A Multiserver Queueing System with Impatient Customers

Boots, Nam Kyoo; Tijms, Henk

doi:10.1287/mnsc.45.3.444

Cited by 57 publications

(39 citation statements)

References 4 publications

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“…Queuing models in which an arriving customer is lost when it waits more than a fixed time in queue have been studied by Tijms (1999), andWhitt (1999). Note that sewer-imposed deadlines are a control device that may improve certain measures of system performance.…”

Section: Successful Accomplishment Probability For Tasks With Deadlinesmentioning

confidence: 99%

Servicing Impatient Tasks That Have Uncertain Outcomes

Gaver¹,

Jacobs²

1999

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Section: Successful Accomplishment Probability For Tasks With Deadlinesmentioning

confidence: 99%

Servicing Impatient Tasks That Have Uncertain Outcomes

Gaver¹,

Jacobs²

1999

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“…An important line of research aims at characterizing the performance and impact of abandonments in systems, we refer to [15,8,14,24,26,2] for single-server models and [13,12,33] for papers dealing with the multi-class case. We also refer to [19] for a recent survey on abandonments in a many-server system.…”

Section: Introductionmentioning

confidence: 99%

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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“…The intuition behind the proof is reminiscent of many papers dealing with traditional (i.e. non-fluid) finite-capacity systems, such as those in Boots & Tijms [3,4]' Gouweleeuw & Tijms [11], Hooghiemstra [12] and Keilson & Servi [13,14]. Our approach can also be applied to the finite-buffer equivalents of the networks considered in [17]- [19].…”

Section: Introductionmentioning

confidence: 99%

A Tandem Fluid Queue With Gradual Input

Scheinhardt

Zwart

2002

Prob. Eng. Inf. Sci.

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For a two-node tandem fluid model with gradual input, we compute the joint steadystate buffer-content distribution. Our proof exploits martingale methods developed by Kella & Whitt [16]. For the case of finite buffers, we use an insightful sample-path argument to extend the proportionality result of Zwart [27] to the network case.2000 Mathematics subject classification: 60K25 (primary), 90B22 (secondary).

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A Multiserver Queueing System with Impatient Customers

Cited by 57 publications

References 4 publications

Servicing Impatient Tasks That Have Uncertain Outcomes

Servicing Impatient Tasks That Have Uncertain Outcomes

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

A Tandem Fluid Queue With Gradual Input

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