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Analysis of K-Capacity Queueing System with Two-Heterogeneous Server

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Analytical and Computational Methods in Probability Theory (ACMPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10684))

Abstract

This study mainly concerned with the K-capacity queueing system with recurrent input and two heterogeneous servers. Interarrival times are independent and have an arbitrary distribution. There are two servers and server k has an exponential distribution with parameter \(\mu _k\). Arriving customers choose server from the empty servers with equal probability. At an arrival time the customer joins the queue when both servers are busy. In addition an arrival leaves without having service when the system capacity is achieved. The defined system is represented by semi-Markov process and embedded Markov chain is obtained. Steady-state probabilities are found and loss probability is calculated by analyzing stream of overflows. Moreover loss probabilities are computed numerically for the queueing systems where the interarrival times are assumed as exponential, Erlang and deterministic distribution.

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References

  1. Gumbel, M.: Waiting lines with heterogeneous servers. Oper. Res. 8, 219–225 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  2. Lin, B.W., Elsayed, E.A.: A general solution for multichannel queueing systems with ordered entry. Comput. Oper. Res. 5, 504–511 (1978)

    Article  Google Scholar 

  3. Fakinos, D.: The blocking system with heterogeneous servers. J. Oper. Res. Soc. 31, 919–927 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  4. Neuts, F.M., Takahashi, Y.: Asymptotic behavior of the stationary distributions in the \(GI\)/\(PH\)/\(c\) queue with heterogeneous servers. Probab. Theory Relat. Field 57, 441–452 (1981)

    MathSciNet  MATH  Google Scholar 

  5. Nawijn, M.W.: A note on many-server queueing systems with ordered entry, with an application to conveyor theory. Eur. J. Oper. Res. 18, 388–395 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  6. Pourbabai, B., Sonderman, D.: Service utilization factors in queueing loss systems with ordered entry and heterogeneous servers. J. Appl. Probab. 23, 236–242 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  7. Alpaslan, F., Shahbazov, A.: An analysis and optimization of stochastic service with heterogeneous channel and poisson arrival. Pure Appl. Math. Sci. XLIII, 15–20 (1996)

    MathSciNet  MATH  Google Scholar 

  8. Isguder, H.O., Kocer, U.K., Celikoglu, C.C.: Generalization of the Takacs’ formula for \(GI\)/\(M\)/\(n\)/0 queuing system with heterogeneous servers. In: Proceedings of the World Congress on Engineering, vol. 1, pp. 45–47 (2011)

    Google Scholar 

  9. Isguder, H.O., Kocer, U.U.: Analysis of \(GI\)/\(M\)/\(n\)/\(n\) queueing system with ordered entry and no waiting line. Appl. Math. Model. 38, 1024–1032 (2014)

    Article  MathSciNet  Google Scholar 

  10. Millhiser, W.P., Sinha, C., Sobel, M.J.: Optimality of the fastest available server policy. Queueing Syst. 84, 237–263 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Selen, J., Adan, I., Kapodistria, S., Leeuwaarden, J.: Steady-state analysis of shortest expected delay routing. Queueing Syst. 84, 309–354 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Isguder, H.O., Kocer, U.U.: Optimization of loss probability for \(GI\)/\(M\)/3/0 queuing system with heterogeneous servers. A. Uni. J. Sci. Tech. 1, 73–89 (2011)

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Dokuz Eylul University, 35390, Izmir, Turkey

    H. Okan Isguder & Umay Uzunoglu Kocer

Authors
  1. H. Okan Isguder
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  2. Umay Uzunoglu Kocer
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Correspondence to H. Okan Isguder .

Editor information

Editors and Affiliations

  1. Department of Applied Probability and Informatics, RUDN University, Moscow, Russia

    Vladimir V. Rykov

  2. City University of Hong Kong, Hong Kong, Hong Kong

    Nozer D. Singpurwalla

  3. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    Andrey M. Zubkov

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Isguder, H.O., Uzunoglu Kocer, U. (2017). Analysis of K-Capacity Queueing System with Two-Heterogeneous Server. In: Rykov, V., Singpurwalla, N., Zubkov, A. (eds) Analytical and Computational Methods in Probability Theory. ACMPT 2017. Lecture Notes in Computer Science(), vol 10684. Springer, Cham. https://doi.org/10.1007/978-3-319-71504-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-71504-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71503-2

  • Online ISBN: 978-3-319-71504-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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