. Process. Appl. 127(4), 1125–1170 (2017)
Maronna, R.M., Victor, J., Yohai, V.J.: Robust functional linear regression based on splines. Comput. Stat. Data Anal. 65, 46–55 (2013)
Muler, N., Yohai, V.J.: Robust estimation for vector autoregressive models. Comput. Stat. Data Anal. 65, 68–79 (2013)
Rank, M.K.: Correlation Methods, vol. 196. Charles Griffin & Company, London (1955)
Boos, D.D., Stefanski, L.A.: Essential Statistical Inference: Theory and Methods, vol. 568 (XVII). Springer, New York (2013)
Wang, B., Wertelecki, W.: Density estimation for data with rounding errors. Comput. Stat. Data Anal. 65, 4–12 (2013)
Luedicke, J., Bernacchia, A.: Self-consistent density estimation. Stata J. 14(2), 237–258 (2014)
Grigelionis, B.: On the convergence of sums of random step processes to a Poisson process. Theory Probab. 8, 177–182 (1963)
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Larkin, E., Bogomolov, A., Gorbachev, D., Privalov, A. (2017). About Approach of the Transactions Flow to Poisson One in Robot Control Systems. In: Ronzhin, A., Rigoll, G., Meshcheryakov, R. (eds) Interactive Collaborative Robotics. ICR 2017. Lecture Notes in Computer Science(), vol 10459. Springer, Cham. https://doi.org/10.1007/978-3-319-66471-2_13
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DOI: https://doi.org/10.1007/978-3-319-66471-2_13
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