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Retrial Queues
01 Apr 1997-
About: The article was published on 1997-04-01 and is currently open access. It has received 612 citations till now. The article focuses on the topics: Retrial queue.
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TL;DR: This work begins with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations, which identifies important problems that have not been addressed and identifies promising directions for future research.
Abstract: Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value--and at the same time fundamentally limited--in their ability to characterize system performance.We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research.
1,415 citations
TL;DR: The present document is an abridged version of a survey that can be downloaded from www.cs.vu.nl/obp/callcenters and ie.technion.il/∼serveng.
Abstract: This is a survey of some academic research on telephone call centers. The surveyed research has its origin in, or is related to, queueing theory. Indeed, the “queueing-view” of call centers is both natural and useful. Accordingly, queueing models have served as prevalent standard support tools for call center management. However, the modern call center is a complex socio-technical system. It thus enjoys central features that challenge existing queueing theory to its limits, and beyond. The present document is an abridged version of a survey that can be downloaded from www.cs.vu.nl/obp/callcenters and ie.technion.ac.il/∼serveng.
354 citations
TL;DR: This paper gives a detailed analysis for reliability of retrial queues using the supplementary variables method and obtains explicit expressions of some main reliability indexes such as the availability, failure frequency and reliability function of the server.
Abstract: Retrial queues have been widely used to model many problems arising in telephone switching systems, telecommunication networks, computer networks and computer systems, etc. It is of basic importance to study reliability of retrial queues with server breakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns on the performance measure of the system. However, so far the repairable retrial queues are analyzed only by queueing theory. In this paper we give a detailed analysis for reliability of retrial queues. By using the supplementary variables method, we obtain the explicit expressions of some main reliability indexes such as the availability, failure frequency and reliability function of the server. In addition, some special queues, for instance, the repairable M/G/1 queue and repairable retrial queue can be derived from our results. These results may be generalized to the repairable multi-server retrial models.
188 citations
TL;DR: To limit the scope of this survey, it is decided to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.
Abstract: We have divided this review into two parts. The first part is concerned with the optimal design of queueing systems and the second part deals with the optimal control of queueing systems. The second part, which has the lion’s share of the review since it has received the most attention, focuses mainly on the modelling aspects of the problem and describes the different kinds of threshold (control) policy models available in the literature. To limit the scope of this survey, we decided to limit ourselves to research on papers dealing with the three policies (N, T, and D), where a cost function is designed specifically and optimal thresholds that yield minimum cost are sought.
159 citations
TL;DR: In this paper, the authors study the contracting issues in an outsourcing supply chain consisting of a user company and a call center that does outsourcing work for the user company, and propose two contracts that can coordinate both staffing and effort.
Abstract: In this paper, we study the contracting issues in an outsourcing supply chain consisting of a user company and a call center that does outsourcing work for the user company. We model the call center as a G/G/s queue with customer abandonment. Each call has a revenue potential, and we model the call center's service quality by the percentage of calls resolved (revenue realized). The call center makes two strategic decisions: how many agents to have and how much effort to exert to achieve service quality.
We are interested in the contracts the user company can use to induce the call center to both staff and exert effort at levels that are optimal for the outsourcing supply chain (i.e., chain coordination). Two commonly used contracts are analyzed first: piecemeal and pay-per-call-resolved contracts. We show that although they can coordinate the staffing level, the resulting service quality is below system optimum. Then, depending on the observability and contractibility of the call center's effort, we propose two contracts that can coordinate both staffing and effort. These contracts suggest that managers pay close attention to service quality and its contractibility in seeking call center outsourcing.
144 citations
References
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TL;DR: A survey of the main results and methods of the theory of retrial queues, concentrating on Markovian single and multi-channel systems, as well as models with batch arrivals, multiclasses, customer impatience, double connection, control devices, two-way communication and buffer.
Abstract: We present a survey of the main results and methods of the theory of retrial queues, concentrating on Markovian single and multi-channel systems. For the single channel case we consider the main model as well as models with batch arrivals, multiclasses, customer impatience, double connection, control devices, two-way communication and buffer. The stochastic processes arising from these models are considered in the stationary as well as the nonstationary regime. For multi-channel queues we survey numerical investigations of stationary distributions, limit theorems for high and low retrial intensities and heavy and light traffic behaviour.
485 citations