Browse > Article
http://dx.doi.org/10.11627/jksie.2022.45.4.053

Analysis of a Queueing Model with a Two-stage Group-testing Policy  

Won Seok Yang (Department of Business Administration, Hannam University)
Publication Information
Journal of Korean Society of Industrial and Systems Engineering / v.45, no.4, 2022 , pp. 53-60 More about this Journal
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.
Keywords
Group Testing; Queueing Model; Bulk Service; Waiting Time; COVID-19;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Abdalhamid, B., Bilder, C.R., McCutchen, E.L., Hinrichs, S.H., Koepsell, S.A., and Iwen, P.C., Assessment of specimen pooling to conserve SARS CoV-2 testing resources, American Journal of Clinical Pathology, 2020, Vol. 153, No. 6, pp. 715-718.    DOI
2 Abolnikov, L. and Dukhovny, A., Optimization in HIV screening problems, Journal of Applied Mathematics and Stochastic Analysis, 2003, Vol. 16, No. 4, pp. 361-374.    DOI
3 Bar-Lev, S.K., Parlar, M., Perry, D., Stadje, W., and Van der Duyn Schouten, F.A., Applications of bulk queues to group testing models with incomplete identification, European Journal of Operational Research, 2007, Vol. 183, No. 1, pp. 226-237.    DOI
4 Berger, T., Mehravari, N., Towsley, D., and Wolf, J., Random multiple-access communication and group testing, IEEE Transactions on Communications, 1984, Vol. 32, No. 7, pp. 769-779.    DOI
5 Chaudhry, M.L. and Templeton, J.G., First Course in Bulk Queues, John Wiley & Sons, 1983. 
6 Dorfman, R., The Detection of Defective Members of Large Populations, The Annals of Mathematical Statistics, 1943, Vol. 14, No. 4, pp. 436-440.    DOI
7 Du, D., Hwang, F.K., and Hwang, F., Combinatorial Group Testing and Its Applications (Vol. 12), World Scientific, 2000. 
8 Garg, J., Singh, V., Pandey, P., Verma, A., Sen, M., Das, A., and Agarwal, J., Evaluation of sample pooling for diagnosis of COVID-19 by Real Time-PCR: A Resource-Saving Combat Strategy, Journal of Medical Virology, 2021, Vol. 93, No. 3, pp. 1526-1531.    DOI
9 Giffin, W.C., Transform Techniques for Probability Modeling, Academic Press, 1975. 
10 Kim, K., The Analysis of COVID-19 Pooled-testing Systems with False Negatives Using a Queueing Model, Journal of the Society of Korea Industrial and Systems Engineering, 2021, Vol. 44, No. 4, pp. 154-168.    DOI
11 Lee, H.W., Lee, S.S., and Chae, K.C., A Fixed-size Batch Service Queue with Vacations, Journal of Applied Mathematics and Stochastic Analysis, 1996, Vol. 9, No. 2, pp. 205-219.    DOI
12 Lee, H.W., Queueing theory, third edition, Sigmapress, 2006. 
13 Seong, J.-T., Group testing scheme for effective diagnosis of COVID-19, The Journal of Korea Institute of Information, Electronics, and Communication Technology, 2021, Vol. 14, No. 6, pp. 445-451.    DOI
14 Seong, J.-T., Performance Analysis of Noisy Group Testing for Diagnosis of COVID-19 infection, The Journal of Korea Institute of Information, 2022, Vol. 15, No. 2, pp. 117-123. 
15 Sobel, M. and Groll, P.A., Binomial Group-testing with an Unknown Proportion of Defectives, Technometrics, 1966, Vol. 8, No. 4, pp. 631-656.    DOI
16 Wolff, R.W., Stochastic Modeling and the Theory of Queues, New Jersey: Prentice Hall, 1989. 
17 Yang, W.S. and Chae, K.C., An efficient blood testing procedure by using group testing, The Korean Journal of Applied Statistics, 1996, Vol. 9, No. 1, pp. 17-29. 
18 Yang, W.S. and Chae, K.C., A Heuristic Approach for Efficient blood testing: The Case of Unknown Prevalence Rate, The Korean Journal of Applied Statistics, 1997, Vol. 10, No. 1, pp. 47-60.