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A Markov-modulated M/G/1 queue II: Busy period and time for buffer overflow

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Abstract

We consider an M/G/1 queue where the arrival and service processes are modulated by a two state Markov chain. We assume that the arrival rate, service time density and the rates at which the Markov chain switches its state, are functions of the total unfinished work (buffer content) in the queue. We compute asymptotic approximations to performance measures such as the mean residual busy period, mean length of a busy period, and the mean time to reach capacity.

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References

  1. C. Knessl, B.J. Matkowsky, Z. Schuss and C. Tier, A Markov-modulated M/G/1 queue I: stationary distribution, Queueing Systems 1(1987)355.

    Google Scholar 

  2. C. Knessl, B.J. Matkowsky, Z. Schuss and C. Tier, An M/G/1 queue with Markov-modulated arrival rates and service time densities I: Stationary distribution, Applied Mathematics Tech. Report No. 8423, Northwestern University (1986).

  3. C. Knessl, B.J. Matkowsky, Z. Schuss and C. Tier, An M/G/1 queue with Markov-modulated arrival rates and service time densities II: Busy period and time for buffer overflow, Applied Mathematics Tech. Report No. 8427, Northwestern University (1986).

  4. C. Knessl, B.J. Matkowsky, Z. Schuss and C. Tier, Asymptotic analysis of a state-dependent M/G/1 queueing system, SIAM J. Appl. Math. 46(1986)483.

    Google Scholar 

  5. C. Knessl, B.J. Matkowsky, Z. Schuss and C. Tier, A finite capacity single server queue with customer loss, Comm. Statist.: Stochastic Models 2(1986)97.

    Google Scholar 

  6. C. Knessl, B.J. Matkowsky, Z. Schuss and C. Tier, System crash in a finite capacity M/G/1 queue, Comm. Statist.: Stochastic Models 2(1986)171.

    Google Scholar 

  7. B.J. Matkowsky and Z. Schuss, The exit problem for randomly perturbed dynamical systems, SIAM J. Appl. Math. 33(1977)365.

    Google Scholar 

  8. C. Knessl, B.J. Matkowsky, Z. Schuss and C. Tier, An asymptotic theory of large deviations for Markov jump processes, SIAM J. Appl. Math. 45(1985)1006.

    Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Sciences and Applied Mathematics, Northwestern University, 60201, Evanston, IL, USA

    C. Knessl & B. J. Matkowsky

  2. Department of Mathematics, Tel Aviv University, Tel Aviv, Israel

    Z. Schuss

  3. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 60680, Chicago, IL, USA

    C. Tier

Authors
  1. C. Knessl
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  2. B. J. Matkowsky
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  3. Z. Schuss
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  4. C. Tier
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Additional information

This research was supported in part by NSF Grants DMS-84-06110, DMS-85-01535 and DMS-86-20267, and grants from the U.S. Israel Binational Science Foundation and the Israel Academy of Sciences.

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Knessl, C., Matkowsky, B.J., Schuss, Z. et al. A Markov-modulated M/G/1 queue II: Busy period and time for buffer overflow. Queueing Syst 1, 375–399 (1987). https://doi.org/10.1007/BF01150671

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  • DOI: https://doi.org/10.1007/BF01150671

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