Skip to main content

2015 | OriginalPaper | Buchkapitel

The Second Order Asymptotic Analysis Under Heavy Load Condition for Retrial Queueing System MMPP/M/1

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

search-config
loading …

Abstract

In the paper, the retrial queueing system of MMPP|M|1 type is studied by means of the second order asymptotic analysis method under heavy load condition. During the investigation, the theorem about the form of the asymptotic characteristic function of the number of calls in the orbit is formulated and proved. The asymptotic distribution is compared with the exact one obtained by means of numerical algorithm. The conclusion about method application area is made.

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 Wilkinson, R.I.: Theories for toll traffic engineering in the USA. Bell Sys. Tech. J. 35(2), 421–507 (1956)CrossRef Wilkinson, R.I.: Theories for toll traffic engineering in the USA. Bell Sys. Tech. J. 35(2), 421–507 (1956)CrossRef
2.
Zurück zum Zitat Cohen, J.W.: Basic problems of telephone trafic and the influence of repeated calls. Philips Telecommun. Rev. 18(2), 49–100 (1957) Cohen, J.W.: Basic problems of telephone trafic and the influence of repeated calls. Philips Telecommun. Rev. 18(2), 49–100 (1957)
3.
Zurück zum Zitat Elldin, A., Lind, G.: Elementary Telephone Trafic Theory. Ericsson Public Telecommunications, Stockholm (1971) Elldin, A., Lind, G.: Elementary Telephone Trafic Theory. Ericsson Public Telecommunications, Stockholm (1971)
4.
Zurück zum Zitat Gosztony, G.: Repeated call attempts and their efect on trafic engineering. Budavox Telecommun. Rev. 2, 16–26 (1976) Gosztony, G.: Repeated call attempts and their efect on trafic engineering. Budavox Telecommun. Rev. 2, 16–26 (1976)
5.
Zurück zum Zitat Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems. A Computational Approach. Springer, Heidelberg (2008)CrossRefMATH Artalejo, J.R., Gomez-Corral, A.: Retrial Queueing Systems. A Computational Approach. Springer, Heidelberg (2008)CrossRefMATH
6.
7.
Zurück zum Zitat Artalejo, J.R., Falin, G.I.: Standard and retrial queueing systems: a comparative analysis. Revista Matematica Complutense 15, 101–129 (2002)MATHMathSciNet Artalejo, J.R., Falin, G.I.: Standard and retrial queueing systems: a comparative analysis. Revista Matematica Complutense 15, 101–129 (2002)MATHMathSciNet
8.
Zurück zum Zitat Stepanov, S.N.: Numerical methods of calculation of retrial queues. Nauka, Moscow (1983). (In Russian) Stepanov, S.N.: Numerical methods of calculation of retrial queues. Nauka, Moscow (1983). (In Russian)
9.
Zurück zum Zitat Neuts, M.F., Rao, B.M.: Numerical investigation of a multiserver retrial model. Queueing Sys. 7(2), 169–189 (2002)CrossRefMATH Neuts, M.F., Rao, B.M.: Numerical investigation of a multiserver retrial model. Queueing Sys. 7(2), 169–189 (2002)CrossRefMATH
10.
Zurück zum Zitat Ridder, A.: Fast simulation of retrial queues. In: Third Workshop on Rare Event Simulation and Related Combinatorial Optimization Problems, pp. 1–5, Pisa (2000) Ridder, A.: Fast simulation of retrial queues. In: Third Workshop on Rare Event Simulation and Related Combinatorial Optimization Problems, pp. 1–5, Pisa (2000)
11.
12.
Zurück zum Zitat Artalejo, J.R., Gomez-Corra, A., Neuts, M.F.: Analysis of multiserver queues with constant retrial rate. Euro. J. Oper. Res. 135, 569–581 (2001)CrossRefMATHMathSciNet Artalejo, J.R., Gomez-Corra, A., Neuts, M.F.: Analysis of multiserver queues with constant retrial rate. Euro. J. Oper. Res. 135, 569–581 (2001)CrossRefMATHMathSciNet
13.
14.
Zurück zum Zitat Falin, G.I.: M/G/1 queue with repeated calls in heavy trafic. Moscow Univ. Math. Bull. 35(6), 48–50 (1980)MATH Falin, G.I.: M/G/1 queue with repeated calls in heavy trafic. Moscow Univ. Math. Bull. 35(6), 48–50 (1980)MATH
15.
