Abstract
In this paper, we consider semi-Markov flow as a bit-level model of traffic. Each request of the flow brings some arbitrary distributed amount of information to the system. The current paper aims to investigate the amount of information received in semi-Markov flow during time unit. We use the asymptotic analysis method under the limit condition of growing time of observation to derive the limiting probability distribution of the amount of information received in the flow and build the approximation of its prelimit distribution function.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Galileyskaya, A., Lisovskaya, E., Fedorova, E.: Resource queueing system with the requirements copying at the second phase. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2019. CCIS, vol. 1141, pp. 352–363. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36625-4_28
Galileyskaya, A., Lisovskaya, E., Pagano, M.: On the total amount of the occupied resources in the multi-resource QS with renewal arrival process. In: Dudin, A., Nazarov, A., Moiseev, A. (eds.) ITMM 2019. CCIS, vol. 1109, pp. 257–269. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-33388-1_21
Gao, J., Rubin, I.: Multifractal analysis and modeling of long-range-dependent traffic. In: 1999 IEEE International Conference on Communications (Cat. No. 99CH36311), vol. 1, pp. 382–386. IEEE (1999)
Klemm, A., Lindemann, C., Lohmann, M.: Modeling IP traffic using the batch Markovian arrival process. Perform. Eval. 54(2), 149–173 (2003)
Li, M.: Long-range dependence and self-similarity of teletraffic with different protocols at the large time scale of day in the duration of 12 years: Autocorrelation modeling. Physica Scripta 95(6), 065222 (2020)
Lisovskaya, E., Moiseeva, S., Pagano, M.: Multiclass GI/GI/\(\infty \) queueing systems with random resource requirements. In: Dudin, A., Nazarov, A., Moiseev, A. (eds.) ITMM/WRQ -2018. CCIS, vol. 912, pp. 129–142. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-97595-5_11
Naumov, V., Samouylov, K., Yarkina, N., Sopin, E., Andreev, S., Samuylov, A.: Lte performance analysis using queuing systems with finite resources and random requirements. In: 2015 7th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), pp. 100–103. IEEE (2015)
Naumov, V.A., Samuilov, K.E., Samuilov, A.K.: On the total amount of resources occupied by serviced customers. Autom. Remote Control 77(8), 1419–1427 (2016). https://doi.org/10.1134/S0005117916080087
Nazarov, A., et al.: Multi-level MMPP as a model of fractal traffic. In: Dudin, A., Nazarov, A., Moiseev, A. (eds.) ITMM 2020. CCIS, vol. 1391, pp. 61–77. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-72247-0_5
Nazarov, A., et al.: Mathematical model of scheduler with semi-markov input and bandwidth sharing discipline. In: 2021 International Conference on Information Technology (ICIT), pp. 494–498. IEEE (2021)
Peng, X., Bai, B., Zhang, G., Lan, Y., Qi, H., Towsley, D.: Bit-level power-law queueing theory with applications in lte networks. In: 2018 IEEE Global Communications Conference (GLOBECOM), pp. 1–6. IEEE (2018)
Salvador, P., Pacheco, A., Valadas, R.: Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs. Comput. Netw. 44(3), 335–352 (2004)
Willinger, W., Taqqu, M.S., Leland, W.E., Wilson, D.V., et al.: Self-similarity in high-speed packet traffic: analysis and modeling of ethernet traffic measurements. Stat. Sci. 10(1), 67–85 (1995)
Yang, T., Zhao, R., Zhang, W., Yang, Q.: On the modeling and analysis of communication traffic in intelligent electric power substations. IEEE Trans. Power Delivery 32(3), 1329–1338 (2016)
Yang, X., Petropulu, A.P.: The extended alternating fractal renewal process for modeling traffic in high-speed communication networks. IEEE Trans. Signal Process. 49(7), 1349–1363 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 Springer Nature Switzerland AG
About this paper
Cite this paper
Nazarov, A. et al. (2022). Semi-markov Resource Flow as a Bit-Level Model of Traffic. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds) Distributed Computer and Communication Networks. DCCN 2021. Communications in Computer and Information Science, vol 1552. Springer, Cham. https://doi.org/10.1007/978-3-030-97110-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-97110-6_17
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-97109-0
Online ISBN: 978-3-030-97110-6
eBook Packages: Computer ScienceComputer Science (R0)