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Generalized Erlang Problem for Service Systems with Finite Total Capacity

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Abstract

A multiserver on-demand system is considered in which each call has three interdependent random characteristics: the required number of servers, capacity, and service time. The total capacity of calls and the total number of servers in the system are limited. The type of a call is defined by the number of servers required for its service. We find a stationary distribution of the number of calls in the system, as well as the loss probability for a call of each type.

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REFERENCES

  1. Gnedenko, B.V. and Kovalenko, I.N., Vvedenie v teoriyu massovogo obsluzhivaniya, Moscow: Nauka, 1987. Translated under the title Introduction to Queueing Theory, Boston: Birkhauser, 1989.

    Google Scholar 

  2. Kaufman, J.S., Blocking in a Shared Resource Environment, IEEE Trans. Commun., 1981, vol. 29, no.10, pp. 1474–1481.

    Article  Google Scholar 

  3. Nazarov, A.A., Engset Formulas for Nonhomogeneous Non-Markov Queueing Systems and Their Application in Communication Networks, Probl. Peredachi Inf., 1998, vol. 34, no.2, pp. 109–116 [Probl. Inf. Trans. (Engl. Transl.), 1998, vol. 34, no. 2, pp. 190–196].

    Google Scholar 

  4. Romm, E.L. and Skitovich, V.V., On One Generalization of the Erlang Problem, Avtomat. Telemekh., 1971, no. 6, pp. 164–167.

  5. Tikhonenko, O.M., Determination of Characteristics of Queueing Systems with Limited Memory, Avtomat. Telemekh., 1997, no. 6, pp. 105–110.

  6. Tikhonenko, O.M. and Klimovich, K.G., Analysis of Queuing Systems for Random-Length Arrivals with Limited Cumulative Volume, Probl. Peredachi Inf., 2001, vol. 37, no.1, pp. 78–88 [Probl. Inf. Trans. (Engl. Transl.), 2001, vol. 37, no. 1, pp. 70–79].

    Google Scholar 

  7. Matveev, V.F. and Ushakov, V.G., Sistemy Massovogo Obsluzhivaniya (Queueing Systems), Moscow: Mosk. Gos. Univ., 1984.

    Google Scholar 

  8. Borovkov, A.A., Teoriya veroyatnostei (Probability Theory), Moscow: Nauka, 1986, 2nd ed.

    Google Scholar 

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Authors and Affiliations

  1. Jan Dlugosz University, Czestochowa, Poland

    O. M. Tikhonenko

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  1. O. M. Tikhonenko
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Translated from Problemy Peredachi Informatsii, No. 3, 2005, pp. 64–75.

Original Russian Text Copyright © 2005 by Tikhonenko.

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Tikhonenko, O.M. Generalized Erlang Problem for Service Systems with Finite Total Capacity. Probl Inf Transm 41, 243–253 (2005). https://doi.org/10.1007/s11122-005-0029-z

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  • DOI: https://doi.org/10.1007/s11122-005-0029-z

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