K competing queues with customer abandonment: optimality of a generalised $$c \mu $$-rule by the Smoothed Rate Truncation method

Bhulai, Sandjai; Blok, H.; Spieksma, Floske M.

doi:10.1007/s10479-019-03131-3

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…In terms of model solution, Bhulai [22] noted that the majority of studies analyzing multiple priority queues relied on Markov processes, with some improved algorithms applied to compute the sojourn probability of the system state. For example, Matthieu [23] estimated the system state sojourn probability by reducing the state dimension through customer type aggregation and server reduction.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers

Yin,

Yan,

Guo

et al. 2023

Mathematics

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This paper presents a queuing system model that incorporates multiple priorities, multiple abandonments, and heterogeneous servers. Waiting for service easily leads to impatient behaviors. The impact of two kinds of impatient behaviors, balking and reneging, on queueing system performance is examined. The problem is formulated as continuous-time Markov chains. It also introduces a special state called the non-sojourn state to record the number of customers who abandon the system. The state transition rate matrix is transformed into a block tridiagonal matrix by appropriately setting the state numbers. A novel indicator called interstate transition frequency is proposed, which aids in distinguishing state transitions during the system evaluation process. Based on the interstate transition frequency, a set of indicators is derived to offer additional analytical perspectives for the queuing system. Finally, the proposed model is applied to an automobile repair shop to validate its effectiveness in practical scenarios.

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Section: Introductionmentioning

confidence: 99%

Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers

Yin,

Yan,

Guo

et al. 2023

Mathematics

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Whittle index approach to multiserver scheduling with impatient customers and DHR service times

Aalto

2024

Queueing Syst

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We consider the optimal scheduling problem in a multiserver queue with impatient customers belonging to multiple classes. We assume that each customer has a random abandonment time, after which the customer leaves the system if its service has not been completed before that. In addition, we assume that the scheduler is not able to anticipate the expiration of the abandonment times but only knows their distributions and how long each customer has been in the system. Many papers consider this scheduling problem under Poisson arrivals and linear holding costs assuming further that both the service times and the abandonment times have exponential distributions. Even with these additional assumptions, the exact solution is known only in very few special cases. To tackle this tricky problem, we apply the Whittle index approach. Unlike the earlier papers, which were restricted to exponential service times, we allow the service time distributions for which the hazard rate is decreasing. The Whittle index approach is applied to the discrete-time multiserver queueing problem with discounted costs. As our main theoretical result, we prove that the related relaxed optimization problem is indexable and derive the corresponding Whittle index explicitly. Based on this discrete-time result, we develop a reasonable heuristic for the original continuous-time multiserver scheduling problem. The performance of the resulting policy is evaluated in the M/G/M setup by numerical simulations, which demonstrate that it, indeed, gives better performance than the other policies included in the comparison.

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Optimal control of admission in service in a queue with impatience and setup costs

Hyon

Jean-Marie

2020

Performance Evaluation

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We consider a single server queue in continuous time, in which customers must be served before some limit sojourn time of exponential distribution. A customer who is not served before this limit leaves the system: it is impatient. The fact of serving customers and the fact of losing them due to impatience induce costs. The fact of holding them in the queue also induces a constant cost per customer and per unit time. The purpose is to decide when to serve the customers so as to minimize costs. We use a Markov Decision Process with infinite horizon and discounted cost. Since the standard uniformization approach is not applicable here, we introduce a family of approximated uniformizable models, for which we establish the structural properties of the stochastic dynamic programming operator, and we deduce that the optimal policy is of threshold type. The threshold is computed explicitly. We then pass to the limit to show that this threshold policy is also optimal in the original model. A particular care is given to the completeness of the proof. We also illustrate the difficulties involved in the proof with numerical examples.

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K competing queues with customer abandonment: optimality of a generalised $$c \mu $$-rule by the Smoothed Rate Truncation method

Cited by 4 publications

References 14 publications

Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers

Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers

Whittle index approach to multiserver scheduling with impatient customers and DHR service times

Optimal control of admission in service in a queue with impatience and setup costs

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