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Numerical investigation of a multiserver retrial model

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Abstract

We consider a queueing model in which customers arrive in a Poisson stream to be served by one ofc servers. Each arriving customer enters a pool of active customers and starts generating requests for service at exponentially distributed time intervals at rate σ until he finds a free server and begins service. An analytical solution of this model is difficult and does not lend itself to numerical implementation. In this paper, we make a simplifying approximation, based on understanding of the physical behavior of the system, which yields an infinitesimal generator with a modified matrix-geometric equilibrium probability vector. That vector can be very efficiently computed even for high congestion levels. Illustrative numerical examples demonstrate the effectiveness of the approximation as well as the effect of the retrial rate on the system behavior for various levels of congestion. This study shows how numerical results for analytically intractable systems can be obtained by combining intuition with efficient algorithmic methods.

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Authors and Affiliations

  1. Department of Systems and Industrial Engineering, University of Arizona, 85721, Tucson, Arizona, USA

    Marcel F. Neuts

  2. Department of Applied Statistics and Operations Research, Bowling Green State University, 43403, Bowling Green, Ohio, USA

    B. M. Rao

Authors
  1. Marcel F. Neuts
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  2. B. M. Rao
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Additional information

This author's research was supported in part by Grants Nos. ECS-88-03061 from the National Science Foundation and AFOSR-88-0076 from the Air Force Office of Scientific Research.

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Neuts, M.F., Rao, B.M. Numerical investigation of a multiserver retrial model. Queueing Syst 7, 169–189 (1990). https://doi.org/10.1007/BF01158473

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  • DOI: https://doi.org/10.1007/BF01158473

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