Scheduling Impatient Jobs in a Clearing System With Insights on Patient Triage in Mass Casualty Incidents

Argon, Nilay Tanık; Ziya, Serhan; Righter, Rhonda

doi:10.1017/s0269964808000272

Cited by 67 publications

(79 citation statements)

References 37 publications

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“…In patient triage applications, abandonments have been used to model medical emergency patients in danger of dying while awaiting treatment. See, for example, Argon et al (2008) and Li and Glazebrook (2010).…”

Section: Introductionmentioning

confidence: 99%

Developing Effective Service Policies for Multiclass Queues with Abandonment: Asymptotic Optimality and Approximate Policy Improvement

James

Glazebrook

Lin

2016

INFORMS Journal on Computing

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Developing effective service policies for multiclass queues with abandonment: asymptotic optimality and approximate policy improvemen James, Terry Informs T. James, K. Glazebrook, K. Lin, "Developing effective service policies for multiclass queues with abandonment: asymptotic optimality and approximate policy improvement," INFORMS Journals on Computing, v.28, no.2 (Spring 2016) e 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 Råà rule-a priority policy that ranks all customer classes based on the product of reward R, service rate å, and abandonment rate à. We show that the Råà rule is asymptotically optimal as customer abandonment rates approach zero and often performs well in cases where the simpler Rå 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.

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Section: Introductionmentioning

confidence: 99%

Developing Effective Service Policies for Multiclass Queues with Abandonment: Asymptotic Optimality and Approximate Policy Improvement

James

Glazebrook

Lin

2016

INFORMS Journal on Computing

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“…We also refer to [19] for a recent survey on abandonments in a many-server system. More related to our present work are the papers that deal with optimal scheduling or control aspects of multi-class queueing systems in the presence of abandonments, see for instance [23,5,25,1,3,20,4,7].…”

Section: Introductionmentioning

confidence: 99%

“…In order to prove the result, the authors use a continuous-time formulation of a Markov decision process (instead of the discrete-time equivalent) in addition to a truncation argument. In the case of no arrivals and non-preemptive service, the authors of [1] provide partial characterizations of the optimal policy and show that an optimal policy is typically state dependent. It is worthwhile to mention that [1] is inspired by a patient triage problem which illustrates that abandonments are as well an important issue in other areas than information technology.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of no arrivals and non-preemptive service, the authors of [1] provide partial characterizations of the optimal policy and show that an optimal policy is typically state dependent. It is worthwhile to mention that [1] is inspired by a patient triage problem which illustrates that abandonments are as well an important issue in other areas than information technology. As far as the authors are aware, the above two settings are the only ones for which structural optimality results have been obtained.…”

Section: Introductionmentioning

confidence: 99%

“…As far as the authors are aware, the above two settings are the only ones for which structural optimality results have been obtained. State-dependent heuristics for the multi-class queue are proposed in [1] for two classes and no arrivals and in [23] for an arbitrary number of classes including new arrivals.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamic fluid-based scheduling in a multi-class abandonment queue

Larrañaga

Ayesta

Verloop

2013

Performance Evaluation

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We investigate how to share a common resource among multiple classes of customers in the presence of abandonments. We consider two different models: (1) customers can abandon both while waiting in the queue and while being served, (2) only customers that are in the queue can abandon. Given the complexity of the stochastic optimization problem we propose a fluid model as a deterministic approximation. For the overload case we directly obtain that thecµ/θ rule is optimal. For the underload case we use Pontryagin's Maximum Principle to obtain the optimal solution for two classes of customers; there exists a switching curve that splits the two-dimensional state-space into two regions such that when the number of customers in both classes is sufficiently small the optimal policy follows thecµ-rule and when the number of customers is sufficiently large the optimal policy follows thecµ/θ-rule. The same structure is observed numerically in the optimal policy of the stochastic model for an arbitrary number of classes. Based on this we develop a heuristic and by numerical experiments we evaluate its performance and compare it to several index policies. We observe that the suboptimality gap of our solution is small.

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Triage in the Aftermath of Mass‐Casualty Incidents

Argon

Ziya

Winslow

2011

Wiley Encyclopedia of Operations Research and Management Science

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Mass‐casualty incidents, such as plane crashes and terrorist attacks, take place rarely but when they happen they may result in a massive number of casualties with severe injuries requiring immediate medical attention. In the aftermath of such an event, medical resources are typically overwhelmed by the sudden jump in demand and hence they need to be rationed in some way to minimize the number of deaths and permanent injuries. This rationing process that determines the priorities according to which patients are given access to the limited resources is called triage . This chapter provides a review of the operations research literature on patient triage and prioritization decisions in the aftermath of mass‐casualty incidents. In the literature, there are two lines of research that take two different approaches to the problem but with similar conclusions. The most important conclusion is that mass‐casualty triage systems should take into account the number of casualties and the capacity of resources to save the maximum number of lives possible. Furthermore, an effective rule that categorizes the patients based on their service requirements, chances of survival, and patterns of health deterioration is essential for the success of the emergency response effort.

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Scheduling Impatient Jobs in a Clearing System With Insights on Patient Triage in Mass Casualty Incidents

Cited by 67 publications

References 37 publications

Developing Effective Service Policies for Multiclass Queues with Abandonment: Asymptotic Optimality and Approximate Policy Improvement

Developing Effective Service Policies for Multiclass Queues with Abandonment: Asymptotic Optimality and Approximate Policy Improvement

Dynamic fluid-based scheduling in a multi-class abandonment queue

Triage in the Aftermath of Mass‐Casualty Incidents

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