DOI 10.17586/0021-3454-2019-62-5-419-423
UDC 519.64; 004.75; 004.94
METHOD OF CALCULATING TASK TREATMENT DURATION IN QUEUEING SYSTEM
WITH CONSIDERATION OF SPLIT-JOIN PROCESSES
Y. I. Ryzhikov
St. Petersburg Institute for Informatics and Automation of Russian Academy of Sciences (SPIIRAS), Laboratory of Information Technologies in Systems Analysis and Modeling; Professor
.
Mozhaisky Military Space Academy, Department of
Mathematics and Software;;
R. S. Khabarov
Mozhaisky Military Space Academy, Department of Mathematics
and Software;;
Read the full article 
Abstract.
A method is proposed for calculating the processing time of initial task in multi-channel queueing system with consideration of the task separation into independent subtasks that are treated parallelly with further assembling of the results. The process duration is represented as the distribution of the maximum from the random durations of the subtasks processing. The starting moments of the desired distribution are found by numerical integration along the semi-axis with the Chebyshev-Laguerre weight. Results of numerical calculations are compared with data obtained by simulations.
Keywords: distributed data processing, concurrent requests, Split-Join service process, distribution
of maximum of random variables, numerical integration by Chebyshev-Laguerre
References:
1. Kyte Th. Expert Oracle Database Architecture: Oracle Database Programming 9i, 10g, and 11g, Techniques and Solutions Apress Berkely, CA, 2010. 2. Dean J., Ghemawat S. MapReduce: Simplified data processing on large clusters, San Francisco, CA, 2004, рр. 1–13. 3. Schriber T.J. Simulation Using GPSS, NY, Wiley, 1974. 4. Olvera-Cravioto M., Ruiz-Lacedelli O. Parallel queues with synchronization, , 2014. 5. Flatto L., Hahn S. SIAM Journal on Appl. Math., 1979, vol. 44, рp. 1041–1053. 6. Wright P.E. Advances in Applied Probability, 1992, vol. 24, рр. 986–1007. 7. Harrison P.G., Zertal S. Proc. of Intern. Conf. on Modelling Techiniques and Tools for Computer Performance Evaluation, Urbano, IL, USA, 2003, рр. 152–168. 8. Fiorini P., Lipsky L. Performance Evaluation Rev., 2015, nо. 2(43), рp. 51–53. 9. Baccelli F. Tech. rep. INRIA-Rocquencourt, 1985, nо. 426. 10. Baccelli F., Makowski A.M., Shwartz A. Advanced in Applied Probability, 1989, vol. 21, рp. 629–660. 11. Nelson R., Tantawi A.N. IEEE Transact. on Computers, 1988, vol. 37, рр. 739–743. 12. Qiu Z., Perez J.G., Harrison P.G. Performance Evaluations, 2015, vol. 91, рp. 99–106. 13. Wang Р., Li J., Shen Z., Zhou Y. Approximations and Bounds for (n, k) Fork-Join Queues: A Linear Transformation Approach, Proceedings of the 18th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID), Washington, DC, USA, 2018. 14. Alomari F., Menasce D.A. IEEE Transact. on Parallel and Distributed Systems, 2014, vol. 25, рp. 1437–1446. 15. Krylov V.I., Shul'gina L.T. Spravochnaya kniga po chislennomu integrirovaniyu (Reference Book on Numerical Integration), Moscow, 1966, 372 р. (in Russ.) 16. Ryzhikov Yu.I. Algoritmicheskiy podkhod k zadacham massovogo obsluzhivaniya (Algorithmic Approach to Queuing Tasks), St. Petersburg, 2013, 496 р. (in Russ.
