Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

Performance of the MAP/G/1 Queue Under the Dyadic Control of Workload and Server Idleness

  • Published:
Discrete Event Dynamic Systems Aims and scope Submit manuscript

Abstract

This paper studies the steady-state queue length process of the MAP/G/1 queue under the dyadic control of the D-policy and multiple server vacations. We derive the probability generating function of the queue length and the mean queue length. We then present computational experiences and compare the MAP queue with the Poisson queue.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Artalejo JR (2001) On the M/G/1 queue with D-policy. Appl Math Model 25:1055–1069

    Article  MATH  Google Scholar 

  • Artalejo JR (2002) A note on the optimality of the N- and D-policies for the M/G/1 queue. Oper Res Lett 30:375–376

    Article  MATH  MathSciNet  Google Scholar 

  • Balachandran KR (1973) Control policies for a single server system. Manage Sci 19:1013–1018

    MATH  MathSciNet  Google Scholar 

  • Balachandran KR, Tijms H (1975) On the D-Policy for the M/G/1 queue. Manage Sci 21:1073–1076

    MATH  MathSciNet  Google Scholar 

  • Boxma OJ (1976) Note on a control problem of Balachandran and Tijms. Manage Sci 22:916–917

    MATH  MathSciNet  Google Scholar 

  • Chae KC, Park YI (1999) On the optimal D-policy for the M/G/1 queue. J Korean Inst Indst Eng (KIIE) 25(4):527–531

    MathSciNet  Google Scholar 

  • Chae KC, Park YI (2001) The queue length distribution for the M/G/1 queue under the D-policy. J Appl Probab 38(1):278–279

    Article  MATH  MathSciNet  Google Scholar 

  • Crabill TB, Gross D, Magazine MJ (1977) A classified bibliography of research on optimal design and control of queue. Oper Res 25:219–232

    MathSciNet  Google Scholar 

  • Doshi BT (1990) Generalizations of the stochastic decomposition results for single server queues with vacations. Stoch Models 6(2):307–333

    Article  MATH  MathSciNet  Google Scholar 

  • Dshalalow JH (1998) Queueing processes in bulk systems under the D-policy. J Appl Probab 35:976–989

    Article  MATH  MathSciNet  Google Scholar 

  • Feinberg UA, Kella O (2002) Optimality of D-policies for an M/G/1 queue with a removable server. Queueing Syst 42:355–376

    Article  MATH  MathSciNet  Google Scholar 

  • Fuhrmann SW, Cooper RB (1985) Stochastic decompositions in the M/G/1 queue with generalized vacations. Oper Res 33(5):1117–1129

    MATH  MathSciNet  Google Scholar 

  • Gakis GK, Rhee HK, Sivazlian BD (1995) Distributions and first moments of the busy and idle periods in controllable M/G/1 queueing models with simple and dyadic policies. Stoch Anal Appl 13(1):47–81

    Article  MATH  MathSciNet  Google Scholar 

  • Heyman DP (1977) The T-policy for the M/G/1 queue. Manage Sci 23:775–778

    Article  MATH  MathSciNet  Google Scholar 

  • Lee HW, Song KS (2004) Queue length analysis of MAP/G/1 queue under D-policy. Stoch Models 20(3):363–380

    Article  MATH  MathSciNet  Google Scholar 

  • Lee HW, Cheon SH, Lee EY, Chae KC (2004) Workload and waiting time analysis of MAP/G/1 queue under D-policy. Queueing Systs 48:421–443

    Article  MATH  MathSciNet  Google Scholar 

  • Lee HW, Cheon SH, Seo WJ (2006) Queue length and waiting time of the M/G/1 queue under D-policy and multiple vacations. Queueing Systs 54:261–280

    Article  MathSciNet  Google Scholar 

  • Lee HW, Lee SW, Seo WJ, Cheon SH, Jeon J (2006) A unified framework for the analysis of the M/G/1 queues controlled by workload. Lecture Note in Computer Science (LNCS) 3982:718–727

