Multiserver Queues with Impatient Customers

Boxma, Onno; Waal, Peter R. de

doi:10.1016/b978-0-444-82031-0.50079-2

Cited by 51 publications

(39 citation statements)

References 10 publications

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“…More recently, Boxma and de Waal (1994) studied the M/M/c queue with generally distributed impatience times, while Altman and Borovkov (1997) investigated the stability issue in a retrial queue with impatient customers. In all the aforementioned works, customers become impatient due to the long waiting time already experienced, although the server provides continuously service.…”

Section: Introductionmentioning

confidence: 99%

Synchronized reneging in queueing systems with vacations

2009

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In this paper we present a detailed analysis of queueing models with vacations and impatient customers, where the source of impatience is the absence of the server. Instead of the standard assumption that customers perform independent abandonments, we consider situations where customers abandon the system simultaneously. This is, for example, the case in remote systems where customers may decide to abandon the system, when a transport facility becomes available.

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Section: Introductionmentioning

confidence: 99%

Synchronized reneging in queueing systems with vacations

2009

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“…They devoted the analysis to characterization of waiting times in the system. Boxma and de Waal (1994) studied the M/M/c queue with generally distributed impatience times, developed several approximations for the abandonment probability and tested them via simulation. Altman and Borovkov (1997) considered impatience of customers in a retrial queue, in which a customer leaves the system if its commulative sojourn time exceeds some random threshold; impatience is shown to have an important impact on the system stability.…”

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confidence: 99%

Analysis of customers’ impatience in queues with server vacations

2006

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Many models for customers impatience in queueing systems have been studied in the past; the source of impatience has always been taken to be either a long wait already experienced at a queue, or a long wait anticipated by a customer upon arrival. In this paper we consider systems with servers vacations where customers' impatience is due to an absentee of servers upon arrival. Such a model, representing frequent behavior by waiting customers in service systems, has never been treated before in the literature. We present a comprehensive analysis of the single-server, M/M/1 and M/G/1 queues, as well as of the multi-server M/M/c queue, for both the multiple and the single-vacation cases, and obtain various closed-form results. In particular, we show that the proportion of customer abandonments under the single-vacation regime is smaller than that under the multiple-vacation discipline. Keywords

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“…General impatience times are analyzed in the context of telecommunication systems in Boxma and de Waal [7]. Focusing on exponential abandonment times Akşin and Harker [2] and Garnett et al [13] treat impatience within specific call center applications.…”

Section: Literature Reviewmentioning

confidence: 99%

The impact of retrials on call center performance

et al. 2004

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This paper models a call center as a Markovian queue with multiple servers, where customer balking, impatience, and retrials are modeled explicitly. The resulting queue is analyzed both in a stationary and non-stationary setting. For the stationary setting a fluid approximation is proposed, which overcomes the computational burden of the continuous time markov chain analysis, and which is shown to provide an accurate representation of the system for large call centers with high system load. An insensitivity property of the retrial rate to key system parameters is established. The fluid approximation is shown to work equally well for the nonstationary setting with time varying arrival rates. Using the fluid approximation, the paper explores the retrial phenomenon for a real call center. The model is used to estimate the real arrival rates based on demand data where retrials cannot be distinguished from first time calls. This is a common problem encountered in call centers. Through numerical examples, it is shown that disregarding the retrial phenomenon in call centers can lead to huge distortions in subsequent forecasting and staffing analysis.

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Multiserver Queues with Impatient Customers

Cited by 51 publications

References 10 publications

Synchronized reneging in queueing systems with vacations

Synchronized reneging in queueing systems with vacations

Analysis of customers’ impatience in queues with server vacations

The impact of retrials on call center performance

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