Abstract
We consider a polling system with adaptive dynamic polling order for modeling a broadband wireless network with a centralized control mechanism. A new algorithm has been developed for calculating the steady-state probability distribution of the number of packets in subscriber stations. The algorithm makes it possible to calculate the average waiting time and other network performance characteristics. We investigate a queuing system with several queues in which the server serves queues in a dynamic polling order. This order of queuing involves skipping queues that had been empty in the previous polling cycle. The queues that have been skipped in the current cycle can be polled by the server only in the next cycle. The specified queue servicing algorithm allows one to reduce the queue polling time and thus increase the system performance. A comparative numerical analysis of various options for constructing and evaluating the performance characteristics of broadband wireless IEEE 802.11 networks with a centralized control mechanism is presented. Numerical studies have been carried out using a software package for evaluating stochastic polling systems.
Similar content being viewed by others
REFERENCES
Vishnevsky, V.M. and Semenova, O.V., Adaptive dynamic polling systems with correlated arrivals, Preprint of Trapeznikov Inst. of Control Sciences, Russ. Acad. Sci., Moscow, 2017.
Vishnevsky, V.M., Larionov, A.A., and Ivanov, R.E., UHF RFID in automatic vehicle identification: analysis and simulation, IEEE J. Radio Frequency Identif., 2017, vol. 1, no. 1, pp. 3–12. https://doi.org/10.1109/JRFID.2017.2751592
Bekker, R., Vis, P., Dorsman, J.L., et al., The impact of scheduling policies on the waiting-time distributions in polling systems, Queueing Syst., 2015, vol. 79, no. 2, pp. 145–172.
Saffer, Z., Telek, M., and Horvath, G., Fluid polling system with Markov modulated load and gated discipline, Lect. Notes Comput. Sci., 2018, vol. 10932, pp. 86–102.
Meyfroyt, T.M.M., Boon, M.A.A., Borst, S.C., and Boxma, O.J., Performance of large-scale polling systems with branching-type and limited service, Performance Eval., 2019, vol. 133, pp. 1–24.
Kim, B. and Kim, J., Analysis of the waiting time distribution for polling systems with retrials and glue periods, Ann. Oper. Res., 2019, vol. 277, no. 2, pp. 197–212.
Gaidamaka, Yu.V., Model with threshold control for analyzing a server with an SIP protocol in the overload mode, Autom. Control Comput. Sci., 2013, vol. 47, no. 4, pp. 211–218.
Sonkin, M.A., Moiseev, A.N., Sonkin, D.M., and Burtovaya, D.A., Object model of application for simulation of cyclic queueing systems, Vestn. Tomsk. Gos. Univ. Upr. Vychisl. Tekh. Inf., 2017, vol. 40, pp. 71–80.
Vishnevsky, V.M., Dudin, A.N., Klimenok, V.I., et al., Approximate method to study M/G/1-type polling system with adaptive polling mechanism, Qual. Technol. Quant. Manage., 2012, vol. 2, pp. 211–228.
Semenova, O.V. and Bui, D.T., Method of generating functions for performance characteristic analysis of the polling systems with adaptive polling and gated service, Commun. Comput. Inf. Sci., 2018, vol. 912, pp. 348–359.
Rykov, V.V., On analysis of periodic polling systems, Autom. Remote Control, 2009, vol. 70, pp. 997–1018.
Matveev, A., Feoktistova, V., and Bolshakova, K., On global near optimality of special periodic protocols for fluid polling systems with setups, J. Optim. Theory Appl., 2016, vol. 171, no. 3, pp. 1055–1070.
Zorine, A.V., On ergodicity conditions in a polling model with Markov modulated input and state-dependent routing, Queueing Syst., 2014, vol. 76, no. 2, pp. 223–241.
Vishnevskii, V.M. and Semenova, O.V., Mathematical methods to study the polling systems, Autom. Remote Control, 2006, vol. 67, no. 2, pp. 173–220.
Boon, M.A.A., van der Mei, R.D., and Winands, E.M.M., Applications of polling systems, Surv. Oper. Res. Manage. Sci., 2011, vol. 16, no. 2, pp. 67–82.
Borst, S.C. and Boxma, O., Polling: past, present, and perspective, TOP, 2018, vol. 26, no. 3, pp. 335–369.
Vishnevskii, V.M. and Semenova, O.V., Sistemy pollinga: teoriya i primenenie v shirokopolosnykh besprovodnykh setyakh (Polling Systems: Theory and Applications in Broadband Wireless Networks), Moscow: Tekhnosfera, 2007.
Vishnevskii, V.M., Dudin, A.N., and Klimenok, V.I., Stokhasticheskie sistemy s korrelirovannymi vkhodnymi potokami. Teoriya i primenenie v telekommunikatsionnykh setyakh (Stochastic Systems with Correlated Arrivals. Theory and Applications in Telecommunication Networks), Moscow: Tekhnosfera, 2018.
Vishnevsky, V.M., Semenova, O.V., and Bui, D.T., Software complex for evaluating the characteristics of stochastic polling systems, Certificate of State Registration of Computer Programs, August 4, 2019, no. 2019614554 RF.
Funding
This work was supported by the Russian Foundation for Basic Research, project no. 19-29-06043.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by V. Potapchouck
Rights and permissions
About this article
Cite this article
Vishnevsky, V.M., Semenova, O.V. & Bui, D.T. Investigation of the Stochastic Polling System and Its Applications to Broadband Wireless Networks. Autom Remote Control 82, 1607–1613 (2021). https://doi.org/10.1134/S0005117921090083
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117921090083