Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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Analysis of a Queueing Model with a Two-stage Group-testing Policy

이단계 그룹검사를 갖는 대기행렬모형의 분석

  • Received : 2022.09.23
  • Accepted : 2022.11.23
  • Published : 2022.12.31
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Abstract

In a group-testing method, instead of testing a sample, for example, blood individually, a batch of samples are pooled and tested simultaneously. If the pooled test is positive (or defective), each sample is tested individually. However, if negative (or good), the test is terminated at one pooled test because all samples in the batch are negative. This paper considers a queueing system with a two-stage group-testing policy. Samples arrive at the system according to a Poisson process. The system has a single server which starts a two-stage group test in a batch whenever the number of samples in the system reaches exactly a predetermined size. In the first stage, samples are pooled and tested simultaneously. If the pooled test is negative, the test is terminated. However, if positive, the samples are divided into two equally sized subgroups and each subgroup is applied to a group test in the second stage, respectively. The server performs pooled tests and individual tests sequentially. The testing time of a sample and a batch follow general distributions, respectively. In this paper, we derive the steady-state probability generating function of the system size at an arbitrary time, applying a bulk queuing model. In addition, we present queuing performance metrics such as the offered load, output rate, allowable input rate, and mean waiting time. In numerical examples with various prevalence rates, we show that the second-stage group-testing system can be more efficient than a one-stage group-testing system or an individual-testing system in terms of the allowable input rates and the waiting time. The two-stage group-testing system considered in this paper is very simple, so it is expected to be applicable in the field of COVID-19.

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References

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