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M/G/1 Queuing Theory and Applications

  • Giovanni Giambene
Chapter

Abstract

The M/G/1 theory is a powerful tool, generalizing the solution of Markovian queues to the case of general service time distributions. There are many applications of the M/G/1 theory in the field of telecommunications; for instance, it can be used to study the queuing of fixed-size packets to be transmitted on a given link (i.e., M/D/1 case). Moreover, this theory yields results which are compatible with the M/M/1 theory, based on birth–death Markov chains.

Keywords

Service Time Arrival Process Packet Delay Poisson Arrival Message Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supplementary material

108201_2_En_6_MOESM1_ESM.pdf (402 kb)
Lesson 7 (PDF 401 kb)
108201_2_En_6_MOESM2_ESM.pptx (807 kb)
Lesson 7 (PPTX 807 kb)
108201_2_En_6_MOESM3_ESM.pdf (156 kb)
Lesson 9 (PDF 156 kb)
108201_2_En_6_MOESM4_ESM.pptx (461 kb)
Lesson 9 (PPTX 460 kb)
108201_2_En_6_MOESM5_ESM.pdf (125 kb)
Lesson 11 (PDF 125 kb)
108201_2_En_6_MOESM6_ESM.pptx (406 kb)
Lesson 11 (PPTX 406 kb)
108201_2_En_6_MOESM7_ESM.pdf (209 kb)
Lesson 19 (PDF 208 kb)
108201_2_En_6_MOESM8_ESM.pptx (509 kb)
Lesson 19 (PPTX 509 kb)

References

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    Kleinrock L (1976) Queuing systems. Wiley, New YorkGoogle Scholar
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    Kleinrock L, Gale R (1996) Queuing systems. Wiley Interscience publication, New YorkGoogle Scholar
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    Gross D, Harris CM (1974) Fundamentals of queueing theory. Wiley, New YorkMATHGoogle Scholar
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    Andreadis A, Giambene G (2002) Protocols for high-efficiency wireless networks. Kluwer, New YorkGoogle Scholar
  6. 6.
    Ramsay CM (2007) Exact waiting time and queue size distributions for equilibrium M/G/1 queues with Pareto service. J Queueing Syst 57(4):147–155CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Giambene G, Hadzic-Puzovic S (2013) Downlink performance analysis for broadband wireless systems with multiple packet sizes. Perform Eval 70(5):364–386CrossRefGoogle Scholar
  8. 8.
    Heines TS (1979) Buffer behavior in computer communication systems. IEEE Trans Comput c-28(8):573–576CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Giovanni Giambene
    • 1
  1. 1.Department of Information Engineering and Mathematical SciencesUniversity of SienaSienaItaly

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