Skip to main content

2015 | OriginalPaper | Buchkapitel

Queueing System \(GI|GI|\infty \) with n Types of Customers

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The research of the queuing system with renewal arrival process, infinite number of n different types servers and arbitrary service time distribution is proposed. Expressions for the characteristic function of the number of busy servers for different types of customers in the system under the asymptotic condition that service time infinitely grows equivalently to each type of customers are derived.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

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!

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!

Literatur
1.
Zurück zum Zitat Pechinkin, A.V.: Boundary of change of stationary queue in queuing systems with various service disciplines. In: Proceedings of the Seminar “Problems of Stability of Stochastic Models”, 109. All-Union Scientific Research Institute for System Studies, Moscow, pp. 118–121 (1985) (in Russian) Pechinkin, A.V.: Boundary of change of stationary queue in queuing systems with various service disciplines. In: Proceedings of the Seminar “Problems of Stability of Stochastic Models”, 109. All-Union Scientific Research Institute for System Studies, Moscow, pp. 118–121 (1985) (in Russian)
2.
Zurück zum Zitat Pechinkin, A.V.: The inversion procedure with probabilistic priority in queuing system with extraordinary incoming flow. Stochastic processes and their applications. Mathematical research, Shtiintsa, Kishinev (1989) (in Russian) Pechinkin, A.V.: The inversion procedure with probabilistic priority in queuing system with extraordinary incoming flow. Stochastic processes and their applications. Mathematical research, Shtiintsa, Kishinev (1989) (in Russian)
3.
Zurück zum Zitat Pechinkin, A.V., Sokolov, I.A., Chaplygin, V.V.: Stationary characteristics ofmulti-line queuing system with simultaneous failures of devices. Comput. Sci. Appl. 1(2), 28–38 (2007). (in Russian) Pechinkin, A.V., Sokolov, I.A., Chaplygin, V.V.: Stationary characteristics ofmulti-line queuing system with simultaneous failures of devices. Comput. Sci. Appl. 1(2), 28–38 (2007). (in Russian)
4.
Zurück zum Zitat Abaev, P.: On mean return time in queueing system with constant service time and bi-level hysteric policy. In: Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks. Proceedings of the International Conference, Minsk, pp. 11–19 (2013) Abaev, P.: On mean return time in queueing system with constant service time and bi-level hysteric policy. In: Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks. Proceedings of the International Conference, Minsk, pp. 11–19 (2013)
6.
Zurück zum Zitat Baum, D.: The infinite server queue with Markov additive arrivals in space. In: Probabilistic Analysis of Rare Events. Proceedings of the International Conference, Riga, pp. 136–142 (1999) Baum, D.: The infinite server queue with Markov additive arrivals in space. In: Probabilistic Analysis of Rare Events. Proceedings of the International Conference, Riga, pp. 136–142 (1999)
7.
Zurück zum Zitat Baum, D., Breuer, L.: The Inhomogeneous \(BMAP|G|\infty \) queue. In: Proceedings of the 11th GI/ITG Conference on Measuring, Modelling and Evaluation of Computer and Communication Systems (MMB 2001), Aachen, pp. 209–223 (2001) Baum, D., Breuer, L.: The Inhomogeneous \(BMAP|G|\infty \) queue. In: Proceedings of the 11th GI/ITG Conference on Measuring, Modelling and Evaluation of Computer and Communication Systems (MMB 2001), Aachen, pp. 209–223 (2001)
8.
Zurück zum Zitat Bojarovich, J., Marchenko, L.: An open queueing network with temporarily non-active customers and rounds. In: Proceedings of the International Conference “Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks”, Minsk, pp. 33–36 (2013) Bojarovich, J., Marchenko, L.: An open queueing network with temporarily non-active customers and rounds. In: Proceedings of the International Conference “Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks”, Minsk, pp. 33–36 (2013)
9.
Zurück zum Zitat Doorn, E.A., Jagers, A.A.: Note on the \(GI|GI|\infty \) system with identical service and interarrival-time distributions. J. Queueing Syst. 47, 45–52 (2004)MathSciNetCrossRefMATH Doorn, E.A., Jagers, A.A.: Note on the \(GI|GI|\infty \) system with identical service and interarrival-time distributions. J. Queueing Syst. 47, 45–52 (2004)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Duffield, N.G.: Queueing at large resources driven by long-tailed \(M|G|\infty \)-modulated processes. Queueing Syst. 28(1–3), 245–266 (1998)MathSciNetCrossRefMATH Duffield, N.G.: Queueing at large resources driven by long-tailed \(M|G|\infty \)-modulated processes. Queueing Syst. 28(1–3), 245–266 (1998)MathSciNetCrossRefMATH
