Advertisement

Mathematical Methods of Operations Research

, Volume 62, Issue 3, pp 437–452 | Cite as

The G/M/1 queue revisited

  • Ivo Adan
  • Onno BoxmaEmail author
  • David Perry
Original Article

Abstract

The G/M/1 queue is one of the classical models of queueing theory. The goal of this paper is two-fold: (a) To introduce new derivations of some well-known results, and (b) to present some new results for the G/M/1 queue and its variants. In particular, we pay attention to the G/M/1 queue with a set-up time at the start of each busy period, and the G/M/1 queue with exceptional first service.

Keywords

Service Time Sojourn Time Busy Period Interarrival Time Idle Period 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Asmussen S (2003) Applied probability and queues. 2nd edn. Springer, Berlin Heidelberg New YorkzbMATHGoogle Scholar
  2. Cohen JW (1982) The single server queue. North-Holland, AmsterdamzbMATHGoogle Scholar
  3. Doshi BT (1985) A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times. J Appl Probab 22:419–428zbMATHCrossRefMathSciNetGoogle Scholar
  4. Kella O, Whitt W (1992) Useful martingales for stochastic storage processes with Lévy input. J Appl Probab 29:396–403zbMATHCrossRefMathSciNetGoogle Scholar
  5. Núñez Queija R (2001) Note on the GI/GI/1 queue with LCFS-PR observed at arbitrary times. Prob Eng Inf Sci 15:179–187CrossRefzbMATHGoogle Scholar
  6. Perry D, Stadje W, Zacks S (1999) Contributions to the theory of first-exit times of some compound processes in queueing theory. Queueing Syst 33:369–379CrossRefzbMATHMathSciNetGoogle Scholar
  7. Perry D, Stadje W (2003) Duality of dams via mountain processes. Oper Res Lett 31:451–458CrossRefzbMATHMathSciNetGoogle Scholar
  8. Perry D, Stadje W, Zacks S (2000) Busy period analysis for M/G/1 and G/M/1-type queues with restricted accessibility. Oper Res Lett 27:163–174CrossRefzbMATHMathSciNetGoogle Scholar
  9. Prabhu NU (1965) Queues and inventories. Wiley, New YorkzbMATHGoogle Scholar
  10. Prabhu NU (1988) Stochastic storage processes. Springer, Berlin Heidelberg New YorkGoogle Scholar
  11. Takács L (1962) Introduction to the theory of queues. Oxford University Press, New YorkGoogle Scholar
  12. Titchmarsh EC (1968) The theory of functions. 2nd edn. Oxford University Press, LondonGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.EURANDOM and Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of StatisticsUniversity of HaifaHaifaIsrael

Personalised recommendations