Top

Published in:

2020 | OriginalPaper | Chapter

Analysis of a Resource-Based Queue with the Parallel Service and Renewal Arrivals

Authors : Ekaterina Lisovskaya, Ekaterina Pankratova, Svetlana Moiseeva, Michele Pagano

Published in: Distributed Computer and Communication Networks

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Classical queueing theory is often not suitable to model modern computer and communication systems, in which the service itself can require random amounts of multiple resources. For instance, this is true for distributed computation and wireless devices connected through different access technologies.

To model such systems we propose a resource queueing system with customer duplication, in which the service time and the amount of requested resources in each block are independent random variables. In more detail, we assume that customers arrive according to a general renewal process and, taking advantage of the dynamic screening and the asymptotic analysis methods, we derive a Gaussian approximation for the stationary probability distribution of the occupied resources in the system blocks. Finally, simulation experiments point out the applicability region (in terms of arrival rate) of the proposed approximation.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Approximate Analysis of the Queuing System with Heterogeneous Servers and N-Policy

next chapter Two-Phase Resource Queueing System with Requests Duplication and Renewal Arrival Process

Andrews, J.G., Buzzi, S., Choi, W., Hanly, S.V., Lozano, A., Soong, A.C.K., Zhang, J.C.: What will 5G be? IEEE J. Sel. Areas Commun. 32(6), 1065–1082 (2014). https://doi.org/10.1109/JSAC.2014.2328098CrossRef

Ayoub, W., Samhat, A.E., Nouvel, F., Mroue, M., Prévotet, J.: Internet of mobile things: overview of LoRaWAN, DASH7, and NB-IoT in LPWANs standards and supported mobility. IEEE Commun. Surv. Tutor. 21(2), 1561–1581 (2019). https://doi.org/10.1109/COMST.2018.2877382CrossRef

Begishev, V., et al.: Quantifying the impact of guard capacity on session continuity in 3GPP new radio systems. IEEE Trans. Veh. Technol. 68(12), 12345–12359 (2019). https://doi.org/10.1109/TVT.2019.2948702CrossRef

Begishev, V., et al.: Resource allocation and sharing for heterogeneous data collection over conventional 3GPP LTE and emerging NB-IoT technologies. Comput. Commun. 120, 93–101 (2018). https://doi.org/10.1016/j.comcom.2018.01.009CrossRef

Buturlin, I., Gaidamaka, Y., Samuylov, A.: Utility function maximization problems for two cross-layer optimization algorithms in OFDM wireless networks. In: 4th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), pp. 63–65 (2012). https://doi.org/10.1109/ICUMT.2012.6459745

Cascone, A., Manzo, R., Pechinkin, A., Shorgin, S.: \(Geom/G/1/n\) system with LIFO discipline without interrupts and constrained total amount of customers. Autom. Remote Control 72(1) (2011). https://doi.org/10.1134/S0005117911010085

Chen, Q., et al.: Single ring slot-based antennas for metal-rimmed 4G/5G smartphones. IEEE Trans. Antennas Propag. 67(3), 1476–1487 (2019). https://doi.org/10.1109/TAP.2018.2883686CrossRef

Gorbunova, A., Naumov, V., Samouylov, K.: Resource queuing systems as models of wireless communication systems. Informatika i ee Primeneniya 12(3), 48–55 (2018). https://doi.org/10.14357/19922264180307CrossRef

Lisovskaya, E., Pankratova, E., Gaidamaka, Y., Moiseeva, S., Pagano, M.: Heterogeneous queueing system MAP/GI\(^{(n)}\)/\(\infty \) with random customers’ capacities. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2019. LNCS, vol. 11965, pp. 315–329. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36614-8_24CrossRef

10.

Lisovskaya, E.Y., Moiseev, A.N., Moiseeva, S.P., Pagano, M.: Modeling of mathematical processing of physics experimental data in the form of a non-Markovian multi-resource queuing system. Russ. Phys. J. 61(12), 2188–2196 (2019). https://doi.org/10.1007/s11182-019-01655-6CrossRef

11.

Moiseev, A., Nazarov, A.: Queueing network \(MAP-(GI/\infty )^K\) with high-rate arrivals. Euro. J. Oper. Res. 254(1), 161–168 (2016). https://doi.org/10.1016/j.ejor.2016.04.011MathSciNetCrossRef

12.