    Article  Google Scholar 

  • Levy H, Yechiali U (1975) Utilization of idle time in an M/G/1 queueing system. Manage Sci 22(2):202–211

    MATH  Google Scholar 

  • Li J, Niu SC (1992) The waiting time distribution for the GI/G/1 queue under the D-policy. Prob Eng Inf Sci 6:287–308

    Article  MATH  Google Scholar 

  • Lillo RE, Martin M (2000) On optimal exhaustive policies for the M/G/1 queue. Oper Res Lett 27:39–46

    Article  MATH  MathSciNet  Google Scholar 

  • Lucantoni DM, Meier-Hellstern K, Neuts MF (1990) A single server queue with server vacations and a class of non-renewal arrival process. Adv Appl Probab 22:676–705

    Article  MATH  MathSciNet  Google Scholar 

  • Lucantoni DM (1991) New results on the single server queue with BMAP. Stoch Models 7(1):1–46

    Article  MATH  MathSciNet  Google Scholar 

  • Lucantoni DM (1993) Models and techniques for performance evaluation of computer and communications systems. In: Donatiello L, Nelson R (eds) The BMAP/G/1 queue: a tutorial. Springer, pp 330–358

  • Neuts MF (1981) Matrix-geometric solutions in stochastic models. The Johns Hopkins University Press, Baltimore

    MATH  Google Scholar 

  • Neuts MF (1989) Structured stochastic matrices of M/G/1 type and their applications. Marcel Dekker, New York

    MATH  Google Scholar 

  • Ramaswami V (1980) The N/G/1 queue and its detailed analysis. Adv Appl Probab 12:222–261

    Article  MATH  MathSciNet  Google Scholar 

  • Rhee HK (1997) Development of a new methodology to find the expected busy periods for controllable M/G/1 queueing models operating under the multi-variable operating policies: concepts and applications to the dyadic policies. J Korean Inst Ind Eng (KIIE) 23(4):729–739

    Google Scholar 

  • Rubin I, Zhang Z (1988) Switch-on policies for communications and queueing systems. De Moraes LFM, de Souza e Solva E, Soares LFG (eds) Data communication systems and Their performance. Elsevier Science (North-Holland), pp 315–325

  • Shanthikumar JG (1988) On stochastic decomposition in M/G/1 type queues with generalized server vacations. Oper Res 36(4):566–569

    MATH  MathSciNet  Google Scholar 

  • Sivazlian BD (1979) Approximate optimal solution for a D-policy in an M/G/1 queueing system. AIIE Trans 11:341–343

    Google Scholar 

  • Tadj L, Choudhury G (2005) Optimal design and control of queues. TOP 13(2):359-412

    Article  MATH  MathSciNet  Google Scholar 

  • Takine T, Takahashi Y (1998) On the relationship between queue length at a random time and at a departure in the stationary queue with BMAP arrivals. Stoch Models 14(3):601–610

    Article  MATH  MathSciNet  Google Scholar 

  • Tijms HC (1976) Optimal control of the workload in an M/G/1 queueing system with removable server. Math Operationsforsch. u. Statist 7:933–943

    MathSciNet  Google Scholar 

  • Tijms HC (1986) Stochastic modeling and analysis: a computational approach. Wiley, Chichester

    Google Scholar 

  • Tijms HC (2003) A first course in stochastic models. Wiley, Chichester

    MATH  Google Scholar 

  • Yadin M, Naor P (1963) Queueing systems with a removable server station. Oper Res Q 14:393–405

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ho Woo Lee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, H.W., Cheon, S.H., Lee, S.W. et al. Performance of the MAP/G/1 Queue Under the Dyadic Control of Workload and Server Idleness. Discrete Event Dyn Syst 18, 537–562 (2008). https://doi.org/10.1007/s10626-007-0024-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10626-007-0024-1

Keywords

Navigation