On Sequential Data Processing Model, that Implements the Backup Storage
Abstract
Resource queue is a system where customers require a device and a random resources amount during their service. This queue have proven their effectiveness in analyzing the performance of modern wireless networks, cloud computing systems and technical devices. However, the study of such systems requires complex analytical calculations. In this article, we propose a combination of methods: the modification of the multidimensional dynamic screened method and the asymptotic analysis method under growing arriving intensity condition for the resource queue study. The obtained approximate results are compared with the simulation results, high approximation accuracy is demonstrated, and the recommended value of the restriction on the resource in the system and the rejection probability are found.
References
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[15] Samuvlov A., Moltchanov D., Krupko A., Kovalchukov R., Moskaleva F., Gaidamaka Y. Performance Analysis of Mixture of Unicast and Multicast Sessions in 5G NR Systems. In: 2018 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Moscow, Russia, 2018, pp. 1-7. (In Eng.) DOI: 10.1109/ICUMT.2018.8631230
[16] Beschastnyi V., Savich V., Ostrikova D., Gudkova I. Araniti G., Shorgin V. Analysis of machine-type communication data transmission by multicasting technology in 5G wireless networks. AIP Conference Proceedings. 2019; 2116(1):090005. (In Eng.) DOI: 10.1063/1.5114070
[17] Galileiskaya A.A., Lisovskaya E.Yu. Asymptotic analysis of a multiphase infinite-linear resource queuing system with an incoming MMPP stream. Tomsk State University Journal of Control and Computer Science. 2018; 45:13-21. (In Russ., abstract in Eng.) DOI: 10.17223/19988605/45/2
[18] Lisovskaya E., Moiseeva S., Pagano M. Infinite–Server Tandem Queue with Renewal Arrivals and Random Capacity of Customers. In: Vishnevskiy V., Samouylov K., Kozyrev D. (eds) Distributed Computer and Communication Networks. DCCN 2017. Communications in Computer and Information Science, vol. 700. Springer, Cham, 2017, pp. 201-216. (In Eng.) DOI: 10.1007/978-3-319-66836-9_17
[19] Lisovskaya E.Yu., Galileiskaya A.A. The total amount of the occupied resource in the queuing resource system GI(ν)/GI(n)/∞ with n types of applications. In: Information Technologies and Mathematical Modeling (ITMM-2018): materials of the XVII A.F. Terpugov, 2018, pp. 88-93. Available at: https://elibrary.ru/item.asp?id=36383943 (accessed 16.07.2019). (In Russ.)
[20] Lisovskaya E.Yu., Moiseev A.N., Moiseeva S.P., Pagano M. Modeling of data processing processes of physical experiments in the form of a non-Markov multi-resource queuing system. Izvestiya vysshikh uchebnykh zavedenii. Fizika. 2018; 61(12):39-46. Available at: https://elibrary.ru/item.asp?id=36651301 (accessed 16.07.2019). (In Russ., abstract in Eng.)
[21] Galileiskaya A.A., Lisovskaya E.Yu., Moiseeva S.P. Gaussian approximation of the probability distribution of the total volume of the occupied resource in a multi-resource infinite-linear queuing system with an incoming MMPP-demand stream. In: Vishnevsky V.M., Samuylov K.E. (eds) Distributed computer and telecommunication networks: control, computation, communication (DCCN-2018) materials of the XXI International Scientific Conference. RUDN, 2018, pp. 7-12. Available at: https://elibrary.ru/item.asp?id=36626335 (accessed 16.07.2019). (In Russ., abstract in Eng.)
