Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-10T10:08:13.240Z Has data issue: false hasContentIssue false
  • English
  • Français

ANALYSIS AND OPTIMIZATION OF BLOOD-TESTING PROCEDURES

Published online by Cambridge University Press:  05 May 2017

Shaul K. Bar-Lev ,
Onno Boxma ,
David Perry  and
Lazaros P. Vastazos
Shaul K. Bar-Lev
Affiliation:
Department of Statistics, Haifa University, Haifa, Israel E-mail: barlev@stat.haifa.ac.il
Onno Boxma
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands E-mail: o.j.boxma@tue.nl
David Perry
Affiliation:
Department of Statistics, Haifa University, Haifa, Israel E-mail: dperry@stat.haifa.ac.il
Lazaros P. Vastazos
Affiliation:
Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands E-mail: l.p.vastazos@hotmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is devoted to the performance analysis and optimization of blood testing procedures. We present a queueing model of two queues in series, representing the two stages of a blood-testing procedure. Service (testing) in stage 1 is performed in batches, whereas it is done individually in stage 2. Since particular elements of blood can only be stored and used within a finite time window, the sojourn time of blood units in the system of two queues in series is an important performance measure, which we study in detail. We also introduce a profit objective function, taking into account blood acquisition and screening costs as well as profits for blood units, which were found uncontaminated and were tested fast enough. We optimize that profit objective function w.r.t. the batch size and the length of the time window.

Keywords

blood testing modelfeedback queuequeues in seriessojourn time distribution
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 3 , July 2017 , pp. 330 - 344
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Bagchi, T.P. & Templeton, J.G.C. (1972). Numerical methods in Markov chains and bulk queues. Berlin: Springer-Verlag.CrossRefGoogle Scholar
2. Bar-Lev, S.K., Boxma, O.J., Perry, D., & Vastazos, L.P. (2015). Analysis and optimization of blood testing procedures. Eurandom Report 2015–2016.Google Scholar
3. van den Berg, J.L. & Boxma, O.J. (1991). The M/G/1 queue with processor sharing and its relation to a feedback queue. Queueing Systems 9: 365–402.CrossRefGoogle Scholar
4. Burke, P.J. (1968). The output process of a stationary M/M/s queueing system. Annals of Mathematical Statistics 39: 1144–1152.CrossRefGoogle Scholar
5. Chiavetta, J.A., Escobar, M., Newman, A.M., He, Y., Driezen, P., Deeks, S., Hone, D.E., O'Brien, S.F., & Sher, G. (2003). Incidence and estimated rates of residual risk for HIV, hepatitis C, hepatitis B and human T-cell lymphotropic viruses in blood donors in Canada, 1990–2000. Canadian Medical Association Journal 169: 767–773.Google ScholarPubMed
6. Cromie, M.V., Chaudry, M.L., & Grassmann, W.K. (1979). Further results for the queueing system M X |M|c . Journal of the Operational Research Society 40: 755–763.Google Scholar
7. Eikeboom, A.M. & Tijms, H.C. (1987). Waiting-time percentiles in the multi-server M X |G|c queue with batch arrivals. Probability in the Engineering and Informational Sciences 1: 75–96.CrossRefGoogle Scholar
8. Ghandforoush, P. & Sen, T.K. (2010). A DSS to manage platelet production supply chain for regional blood centers. Decision Support Systems 50: 32–42.CrossRefGoogle Scholar
9. Harchol-Balter, M. (2013). Performance modeling and design of computer systems. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
10. Haviv, M. (2013). Queues. Berlin: Springer-Verlag.CrossRefGoogle Scholar
11. Hourfar, M.K., Jork, C., Schottstedt, V., Weber-Schehl, M., Brixner, V., Busch, M.P., Geusendam, G., Gubbe, K., Mahnhardt, C., Mayr-Wohlfart, U., Pichl, L., Roth, W.K., Schmidt, M., Seifried, E., & Wright, D.J. (2008). Experience of German Red Cross blood donor services with nucleic acid testing: results of screening more than 30 million blood donations for human immunodeficiency virus-1, hepatitis C virus, and hepatitis B virus. Transfusion 48(8): 1558–1566.CrossRefGoogle ScholarPubMed
12. Jackson, B.R., Busch, M.P., Stramer, S.L., & AuBuchon, J.P. (2003). The cost-effectiveness of NAT for HIV, HCV, and HBV in whole-blood donations. Transfusion 43: 721–729.CrossRefGoogle ScholarPubMed
13. Marshall, D.A., Kleinman, S.H., Wong, J.B., AuBuchon, J.P., Grima, D.T., Kulin, N.A., & Weinstein, M.C. (2004). Cost-effectiveness of nucleic acid test screening of volunteer blood donations for hepatitis B, hepatitis C and human immunodeficiency virus in the United States. Vox Sanguinis 86: 28–40.CrossRefGoogle ScholarPubMed
14. Schottstedt, V., Tuma, W., Bünger, G., & Lefèvre, H. (1998). PCR for HCV and HIV-1 experiences and first results from routine screening programme in a large blood transfusion service. Biologicals 26: 101–104.CrossRefGoogle Scholar
15. Stramer, S.L., Glynn, S.A., Kleinman, S.H., Strong, D.M., Caglioti, S., Wright, D.J., Dodd, R.Y., & Busch, M.P. (2004). Detection of HIV-1 and HCV infections among antibody-negative blood donors by nucleic acid-amplification testing. The New England Journal of Medicine 351(8): 760–768.CrossRefGoogle ScholarPubMed
16. Stramer, S.L., Wend, U., Candotti, D., Foster, G.A., Hollinger, F.B., Dodd, R.Y., Allain, J.-P., & Gerlich, W. (2011). Nucleic acid testing to detect HBV infection in blood donors. New England Journal of Medicine 364: 236–247.CrossRefGoogle ScholarPubMed
17. Tijms, H.C. (1994). Stochastic models – an algorithmic approach. New York: Wiley.Google Scholar
18. Vastazos, L.P. (2014). Queueing models in blood testing procedures. MSc Thesis, Eindhoven University of Technology, Eindhoven, The Netherlands.Google Scholar