11.
12.
Zurück zum Zitat Girlich, E., Kovalev, M., Listopad, N.: Optimal choice of the capacities of telecommunication networks to provide QoS-Routing. In: Proceedings of the International Conference “Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks”, Minsk, pp. 93–104 (2013) Girlich, E., Kovalev, M., Listopad, N.: Optimal choice of the capacities of telecommunication networks to provide QoS-Routing. In: Proceedings of the International Conference “Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks”, Minsk, pp. 93–104 (2013)
13.
14.
Zurück zum Zitat Parulekar, M., Makowski, A.M.: Tail probabilities for \(M|G|\infty \) input processes: I. Preliminary asymptotics. Queueing Syst. 27(3–4), 271–296 (1997)MathSciNetCrossRefMATH Parulekar, M., Makowski, A.M.: Tail probabilities for \(M|G|\infty \) input processes: I. Preliminary asymptotics. Queueing Syst. 27(3–4), 271–296 (1997)MathSciNetCrossRefMATH
15.
Zurück zum Zitat Basharin, G.P., Samouylov, K.E., Yarkina, N.V., Gudkova, I.A.: A new stage in mathematical teletraffic theory. Autom. Remote Contr. 70(12), 1954–1964 (2009)MathSciNetCrossRefMATH Basharin, G.P., Samouylov, K.E., Yarkina, N.V., Gudkova, I.A.: A new stage in mathematical teletraffic theory. Autom. Remote Contr. 70(12), 1954–1964 (2009)MathSciNetCrossRefMATH
16.
Zurück zum Zitat Movaghar, A.: Analysis of a dynamic assignment of impatient customers to parallel queues. Queueing Syst. 67(3), 251–273 (2011)MathSciNetCrossRefMATH Movaghar, A.: Analysis of a dynamic assignment of impatient customers to parallel queues. Queueing Syst. 67(3), 251–273 (2011)MathSciNetCrossRefMATH
17.
Zurück zum Zitat Kargahi, M., Movaghar, A.: Utility accrual dynamic routing in real-time parallel systems. In: Transactions on Parallel and Distributed Systems (TDPS), vol. 21(12), pp. 1822–1835. IEEE (2010) Kargahi, M., Movaghar, A.: Utility accrual dynamic routing in real-time parallel systems. In: Transactions on Parallel and Distributed Systems (TDPS), vol. 21(12), pp. 1822–1835. IEEE (2010)
18.
19.
20.
Zurück zum Zitat Bambos, N., Michailidis, G.: Queueing networks of random link topology: stationary dynamics of maximal throughput schedules. Queueing Syst. 50(1), 5–52 (2005)MathSciNetCrossRefMATH Bambos, N., Michailidis, G.: Queueing networks of random link topology: stationary dynamics of maximal throughput schedules. Queueing Syst. 50(1), 5–52 (2005)MathSciNetCrossRefMATH
21.
Zurück zum Zitat Ivanovskaya (Sinyakova), I., Moiseeva, S.: Investigation of the queuing system \(MMP^{(2)}|M_2|\infty \) by method of the moments. In: Proceedings of the Third International Conference “Problems of Cybernetics and Informatics”, Baku, vol. 2, pp. 196–199 (2010) Ivanovskaya (Sinyakova), I., Moiseeva, S.: Investigation of the queuing system \(MMP^{(2)}|M_2|\infty \) by method of the moments. In: Proceedings of the Third International Conference “Problems of Cybernetics and Informatics”, Baku, vol. 2, pp. 196–199 (2010)
22.
Zurück zum Zitat Sinyakova, I., Moiseeva, S.: Investigation of queuing system \(GI^{(2)}|M_2|\infty \). In: Proceedings of the International Conference “Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks”, Minsk, pp. 219–225 (2011) Sinyakova, I., Moiseeva, S.: Investigation of queuing system \(GI^{(2)}|M_2|\infty \). In: Proceedings of the International Conference “Modern Probabilistic Methods for Analysis and Optimization of Information and Telecommunication Networks”, Minsk, pp. 219–225 (2011)
23.
Zurück zum Zitat Pankratova, E., Moiseeva, S.: Queueing system \(MAP|M|\infty \) with \(n\) types of customers. In: Proceedings of the 13th International Science Conference, ITMM 2014 named after A.F.Terpugov, Anzhero-Sudzhensk, pp. 356–366 (2014) Pankratova, E., Moiseeva, S.: Queueing system \(MAP|M|\infty \) with \(n\) types of customers. In: Proceedings of the 13th International Science Conference, ITMM 2014 named after A.F.Terpugov, Anzhero-Sudzhensk, pp. 356–366 (2014)
24.
Zurück zum Zitat Pankratova E., Moiseeva S.: Queueing system with renewal arrival process and two types of customers. In: Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), pp. 514–517. IEEE (2014) Pankratova E., Moiseeva S.: Queueing system with renewal arrival process and two types of customers. In: Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), pp. 514–517. IEEE (2014)
Metadaten
Titel
Queueing System with n Types of Customers
verfasst von
Ekaterina Pankratova
Svetlana Moiseeva
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-25861-4_19