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Statistical group testing with queueing involved

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Abstract

We consider a queueing model in which items wait to undergo group testing in batches of sizem. However, if fewer thanm items are present at the beginning of a service, items are tested singly. Ifm or more items are waiting at such an epoch, a group of sizem is tested and, if the group passes the test, allm items leave the system. When a group is found to contain at least one defective item, them items in it are retested individually. An algorithm is developed to compute many steady-state probabilities related to this queue. Comparisons of these probabilities are used to assess the effect of the group sizem on the behavior of the queue of items waiting for testing.

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References

  1. M.F. Neuts, Moment formulas for the Markov renewal branching process, Adv. Appl. Prob. 8 (1976) 690–711.

    Google Scholar 

  2. M.F. Neuts, Queues solvable without Rouche's theorem, Opns. Res. 27 (1979) 767–781.

    Google Scholar 

  3. M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (The Johns Hopkins University Press, Baltimore, 1981).

    Google Scholar 

  4. C.C. Paige, G.P.H. Styan and P.T. Wachter, Computation of the stationary distribution of a Markov chain, J. Statist. Comput. Simul. 4 (1975) 173–186.

    Google Scholar 

  5. V. Ramaswami, Nonlinear matrix equations in applied probability: solution techniques and open problems, Manuscript, Bell Communications Research, Morris Township, New Jersey, 1986.

    Google Scholar 

  6. M. Sobel and P.A. Groll, Group testing to eliminate efficiently all defectives in a binomial sample, Bell Syst. Tech. J. 38 (1959) 1179–1224.

    Google Scholar 

  7. G.S. Watson, A study of the group screening method, Technometrics 3 (1961) 371–388.

    Google Scholar 

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Authors and Affiliations

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

    Marcel F. Neuts & Y. Chandramouli

Authors
  1. Marcel F. Neuts
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  2. Y. Chandramouli
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Additional information

This research was supported in part by Grant Nr. ECS-8601203 from the National Science Foundation.

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Neuts, M.F., Chandramouli, Y. Statistical group testing with queueing involved. Queueing Syst 2, 19–39 (1987). https://doi.org/10.1007/BF01182932

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  • DOI: https://doi.org/10.1007/BF01182932

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