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The stationary distribution of the waiting time in a queueing system with negative customers and a bunker for superseded customers in the case of the LAST-LIFO-LIFO discipline

Abstract

A queueing system with one service device and Poisson flows of ordinary and negative customers is considered. There is an infinite buffer for ordinary customers. A negative customer arriving at the system knocks out an ordinary customer queueing in the buffer and moves it to an infinite bunker and itself leaves the system. The customers from the bunker are served with a relative priority. The service durations for customers from the buffer and bunker have exponential distributions with different parameters. It is assumed that a negative customer knocks out the last customer queueing in the buffer and that the last customer queueing in the buffer or bunker is chosen to be served.

for the system considered, the stationary waiting time distribution of ordinary customer arriving at the system is found in terms of the Laplace-Stieltjes transformation.

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Correspondence to A. V. Pechinkin.

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Original Russian Text © A.V. Pechinkin, R.V. Razumchik, 2012, published in Informatsionnye Protsessy, 2012, Vol. 12, No. 3, pp. 159–171.

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Pechinkin, A.V., Razumchik, R.V. The stationary distribution of the waiting time in a queueing system with negative customers and a bunker for superseded customers in the case of the LAST-LIFO-LIFO discipline. J. Commun. Technol. Electron. 57, 1331–1339 (2012). https://doi.org/10.1134/S1064226912120054

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Keywords

  • queueing system
  • negative customers
  • waiting time
  • busy period