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Stationary distribution of queue length in G / M / 1 queue with two-stage service policy

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Abstract

We consider a G / M / 1 queue with two-stage service policy. The server starts to serve with rate of μ1 customers per unit time until the number of customers in the system reaches λ. At this moment, the service rate is changed to that of μ2 customers per unit time and this rate continues until the system is empty. We obtain the stationary distribution of the number of customers in the system.

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References

  • Bae J, Kim S, Lee EY (2002) A P M λ-policy for an M/G/1 queueing system. Appl Math Model 26:929-939

    Article  MATH  Google Scholar 

  • Dudin A, Chakravarthy S (2002) Optimal hysteretic control for the BMAP/G/1 system with single and group service modes. Ann Oper Res 112:153–169

    Article  MATH  MathSciNet  Google Scholar 

  • Dudin AN, Klimenok VI (1991) Optimization of dynamic control of input load at a node of a computer/information network. Autom Control Comput Sci 25(2):19–25

    MATH  Google Scholar 

  • Faddy MJ (1974) Optimal control of finite dams: discrete(2-stage) output procedure. J Appl Probab 11:111–121

    Article  MATH  MathSciNet  Google Scholar 

  • Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Lee EY, Ahn SK (1998) P M λ-policy for a dam with input formed by a compound Poisson process. J Appl Probab 35:482–488

    Article  MATH  MathSciNet  Google Scholar 

  • Lu FV, Serfozo RF (1984) M/M/1 queueing decision processes with monotone hysteretic optimal policies. Oper Res 32:1116–1132

    Article  MATH  MathSciNet  Google Scholar 

  • Pakes AG (1969) Some conditions for ergodicity and recurrence of Markov chains. Oper Res 17:1058–1061

    MATH  MathSciNet  Google Scholar 

  • Ross SM (1996) Stochastic processes, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  • Wolff RW (1989) Stochastic modeling and the theory of queues. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  • Zhang ZG, Tian N (2004) The N threshold policy for the GI/M/1 queue. Oper Res Lett 32:77–84

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Information Statistics, Gyeongsang National University, Jinju, 660-701, Republic of Korea

    Sunggon Kim

  2. Statistical Research Center for Complex Systems, Seoul National University, Seoul, 151-742, Republic of Korea

    Jongwoo Kim

  3. Department of Statistics, Sookmyung Women’s University, Seoul, 140-742, Republic of Korea

    Eui Yong Lee

Authors
  1. Sunggon Kim
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  2. Jongwoo Kim
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  3. Eui Yong Lee
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Corresponding author

Correspondence to Jongwoo Kim.

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Kim, S., Kim, J. & Lee, E.Y. Stationary distribution of queue length in G / M / 1 queue with two-stage service policy. Math Meth Oper Res 64, 467–480 (2006). https://doi.org/10.1007/s00186-006-0096-y

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  • DOI: https://doi.org/10.1007/s00186-006-0096-y

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