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Tandem Queues with Impatient Customers for Blood Screening Procedures

Author

Listed:
  • Shaul K. Bar-Lev

    (University of Haifa)

  • Hans Blanc

    (Tilburg University)

  • Onno Boxma

    (Eindhoven University of Technology)

  • Guido Janssen

    (Eindhoven University of Technology)

  • David Perry

    (University of Haifa)

Abstract

We study a blood testing procedure for detecting viruses like HIV, HBV and HCV. In this procedure, blood samples go through two screening steps. The first test is ELISA (antibody Enzyme Linked Immuno-Sorbent Assay). The portions of blood which are found not contaminated in this first phase are tested in groups through PCR (Polymerase Chain Reaction). The ELISA test is less sensitive than the PCR test and the PCR tests are considerably more expensive. We model the two test phases of blood samples as services in two queues in series; service in the second queue is in batches, as PCR tests are done in groups. The fact that blood can only be used for transfusions until a certain expiration date leads, in the tandem queue, to the feature of customer impatience. Since the first queue basically is an infinite server queue, we mainly focus on the second queue, which in its most general form is an S-server M/G [k, K]/S + G queue, with batches of sizes which are bounded by k and K. Our objective is to maximize the expected profit of the system, which is composed of the amount earned for items which pass the test (and before their patience runs out), minus costs. This is done by an appropriate choice of the decision variables, namely, the batch sizes and the number of servers at the second service station. As will be seen, even the simplest version of the batch queue, the M/M [k, K]/1 + M queue, already gives rise to serious analytical complications for any batch size larger than 1. These complications are discussed in detail, and handled for K = 2. In view of the fact that we aim to solve realistic optimization problems for blood screening procedures, these analytical complications force us to take recourse to either a numerical approach or approximations. We present a numerical solution for the queue length distribution in the M/M [k, K]/S + M queue and then formulate and solve several optimization problems. The power-series algorithm, which is a numerical-analytic method, is also discussed.

Suggested Citation

  • Shaul K. Bar-Lev & Hans Blanc & Onno Boxma & Guido Janssen & David Perry, 2013. "Tandem Queues with Impatient Customers for Blood Screening Procedures," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 423-451, June.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:2:d:10.1007_s11009-011-9250-y
    DOI: 10.1007/s11009-011-9250-y
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    Cited by:

    1. Bar-Lev, Shaul K. & Boxma, Onno & Kleiner, Igor & Perry, David & Stadje, Wolfgang, 2017. "Recycled incomplete identification procedures for blood screening," European Journal of Operational Research, Elsevier, vol. 259(1), pages 330-343.
    2. Antonio Di Crescenzo & Barbara Martinucci & Paola Paraggio, 2023. "Vessels Arrival Process and its Application to the SHIP/M/ $$\infty$$ ∞ Queue," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-33, March.

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