[22] Shorgin S., Pechinkin A., Samouylov K., Gaidamaka Y., Sopin E., Mokrov E. Queuing systems with multiple queues and batch arrivals for cloud computing system performance analysis. In: 2014 International Science and Technology Conference (Modern Networking Technologies) (MoNeTeC), Moscow, 2014, pp. 1-4. (In Eng.) DOI: 10.1109/MoNeTeC.2014.6995600
[23] Cao J., Li K., Stojmenovic I. Optimal Power Allocation and Load Distribution for Multiple Heterogeneous Multicore Server Processors across Clouds and Data Centers. IEEE Transactions on Computers. 2014; 63(1):45-58. (In Eng.) DOI: 10.1109/TC.2013.122
[24] Firdhous M., Ghazali O., Hassan S. Modeling of cloud system using Erlang formulas. In: The 17th Asia Pacific Conference on Communications, Sabah, 2011, pp. 411-416. (In Eng.) DOI: 10.1109/APCC.2011.6152844
[25] Moiseev A., Nazarov A. Asymptotic analysis of a multistage queuing system with a high-rate renewal arrival process. Optoelectronics, Instrumentation and Data Processing. 2014; 50(2):163-171. (In Eng.) DOI: 10.3103/S8756699014020083
[26] Pankratova E., Moiseeva S., Farhadov M., Moiseev A. Heterogeneous System MMPP/GI(2)/∞ with Random Customers Capacities. Journal of Siberian Federal University. Mathematics & Physics. 2019; 12(2):231-239. (In Eng., abstract in Russ.) DOI: 10.17516/1997-1397-2019-12-2-231-239
[2] Galinina O., Andreev S.D., Gerasimenko M., Koucheryavy Y., Himayat N., Yeh S.P., Talwar S. Capturing Spatial Randomness of Heterogeneous Cellular/WLAN Deployments With Dynamic Traffic. IEEE Journal on Selected Areas in Communications. 2014; 32(6):1083-1099. (In Eng.) DOI: 10.1109/JSAC.2014.2328172
[3] Naumov V.A., Samuylov K.E., Samuylov A.K. About the total amount of resources occupied by serviced applications. Automation and Telemechanics. 2016; 8:125-135. (In Russ., abstract in Eng.) DOI: 10.1134/S0005117916080087
[4] Galinina O., Andreev S., Turlikov A., Koucheryavy Y. Optimizing Energy Efficiency of a Multi-Radio Mobile Device in Heterogeneous Beyond-4G Networks. Performance Evaluation. 2014; 78:18-41. (In Eng.) DOI: 10.1016/j.peva.2014.06.002
[5] Gudkova I., Samouylov K., Buturlin I., Borodakiy V., Gerasimenko M., Galinina O., Andreev S. Analyzing Impacts of Coexistence between M2M and H2H Communication on 3GPP LTE System. In: Mellouk A., Fowler S., Hoceini S., Daachi B. (eds) Wired/Wireless Internet Communications. WWIC 2014. Lecture Notes in Computer Science, vol. 8458. Springer, Cham, 2014, pp. 162-174. (In Eng.) DOI: 10.1007/978-3-319-13174-0_13
[6] Romm E.L., Skitovich V.V. On certain generalization of problem of Erlang. Automation and Telemechanics. 1971; 32(6):1000-1003. (In Eng.)
[7] Katz B.A. On servicing messages of random length. In: Queuing theory: Proceedings of the 3rd All-Union. meeting schools on queuing theory. 1976, pp. 157-168. (In Russ.)
[8] Gimpelson L.A. Analysis of Mixtures of Wide- and Narrow-Band Traffic. IEEE Transactions on Communication Technology. 1965; 13(3):258-266. (In Eng.) DOI: 10.1109/TCOM.1965.1089121
[9] Basharin G.P., Samouylov K.E., Yarkina N.V., Gudkova I.A. A new stage in mathematical teletraffic theory. Automation and Remote Control. 2009; 70(12):1954-1964. DOI: 10.1134/S0005117909120030
[10] Gorbunova A.V., Naumov V.A., Gaidamaka Yu.V., Samouylov K.E. Resource Queuing Systems as Models of Wireless Communication Systems. Informatics and Applications. 2018; 12(3):48-55. (In Russ., abstract in Eng.) DOI: 10.14357/19922264180307
[11] Naumov V., Samouylov K. Analysis of multi-resource loss system with state-dependent arrival and service rates. Probability in the Engineering and Informational Sciences. 2017; 31(4):413-419. (In Eng.) DOI: 10.1017/S0269964817000079
[12] Lisovskaya E., Moiseeva S., Pagano M. Multiclass GI/GI/∞ Queueing Systems with Random Resource Requirements. In: Dudin A., Nazarov A., Moiseev A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2018, WRQ 2018. Communications in Computer and Information Science, vol. 912. Springer, Cham, 2018, pp. 129-142. (In Eng.) DOI: 10.1007/978-3-319-97595-5_11
[13] Ageev K., Sopin E., Konstantin S. Simulation of the Limited Resources Queuing System with Signals. In: 2018 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Moscow, Russia, 2018, pp. 1-5. (In Eng.) DOI: 10.1109/ICUMT.2018.8631246
[14] Sopin E., Vikhrova O., Samouylov K. LTE network model with signals and random resource requirements. In: 9th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Munich, 2017, pp. 101-106. (In Eng.) DOI: 10.1109/ICUMT.2017.8255155