Naumov, V.A., Samuilov, K.E.: Analysis of networks of the resource queuing systems. Autom. Remote Control 79(5), 822–829 (2018). https://doi.org/10.1134/S0005117918050041MathSciNetCrossRef

13.

Naumov, V., Samouylov, K.: Conditions for the product form of the stationary probability distribution of Markovian resource loss systems. Tomsk State University Journal of Control and Computer Science (46), 64–72 (2019). https://doi.org/10.17223/19988605/46/8. (in Russian)

14.

Naumov, V., Samouylov, K., Sopin, E., Andreev, S.: Two approaches to analyzing dynamic cellular networks with limited resources. In: 6th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), pp. 485–488 (2014)

15.

Naumov, V., Samouylov, K.: On the modeling of queueing systems with multiple resources. Discrete Continuous Models Appl. Comput. Sci. 3, 60–64 (2014)

16.

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/S0005117916080087MathSciNetCrossRef

17.

Naumov, V., Beschastnyi, V., Ostrikova, D., Gaidamaka, Y.: 5G new radio system performance analysis using limited resource queuing systems with varying requirements. In: Vishnevskiy, V.M., Samouylov, K.E., Kozyrev, D.V. (eds.) DCCN 2019. LNCS, vol. 11965, pp. 3–14. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36614-8_1CrossRef

18.

Nazarov, A.A., Moiseev, A.N.: Analysis of the GI/PH/\({\infty }\) system with high-rate arrivals. Autom. Control Comput. Sci. 49(6), 328–339 (2015). https://doi.org/10.3103/S0146411615060085CrossRef

19.

Pankratova, E., Moiseeva, S.: Queueing system \(GI|GI|\infty \) with n types of customers. In: Dudin, A., Nazarov, A., Yakupov, R. (eds.) ITMM 2015. CCIS, vol. 564, pp. 216–225. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25861-4_19CrossRef

20.

Pankratova, E., Moiseeva, S., Farkhadov, M., Moiseev, A.: Heterogeneous system \(MMPP/GI(2)/\infty \) with random customers capacities. J. Siberian Fed. Univ. Math. Phys. 12(2), 231–239 (2019). https://doi.org/10.17516/1997-1397-2019-12-2-231-239MathSciNetCrossRef

21.

Romm, E., Skitovich, V.: On certain generalization of problem of erlang. Autom. Remote Control 32(6), 1000–1003 (1971)

22.

Samuylov, A., et al.: Characterizing resource allocation trade-offs in 5G NR serving multicast and unicast traffic. IEEE Trans. Wirel. Commun. 19(5), 3421–3434 (2020). https://doi.org/10.1109/TWC.2020.2973375CrossRef

23.

Samuylov, A., Beschastnyi, V., Moltchanov, D., Ostrikova, D., Gaidamaka, Y., Shorgin, V.: Modeling coexistence of unicast and multicast communications in 5G new radio systems. In: 30th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), pp. 1–6 (2019). https://doi.org/10.1109/PIMRC.2019.8904350

24.

Sinyakova, I., Moiseeva, S.: Investigation of output flows in the system with parallel service of multiple requests. In: IV International Conference "Problems of Cybernetics and Informatics" (PCI’2012), pp. 180–181 (2012)

25.

Tikhonenko, O.: Queuing system with processor sharing and limited resources. Autom. Remote Control 71(5), 803–815 (2010). https://doi.org/10.1134/S0005117910050073MathSciNetCrossRef

26.

Tikhonenko, O., Kempa, W.: On the queue-size distribution in the multi-server system with bounded capacity and packet dropping. Kybernetika 49(6), 855–867 (2013)MathSciNet

Title: Analysis of a Resource-Based Queue with the Parallel Service and Renewal Arrivals
Authors: Ekaterina Lisovskaya
Ekaterina Pankratova
Svetlana Moiseeva
Michele Pagano
Publisher: Springer International Publishing
Book: Distributed Computer and Communication Networks
Print ISBN: 978-3-030-66470-1

Electronic ISBN: 978-3-030-66471-8

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-66471-8_26

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner