A New Look at Organ Transplantation Models and Double Matching Queues

Boxma, OJ Onno; David, Israel; Perry, David; Stadje, Wolfgang

doi:10.1017/s0269964810000318

Cited by 47 publications

(42 citation statements)

References 27 publications

(51 reference statements)

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“…Such t (m) exists either when the initial queue length is nonzero, or there exists a time interval where λ p (t) = λ d (t). If such t (m) does not exist, then we must have zero initial queue length and λ p (t) = λ d (t) for t ∈ [0, T ], which indicates that the expected queue length E(Q(t)) in (7) and the fluid queue length q(t) in (9) are both zero in [0, T ]. Theorem 3.2 is trivial under this case.…”

Section: 2mentioning

confidence: 99%

“…Double-ended queues have been studied for many applications, including taxi-service systems, perishable inventory systems, organ transplant systems, and finance (cf. [14,1,36,32,7,13]). In particular, [14] studied a perishable inventory system with Poisson arrivals for both supplies and demands.…”

mentioning

confidence: 99%

“…Note that in general, E[Q + (s)] = (E[Q(t)]) + and E[Q − (s)] = (E[Q(t)]) − , and hence {E[Q(t)]; t ∈ [0, T ]} cannot be determined by (7). However, to develop a fluid model, we will replace E[Q(t)] by a deterministic q(t), E[Q + (s)] by q + (t), and E[Q − (s)] by q − (t) in(6) and(7), and derive the following deterministic control problem, which will be referred to as the fluid control problem (FCP) associated with M.…”

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confidence: 99%

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Optimal Control of a Time-Varying Double-Ended Production Queueing Model

Lee

Liu

et al. 2019

SSRN Journal

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Section: 2mentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Optimal Control of a Time-Varying Double-Ended Production Queueing Model

Lee

Liu

et al. 2019

SSRN Journal

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“…The present setting is reminiscent of an organ transplantation problem, where there is either a queue of persons waiting to receive an organ, or a queue of donor organs. The perishability/impatience aspect features there, too; Boxma et al (2011 setting is that of insurance risk. We refer to Albrecher and Lautscham (2013) who extend the classical Cramér-Lundberg insurance risk model by allowing the capital of an insurance company to become negative-a situation that is usually indicated by "ruin" in the insurance literature.…”

Section: Conclusion and Suggestions For Further Researchmentioning

confidence: 99%

A Blood Bank Model with Perishable Blood and Demand Impatience

Bar‐Lev

Boxma²,

Mathijsen³

et al. 2017

Stochastic Systems

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Full terms and conditions of use: http://pubsonline.informs.org/page/terms-and-conditionsThis article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact permissions@informs.org.The Publisher does not warrant or guarantee the article's accuracy, completeness, merchantability, fitness for a particular purpose, or non-infringement. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. Copyright © 2017, The Author(s) Please scroll down for article-it is on subsequent pagesINFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics. Abstract. We consider a stochastic model for a blood bank, in which amounts of blood are offered and demanded according to independent compound Poisson processes. Blood is perishable, i.e., blood can only be kept in storage for a limited amount of time. Furthermore, demand for blood is impatient, i.e., a demand for blood may be canceled if it cannot be satisfied soon enough. For a range of perishability functions and demand impatience functions, we derive the steady-state distributions of the amount of blood kept in storage, and of the amount of demand for blood (at any point in time, at most one of these quantities is positive). Under certain conditions we also obtain the fluid and diffusion limits of the blood inventory process, showing in particular that the diffusion limit process is an Ornstein-Uhlenbeck process.

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“…To our knowledge, this paper is the first to establish closed-form results for a double-sided queueing model with batch arrivals and abandonment. Previous work on double-sided queues has considered batch queues without abandonment (e.g., Kashyap 1966) and single-unit arrivals with abandonment (e.g., Zenios 1999, Boxma et al 2011. Further, we consider heterogeneous customers with type-and side dependent arrival rates, batch sizes, and abandonment behavior, previously not considered.…”

Section: Introductionmentioning

confidence: 99%

Double-Sided Batch Queues with Abandonment: Modeling Crossing Networks

Afèche

Diamant

Milner

2014

Operations Research

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We study a double-sided queue with batch arrivals and abandonment. There are two types of customers, patient ones who queue but may later abandon, and impatient ones who depart immediately if their order is not filled. The system matches units from opposite sides of the queue based on a first-come first-served policy. The model is particularly applicable to a class of alternative trading systems called crossing networks that are increasingly important in the operation of modern financial markets. We characterize, in closed form, the steady-state queue length distribution and the system-level average system time and fill rate. These appear to be the first closed-form results for a double-sided queuing model with batch arrivals and abandonment. For a customer who arrives to the system in steady state, we derive formulae for the expected fill rate and system time as a function of her order size and deadline. We compare these system-and customer-level results for our model that captures abandonment in aggregate, to simulation results for a system in which customers abandon after some random deadline. We find close correspondence between the predicted performance based on our analytical results and the performance observed in the simulation. Our model is particularly accurate in approximating the performance in systems with low fill rates, which are representative of crossing networks.

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A New Look at Organ Transplantation Models and Double Matching Queues

Cited by 47 publications

References 27 publications

Optimal Control of a Time-Varying Double-Ended Production Queueing Model

Optimal Control of a Time-Varying Double-Ended Production Queueing Model

A Blood Bank Model with Perishable Blood and Demand Impatience

Double-Sided Batch Queues with Abandonment: Modeling Crossing Networks

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