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Exponential queuing system with negative customers and bunker for ousted customers


Consideration was given to the queuing system with Poisson flows of incoming positive and negative customers. For the positive customers, there is an infinite-capacity buffer. The arriving negative customer knocks out a positive customer queued in the buffer and moves it to an infinite-capacity buffer of ousted customers (bunker). If the buffer is empty, then the negative customer discharges the system without affecting it. After servicing the current customer, the server receives a customer from the buffer or, if the buffer is empty, the bunker. The customers arriving from both the buffer and bunker are distributed exponentially with the same parameter. Relations for calculation of the stationary distributions of the queues in the buffer and bunker were obtained.

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  1. 1.

    Gelenbe, E., Glynn, P., and Sigman, K., Queues with Negative Arrivals, J. Appl. Prob., 1991, vol. 28, pp. 245–250.

    MATH  Article  MathSciNet  Google Scholar 

  2. 2.

    Bocharov, P.P. and Vishnevskii, V.M., G Networks: Development of the Theory of Multiplicative Networks, Avtom. Telemekh., 2003, no. 5, pp. 46–74.

  3. 3.

    Bocharov, P.P. and Pechinkin, A.V., Teoriya massovogo obsluzhivaniya (Queuing Theory), Moscow: Ross. Univ. Druzhby Narodov, 1995.

    Google Scholar 

  4. 4.

    Boev, V.D., Modelirovanie sistem. Instrumental’nye sredstva GPSS World (System Modeling. Instrumental Facilites of GPSS World), St. Petersburg: BKHV-Peterburg, 2004.

    Google Scholar 

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Correspondence to R. Manzo.

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Original Russian Text © R. Manzo, N. Cascone, R.V. Razumchik, 2008, published in Avtomatika i Telemekhanika, 2008, No. 9, pp. 103–113.

This work was supported by the Russian Foundation for Basic Research, project no. 06-07-89056.

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Manzo, R., Cascone, N. & Razumchik, R.V. Exponential queuing system with negative customers and bunker for ousted customers. Autom Remote Control 69, 1542–1551 (2008).

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PACS number

  • 02.50.-r