Zurück zum Zitat Anisimov, V.V.: Asymptotic Analysis of Reliability for Switching Systems in Light and Heavy Trafic Conditions. Statistics for Industry and Technology. Birkhauser Boston, Boston (2000)MATH Anisimov, V.V.: Asymptotic Analysis of Reliability for Switching Systems in Light and Heavy Trafic Conditions. Statistics for Industry and Technology. Birkhauser Boston, Boston (2000)MATH
16.
Zurück zum Zitat Yang, T., Posner, M.J.M., Templeton, J.G.C., Li, H.: An approximation method for the M/G/1 retrial queue with general retrial times. Euro. J. Oper. Res. 76, 552–562 (1994)CrossRefMATH Yang, T., Posner, M.J.M., Templeton, J.G.C., Li, H.: An approximation method for the M/G/1 retrial queue with general retrial times. Euro. J. Oper. Res. 76, 552–562 (1994)CrossRefMATH
17.
Zurück zum Zitat Diamond, J.E., Alfa, A.S.: Approximation method for M/PH/1 retrial queues with phase type inter-retrial times. Euro. J. Oper. Res. 113, 620–631 (1999)CrossRefMATH Diamond, J.E., Alfa, A.S.: Approximation method for M/PH/1 retrial queues with phase type inter-retrial times. Euro. J. Oper. Res. 113, 620–631 (1999)CrossRefMATH
18.
Zurück zum Zitat Pourbabai, B.: Asymptotic analysis of G/G/K queueing-loss system with retrials and heterogeneous servers. Int. J. Sys. Sci. 19, 1047–1052 (1988)CrossRefMATHMathSciNet Pourbabai, B.: Asymptotic analysis of G/G/K queueing-loss system with retrials and heterogeneous servers. Int. J. Sys. Sci. 19, 1047–1052 (1988)CrossRefMATHMathSciNet
19.
Zurück zum Zitat Aissani, A.: Heavy loading approximation of the unreliable queue with repeated orders. In: Actes du Colloque Methodes et Outils d’Aide ’a la Decision (MOAD 1992), pp. 97–102, Bejaa (1992) Aissani, A.: Heavy loading approximation of the unreliable queue with repeated orders. In: Actes du Colloque Methodes et Outils d’Aide ’a la Decision (MOAD 1992), pp. 97–102, Bejaa (1992)
20.
Zurück zum Zitat Stepanov, S.N.: Asymptotic analysis of models with repeated calls in case of extreme load. Prob. Inf. Transm. 29(3), 248–267 (1993) Stepanov, S.N.: Asymptotic analysis of models with repeated calls in case of extreme load. Prob. Inf. Transm. 29(3), 248–267 (1993)
21.
Zurück zum Zitat Pankratova, E., Moiseeva, S.: Queueing System \(MAP/M/\infty \) with n Types of Customers. In: Dudin, A., et al. (eds.) Information Technologies and Mathematical Modelling. CCIS, vol. 487, pp. 356–366. Springer International Publishing, Switzerland (2014) Pankratova, E., Moiseeva, S.: Queueing System \(MAP/M/\infty \) with n Types of Customers. In: Dudin, A., et al. (eds.) Information Technologies and Mathematical Modelling. CCIS, vol. 487, pp. 356–366. Springer International Publishing, Switzerland (2014)
22.
Zurück zum Zitat Nazarov, A., Moiseev, A.: Analysis of an open non-Markovian \(GI-(GI|\infty )^K\) queueing network with high-rate renewal arrival process. Prob. Inf. Trans. 49(2), 167–178 (2013)CrossRefMATHMathSciNet Nazarov, A., Moiseev, A.: Analysis of an open non-Markovian \(GI-(GI|\infty )^K\) queueing network with high-rate renewal arrival process. Prob. Inf. Trans. 49(2), 167–178 (2013)CrossRefMATHMathSciNet
23.
Zurück zum Zitat Nazarov, A.A., Moiseeva, E.A.: The research of retrial queueing system \(MMPP|M|1\) by the method of asymptotic analysis under heavy load. Bull. Tomsk Polytechnic Univ. 322(2), 19–23 (2013). (In Russian) Nazarov, A.A., Moiseeva, E.A.: The research of retrial queueing system \(MMPP|M|1\) by the method of asymptotic analysis under heavy load. Bull. Tomsk Polytechnic Univ. 322(2), 19–23 (2013). (In Russian)
25.
Zurück zum Zitat Lucantoni, D.M.: New results on the single server queue with a batch Markovian arrival process. Stoch. Models 7, 1–46 (1991)CrossRefMATHMathSciNet Lucantoni, D.M.: New results on the single server queue with a batch Markovian arrival process. Stoch. Models 7, 1–46 (1991)CrossRefMATHMathSciNet
Metadaten
Titel
The Second Order Asymptotic Analysis Under Heavy Load Condition for Retrial Queueing System MMPP/M/1
verfasst von
Ekaterina Fedorova
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-25861-4_29

Premium Partner