Tandem Queues with Impatient Customers for Blood Screening Procedures

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. 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.

Block-accelerated aggregation multigrid for Markov chains with application to PageRank problems

“…In the next example, we consider several Markov chains that come from tandem queuing networks [1] . Tandem queuing networks have been applied in wireless networks [30] and blood screening procedures [5] . For each tandem queuing network, there are two finite queues with single-servers, customers arrive according to a Poisson distribution with rate μ, and the service time distributions at the two single-server stations are Poisson with rates μ 1 and μ 2 , respectively [7] .…”

“…Markov chains have been applied in many areas, including performance modelling of communication systems [1] , Web page ranking [2,3] and gene ranking [4] , blood screening procedures [5] , etc. In this study, we are concerned with computing stationary distributions of homogeneous irreducible Markov chains.…”

A Cost-Effective Smoothed Multigrid with Modified Neighborhood-Based Aggregation for Markov Chains

“…Tandem queuing network exists in some practical applications, for example, in wireless networks [25] and blood screening procedures [26]. Following the settings and description in [17], we consider the situation that there are two finite queues with single servers, customers arrive according to a Poisson distribution with rate , and the service time distribution at the two single-server stations is Poisson with rates 1 and 2 .…”

Staffing Tandem Queues with Impatient Customers Application in Financial Service Operations

“…Tandem queueing networks, where customers need to visit several stations in sequence, abound in the modern economy. Examples range from call centers, where customers talk to general call-takers before being transferred to specialists (see, e.g., Gans et al 2003), to hospital emergency rooms, where patients are admitted by triage nurses before going on to have a number of medical tests and procedures (see, e.g., Zayas-Cabán et al 2013), to cost-efficient blood screenings, where a less sensitive but inexpensive test is conducted before a more sensitive and expensive one (see, e.g., Bar-Lev et al 2013). In these applications, abandonment (i.e., leaving the queue before or while being served) is an important phenomenon.…”