Tandem queues with impatient customers for blood screening procedures

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 theM=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

Multi-Queue Request Scheduling for Profit Maximization in IaaS Clouds

[EN] In cloud computing, service providers rent heterogeneous servers from cloud providers, i.e., Infrastructure as a Service (IaaS), to meet requests of consumers. The heterogeneity of servers and impatience of consumers pose great challenges to service providers for profit maximization. In this article, we transform this problem into a multi-queue model where the optimal expected response time of each queue is theoretically analyzed. A multi-queue request scheduling algorithm framework is proposed to maximize the total profit of service providers, which consists of three components: request stream splitting, requests allocation, and server assignment. A request stream splitting algorithm is designed to split the arriving requests to minimize the response time in the multi-queue system. An allocation algorithm, which adopts a one-step improvement strategy, is developed to further optimize the response time of the requests. Furthermore, an algorithm is developed to determine the appropriate number of required servers of each queue. After statistically calibrating parameters and algorithm components over a comprehensive set of random instances, the proposed algorithms are compared with the state-of-the-art over both simulated and real-world instances. The results indicate that the proposed multi-queue request scheduling algorithm outperforms the other algorithms with acceptable computational time.This work was supported in part by the National Key Research and Development Program of China under Grant 2017YFB1400800, in part by the National Natural Science Foundation of China under Grants 61872077 and 61832004, and in part by the Collaborative InnovationCenter of Wireless Communications Technology. The work of Quan Z. Sheng was supported in part by Australian Research Council Future Fellowship under Grant FT140101247 and in part by Discovery Project under Grant DP180102378. The work of Ruben Ruiz was supported in part by the Spanish Ministry of Science, Innovation, and Universities through the project OPTEP-Port Terminal Operations Optimization under Grant RTI2018-094940-B-I00 financed with FEDER fundsWang, S.; Li, X.; Sheng, QZ.; Ruiz García, R.; Zhang, J.; Beheshti, A. (2021). Multi-Queue Request Scheduling for Profit Maximization in IaaS Clouds. IEEE Transactions on Parallel and Distributed Systems. 32(11):2838-2851. https://doi.org/10.1109/TPDS.2021.3075254S28382851321

Developing effective service policies for multiclass queues with abandonment:asymptotic optimality and approximate policy improvement

We study a single server queuing model with multiple classes and impatient customers. The goal is to determine a service policy to maximize the long-run reward rate earned from serving customers net of holding costs and penalties respectively due to customers waiting for and leaving before receiving service. We first show that it is without loss of generality to study a pure-reward model. Since standard methods can usually only compute the optimal policy for problems with up to three customer classes, our focus is to develop a suite of heuristic approaches, with a preference for operationally simple policies with good reward characteristics. One such heuristic is the Rμθ rule—a priority policy that ranks all customer classes based on the product of reward R, service rate μ, and abandonment rate θ. We show that the Rμθ rule is asymptotically optimal as customer abandonment rates approach zero and often performs well in cases where the simpler Rμ rule performs poorly. The paper also develops an approximate policy improvement method that uses simulation and interpolation to estimate the bias function for use in a dynamic programming recursion. For systems with two or three customer classes, our numerical study indicates that the best of our simple priority policies is near optimal in most cases; when it is not, the approximate policy improvement method invariably tightens up the gap substantially. For systems with five customer classes, our heuristics typically achieve within 4% of an upper bound for the optimal value, which is computed via a linear program that relies on a relaxation of the original system. The computational requirement of the approximate policy improvement method grows rapidly when the number of customer classes or the traffic intensity increases