Abstract
In this paper, we develop the queuing system model with processor sharing discipline with random serving rate coefficients. Each arriving customer is characterized by its length (job volume) and a serving rate coefficient determined by some probability distributions. The coefficients remain constant during the service process of customers. The proposed model is aimed to model the service process of elastic sessions in wireless networks, in which each session is assigned to one of modulation and coding schemes (MCSs) according to the state of the radio channel. Each MCS is characterized by its value of the spectral efficiency, which is modeled by serving rate coefficients.
First, we analyze the proposed model. Then we apply a simplification that significantly reduces the complexity of the analysis and allows us to deduce formulas for the blocking probability and the average sojourn time. Finally, we conduct a numerical analysis of the considered model.
The reported study was funded by RSF, project no. 20-71-00124 (recipient Sopin E., mathematical model and analysis). This paper has been supported by the RUDN University Strategic Academic Leadership Program (recipient Korshikov M., numerical analysis).
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References
3GPP TS 36.213 V13.15.0. Evolved Universal Terrestrial Radio Access (E-UTRA); Physical layer procedures (Release 13). https://www.3gpp.org/ftp/Specs/archive/36_series/36.213/36213-df0.zip. Accessed 25 Jan 2021
3GPP TS 38.211 V16.4.0. NR; Physical channels and modulation (Release 16). https://www.3gpp.org/ftp//Specs/archive/38_series/38.211/38211-g40.zip. Accessed 25 Jan 2021
Sopin, E., Samouylov, K., Vikhrova, O., Kovalchukov, R., Moltchanov, D., Samuylov, A.: Evaluating a case of downlink uplink decoupling using queuing system with random requirements. In: Galinina, O., Balandin, S., Koucheryavy, Y. (eds.) NEW2AN/ruSMART -2016. LNCS, vol. 9870, pp. 440–450. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46301-8_37
Yashkov, S.F., Yashkova, A.S.: Processor sharing: a survey of the mathematical theory. Autom. Remote Control 68(9), 1662–1731 (2007). https://doi.org/10.1134/S0005117907090202
Zhang, J., Zwart, B.: Steady state approximations of limited processor sharing queues in heavy traffic. Queueing Syst. 60, 227–246 (2008). https://doi.org/10.1007/s11134-008-9095-4
Samouylov, K., Naumov, K.: Stochastic lists of multiple resources. In: The 5th International Conference on Stochastic Methods (ICSM-2020). Springer Proceedings in Mathematics and Statistics (in print)
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
Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003). https://doi.org/10.1007/b97236
Samouylov, K., Naumov, V., Sopin, E., Gudkova, I., Shorgin, S.: Sojourn time analysis for processor sharing loss system with unreliable server. In: Wittevrongel, S., Phung-Duc, T. (eds.) ASMTA 2016. LNCS, vol. 9845, pp. 284–297. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-43904-4_20
Wolff, R.W.: Poisson arrivals see time averages. Oper. Res. 30(2), 223–231 (1982)
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Sopin, E., Korshikov, M. (2021). Analysis of the Queuing Systems with Processor Sharing Service Discipline and Random Serving Rate Coefficients. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2020. Communications in Computer and Information Science, vol 1391. Springer, Cham. https://doi.org/10.1007/978-3-030-72247-0_17
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DOI: https://doi.org/10.1007/978-3-030-72247-0_17
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