Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Enhanced C-RAN Architecture Supporting SDN and NFV Functionalities for D2D Communications Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Sojourn Time Analysis for Processor Sharing Loss Queuing System with Service Interruptions and MAP Arrivals

Authors : Konstantin Samouylov, Eduard Sopin, Irina Gudkova

Published in: Distributed Computer and Communication Networks

Publisher: Springer International Publishing

Log in

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

search-config
loading …

Abstract

Processor sharing (PS) queuing systems are widely investigated by research community and applied for the analysis of wire and wireless communication systems and networks. Nevertheless, only few works focus on finite queues with both PS discipline and service interruptions. In the paper, compared with the previous results we analyze a finite capacity PS queuing system with Markovian arrival process, unreliable server, service interruptions, and an upper limit of the number of customers it serves simultaneously. For calculating the mean sojourn time, unlike a popular but computational complex technique of inverse Laplace transform we use an effective method based on embedded Markov chain. A practical example concludes the paper.

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 Convergence Evaluation of Adaptation to Losses: The Case of Subscription Notification Delivery to Mobile Users in Smart Spaces
next chapter The Estimation of Probability Characteristics of Cloud Computing Systems with Splitting of Requests
Literature
1.
Fredj, S.B., Bonald, T., Proutiere, A., Regnie, G., Roberts, J.W.: Statistical bandwidth sharing: a study of congestion at flow level. In: ACM SIGCOMM 2001, pp. 111–122
2.
Kleinrock, L.: Time-shared systems: a theoretical treatment. J. ACM 14, 242–261
3.
Yashkov, S.F., Yashkova, A.S.: Processor sharing: a survey of the mathematical theory. Autom. Remote Control 68, 1662–1731
4.
Morrison, J.A.: Response-time distribution for a processor-sharing system. SIAM J. Appl. Math. 45, 152–167
5.
Knessl, C.: On finite capacity processor-shared queues. SIAM J. Appl. Math. 50, 264–287
6.
Zhen, Q., Knessl, C.: On sojourn times in the finite capacity M/M/1 queue with processor sharing. Oper. Res. Lett. 37, 447–450
7.
Rege, K., Sengupta, B.: Sojourn time distribution in a multiprogrammed computer system. AT&T Tech. J. 64, 1077–1090
8.
Masuyama, H., Takine, T.: Sojourn time distribution in a MAP/M/1 processor-sharing queue. Oper. Res. Lett. 31, 406–412
9.
Nunez-Queija, R.: Sojourn times in non-homogeneous QBD processes with processor-sharing. Stoch. Models 17, 61–92
10.
Zhen, Q., Knessl, C.: Asymptotic analysis of spectral properties of finite capacity processor shared queues. Stud. Appl. Math. 131, 179–210
11.
Samouylov, K., Gudkova, I.: Recursive computation for a multi-rate model with elastic traffic and minimum rate guarantees. In: 2nd International Congress on Ultra Modern Telecommunications and Control Systems ICUMT, pp. 1065–1072
12.
Basharin, G.P., Naumov, V.A.: Simple matrix description of peaked and smooth traffic and its applications. In: Proceedings of the 3rd International Seminar on Teletraffic Theory “Fundamentals of Teletraffic Theory”, Moscow, VINITI, pp. 38–44
13.
Lucantoni, D.M., Meier-Hellstern, K.S., Neuts, M.F.: A single server queue with server vacations and a class of non-renewal arrival processes. Adv. Appl. Probab. 22, 676–705
14.
Asmussen, S.: Applied Probability and Queues, vol. 51. Springer, New York (2003)MATH
15.
Naumov, V.A., Samouylov, K.E., Gaidamaka, Y.V.: Multiplicative solutions for the finite Markov chains. RUDN
16.
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, Heidelberg (2016). doi:10.​1007/​978-3-319-43904-4_​20 CrossRef
Metadata
Title
Sojourn Time Analysis for Processor Sharing Loss Queuing System with Service Interruptions and MAP Arrivals
Authors
Konstantin Samouylov
Eduard Sopin
Irina Gudkova
Copyright Year
2016
Book
Distributed Computer and Communication Networks

Print ISBN: 978-3-319-51916-6

Electronic ISBN: 978-3-319-51917-3

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-51917-3_36

Premium Partner

    Image Credits