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A maximum entropy approach for the busy period of the M/G/1 retrial queue

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Abstract

This paper concerns the busy period of a single server queueing model with exponentially distributed repeated attempts. Several authors have analyzed the structure of the busy period in terms of the Laplace transform but, the information about the density function is limited to first and second order moments. We use the maximum entropy principle to find the least biased density function subject to several mean value constraints. We perform results for three different service time distributions: 3-stage Erlang, hyperexponential and exponential. Also a numerical comparative analysis between the exact Laplace transform and the corresponding maximum entropy density is presented.

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References

  • Artalejo, J.R. (1999a). “Accessible Bibliography on Retrial Queues.” Mathematical and Computer Modelling 30, 1–6.

    Article  Google Scholar 

  • Artalejo, J.R. (1999b). “A Classified Bibliography of Research on Retrial Queues: Progress in 1990–1999.” Top 7, 187–211.

    Google Scholar 

  • Artalejo, J.R. and M.J. Lopez-Herrero. (2000). “On the Busy Period of the M/G/1 Retrial Queue.” Naval Research Logistics 47, 115–127.

    Article  Google Scholar 

  • Artalejo, J.R., G.I. Falin and M.J. Lopez-Herrero. (2002). “A Second Order Analysis of the Waiting Time in the M/G/1 Retrial Queue.” Asia-Pacific Journal of Operational Research 19, 131–148.

    Google Scholar 

  • El-Affendi, M.A. and D.D. Kouvatsos. (1983). “A Maximum Entropy Analysis of the M/G/1 and G/M/1 Queueing Systems at Equilibrium.” Acta Informatica 19, 339–355.

    Article  Google Scholar 

  • Falin, G.I. (1979). “A Single-line with Secondary Orders.” Engineering Cybernetics Review 17, 76–83.

    Google Scholar 

  • Falin, G.I. (1990). “A Survey of Retrial Queues.” Queueing Systems 7, 127–167.

    Article  Google Scholar 

  • Falin, G.I. and J.G.C. Templeton. (1997). Retrial Queues. Chapman and Hall, London.

    Google Scholar 

  • Kouvatsos, D.D. (1994). “Entropy Maximisation and Queueing Networks Models.” Annals of Operations Research 48, 63–126.

    Article  Google Scholar 

  • Lopez-Herrero, M.J. (2002). “On the Number of Customers Served in the M/G/1 Retrial Queue: first Moments and Maximum Entropy Approach.” Computers & Operations Research 29, 1739–1757.

    Article  Google Scholar 

  • Nelder, J.A. and R. Mead. (1964). “A Simplex Method for Function Minimization.” Computer Journal 7, 308–313.

    Google Scholar 

  • Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery. (1992). Numerical Recipes in Fortran, The Art of Scientific Computing. Cambridge University Press, Cambridge.

    Google Scholar 

  • Shore, J.E. (1982). “Information Theoretic Approximations for M/G/1 and G/G/1 Queueing Systems.” Acta Informatica 17, 43–61.

    Article  Google Scholar 

  • Tadj, L. and A. Hamdi. (2002). “Maximum Entropy Solution to a Quorum Queueing System.” Mathematical and Computing Modelling 34, 19–27.

    Article  Google Scholar 

  • Wagner, U. and A.L.J. Geyer. (1995). “A Maximum Entropy Method for Inverting Laplace Transforms of Probability Density Functions.” Biometrika 82, 887–892.

    Article  Google Scholar 

  • Wang, K.H., S.L. Chuang, and W.L. Pearn. (2002). “Maximum Entropy Analysis to the N Policy M/G/1 Queueing Systems with a Removable Server.” Applied Mathematical Modelling 26, 1151–1162.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Statistics, Complutense University of Madrid, Madrid, 28040, Spain

    M. J. Lopez-Herrero

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  1. M. J. Lopez-Herrero
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Correspondence to M. J. Lopez-Herrero.

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AMS subject classification: 90B05 90B22

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Lopez-Herrero, M.J. A maximum entropy approach for the busy period of the M/G/1 retrial queue. Ann Oper Res 141, 271–281 (2006). https://doi.org/10.1007/s10479-006-5302-z

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  • DOI: https://doi.org/10.1007/s10479-006-5302-z

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