Applications of bulk queues to group testing models with incomplete identification |
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Authors: | Shaul K. Bar-Lev Mahmut Parlar David Perry Wolfgang Stadje Frank A. Van der Duyn Schouten |
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Affiliation: | 1. Department of Statistics, University of Haifa, Haifa 31905, Israel;2. DeGroote School of Business, McMaster University, Hamilton, Ont., Canada L8S 4M4;3. Department of Statistics, University of Haifa, Haifa, 31905, Israel;4. Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany;5. Center for Economic Research, Tilburg University, 5000 LE Tilburg, The Netherlands |
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Abstract: | A population of items is said to be “group-testable”, (i) if the items can be classified as “good” and “bad”, and (ii) if it is possible to carry out a simultaneous test on a batch of items with two possible outcomes: “Success” (indicating that all items in the batch are good) or “failure” (indicating a contaminated batch). In this paper, we assume that the items to be tested arrive at the group-testing centre according to a Poisson process and are served (i.e., group-tested) in batches by one server. The service time distribution is general but it depends on the batch size being tested. These assumptions give rise to the bulk queueing model M/G(m,M)/1, where m and M(>m) are the decision variables where each batch size can be between m and M. We develop the generating function for the steady-state probabilities of the embedded Markov chain. We then consider a more realistic finite state version of the problem where the testing centre has a finite capacity and present an expected profit objective function. We compute the optimal values of the decision variables (m, M) that maximize the expected profit. For a special case of the problem, we determine the optimal decision explicitly in terms of the Lambert function. |
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Keywords: | Applied probability Queueing Quality control |
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