Statistical group testing with queueing involved

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