[15] Samuvlov A., Moltchanov D., Krupko A., Kovalchukov R., Moskaleva F., Gaidamaka Y. Performance Analysis of Mixture of Unicast and Multicast Sessions in 5G NR Systems. In: 2018 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Moscow, Russia, 2018, pp. 1-7. (In Eng.) DOI: 10.1109/ICUMT.2018.8631230
[16] Beschastnyi V., Savich V., Ostrikova D., Gudkova I. Araniti G., Shorgin V. Analysis of machine-type communication data transmission by multicasting technology in 5G wireless networks. AIP Conference Proceedings. 2019; 2116(1):090005. (In Eng.) DOI: 10.1063/1.5114070
[17] Galileiskaya A.A., Lisovskaya E.Yu. Asymptotic analysis of a multiphase infinite-linear resource queuing system with an incoming MMPP stream. Tomsk State University Journal of Control and Computer Science. 2018; 45:13-21. (In Russ., abstract in Eng.) DOI: 10.17223/19988605/45/2
[18] Lisovskaya E., Moiseeva S., Pagano M. Infinite–Server Tandem Queue with Renewal Arrivals and Random Capacity of Customers. In: Vishnevskiy V., Samouylov K., Kozyrev D. (eds) Distributed Computer and Communication Networks. DCCN 2017. Communications in Computer and Information Science, vol. 700. Springer, Cham, 2017, pp. 201-216. (In Eng.) DOI: 10.1007/978-3-319-66836-9_17
[19] Lisovskaya E.Yu., Galileiskaya A.A. The total amount of the occupied resource in the queuing resource system GI(ν)/GI(n)/∞ with n types of applications. In: Information Technologies and Mathematical Modeling (ITMM-2018): materials of the XVII A.F. Terpugov, 2018, pp. 88-93. Available at: https://elibrary.ru/item.asp?id=36383943 (accessed 16.07.2019). (In Russ.)
[20] Lisovskaya E.Yu., Moiseev A.N., Moiseeva S.P., Pagano M. Modeling of data processing processes of physical experiments in the form of a non-Markov multi-resource queuing system. Izvestiya vysshikh uchebnykh zavedenii. Fizika. 2018; 61(12):39-46. Available at: https://elibrary.ru/item.asp?id=36651301 (accessed 16.07.2019). (In Russ., abstract in Eng.)
[21] Galileiskaya A.A., Lisovskaya E.Yu., Moiseeva S.P. Gaussian approximation of the probability distribution of the total volume of the occupied resource in a multi-resource infinite-linear queuing system with an incoming MMPP-demand stream. In: Vishnevsky V.M., Samuylov K.E. (eds) Distributed computer and telecommunication networks: control, computation, communication (DCCN-2018) materials of the XXI International Scientific Conference. RUDN, 2018, pp. 7-12. Available at: https://elibrary.ru/item.asp?id=36626335 (accessed 16.07.2019). (In Russ., abstract in Eng.)
[22] Shorgin S., Pechinkin A., Samouylov K., Gaidamaka Y., Sopin E., Mokrov E. Queuing systems with multiple queues and batch arrivals for cloud computing system performance analysis. In: 2014 International Science and Technology Conference (Modern Networking Technologies) (MoNeTeC), Moscow, 2014, pp. 1-4. (In Eng.) DOI: 10.1109/MoNeTeC.2014.6995600
[23] Cao J., Li K., Stojmenovic I. Optimal Power Allocation and Load Distribution for Multiple Heterogeneous Multicore Server Processors across Clouds and Data Centers. IEEE Transactions on Computers. 2014; 63(1):45-58. (In Eng.) DOI: 10.1109/TC.2013.122
[24] Firdhous M., Ghazali O., Hassan S. Modeling of cloud system using Erlang formulas. In: The 17th Asia Pacific Conference on Communications, Sabah, 2011, pp. 411-416. (In Eng.) DOI: 10.1109/APCC.2011.6152844
[25] Moiseev A., Nazarov A. Asymptotic analysis of a multistage queuing system with a high-rate renewal arrival process. Optoelectronics, Instrumentation and Data Processing. 2014; 50(2):163-171. (In Eng.) DOI: 10.3103/S8756699014020083
[26] Pankratova E., Moiseeva S., Farhadov M., Moiseev A. Heterogeneous System MMPP/GI(2)/∞ with Random Customers Capacities. Journal of Siberian Federal University. Mathematics & Physics. 2019; 12(2):231-239. (In Eng., abstract in Russ.) DOI: 10.17516/1997-1397-2019-12-2-231-239
Published
2019-09-30
How to Cite
GALILEYSKAYA, Anastasia Alexandrovna et al.
On Sequential Data Processing Model, that Implements the Backup Storage.
Modern Information Technologies and IT-Education, [S.l.], v. 15, n. 3, p. 579-587, sep. 2019.
ISSN 2411-1473. Available at: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/603>. Date accessed: 08 feb. 2026.
doi: https://doi.org/10.25559/SITITO.15.201903.579-587.
Section
Theoretical Questions of Computer Science, Computer Mathematics
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