Finite-source M/M/S retrial queue with search for balking and impatient customers from the orbit

  • Authors:

  • Patrick Wüchner;János Sztrik;Hermann de Meer

  • Affiliations:

  • Faculty of Informatics and Mathematics, University of Passau, Innstraíe 43, 94032 Passau, Bavaria, Germany;Faculty of Informatics, University of Debrecen, Egyetem tér 1, P.O. Box 12, 4010 Debrecen, Hungary;Faculty of Informatics and Mathematics, University of Passau, Innstraíe 43, 94032 Passau, Bavaria, Germany

  • Venue:
  • Computer Networks: The International Journal of Computer and Telecommunications Networking
  • Year:
  • 2009

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Abstract

The present paper deals with a generalization of the homogeneous multi-server finite-source retrial queue with search for customers in the orbit. The novelty of the investigation is the introduction of balking and impatience for requests who arrive at the service facility with a limited capacity and FIFO queue. Arriving customers may balk, i.e., they either join the queue or go to the orbit. Moreover, the requests are impatient and abandon the buffer after a random time and enter the orbit, too. In case of an empty buffer, each server searches for a customer in the orbit after finishing service. All random variables involved in the model construction are supposed to be exponentially distributed and independent of each other. The primary aim of this analysis is to show the effect of balking, impatience, and buffer size on the steady-state performance measures. Concentrating on the mean response time, several numerical examples are investigated by the help of the MOSEL-2 tool used for creating the model and calculating the stationary characteristics.