Applications of bulk queues to group testing models with incomplete identification

Shaul K. Bar-Lev, Mahmut Parlar, David Perry, Wolfgang Stadje, Frank A. Van der Duyn Schouten

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)226-237
Number of pages12
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - 16 Nov 2007


  • Applied probability
  • Quality control
  • Queueing

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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