Queueing model for call blending in call centers

Bhulai, Sandjai; Koole, Ger

doi:10.1109/tac.2003.815038

Cited by 93 publications

(80 citation statements)

References 7 publications

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“…A customer of a certain priority can enter service only if there are no higher-priority customers waiting, and the number of idle servers exceeds a class-dependent threshold. A similar threshold policy has also been proposed in a call blending environment (i.e., call centers that handle both inbound and outbound calls) (Bhulai andKoole 2003, Gans andZhou 2003). The role of the thresholds is to ensure that enough servers are available to serve future arrivals of higher priorities.…”

Section: Resultsmentioning

confidence: 99%

Service-Level Differentiation in Call Centers with Fully Flexible Servers

2008

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W e study large-scale service systems with multiple customer classes and many statistically identical servers.The following question is addressed: How many servers are required (staffing) and how does one match them with customers (control) to minimize staffing cost, subject to class-level quality-of-service constraints? We tackle this question by characterizing scheduling and staffing schemes that are asymptotically optimal in the limit, as system load grows to infinity. The asymptotic regimes considered are consistent with the efficiencydriven (ED), quality-driven (QD), and quality-and-efficiency-driven (QED) regimes, first introduced in the context of a single-class service system.Our main findings are as follows: (a) Decoupling of staffing and control, namely, (i) staffing disregards the multiclass nature of the system and is analogous to the staffing of a single-class system with the same aggregate demand and a single global quality-of-service constraint, and (ii) class-level service differentiation is obtained by using a simple idle-server-based threshold-priority (ITP) control (with state-independent thresholds); and (b) robustness of the staffing and control rules: our proposed single-class staffing (SCS) rule and ITP control are approximately optimal under various problem formulations and model assumptions. Particularly, although our solution is shown to be asymptotically optimal for large systems, we numerically demonstrate that it performs well also for relatively small systems.

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Section: Resultsmentioning

confidence: 99%

Service-Level Differentiation in Call Centers with Fully Flexible Servers

2008

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“…Then, call blending is primarily a way to increase overall productivity, by increasing operator utilization, potentially through a control policy. A mathematical analysis and optimization of such a policy is presented in [5]. -Secondly, it may occur as an integral part of the tasks performed at the call center.…”

Section: Introductionmentioning

confidence: 99%

Two Way Communication Retrial Queues with Balanced Call Blending

Phung-Duc

Rogiest

2012

Analytical and Stochastic Modeling Techniques and Applications

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Abstract. In call centers, call blending consists in the mixing of incoming and outgoing call activity. Artalejo and Phung-Duc recently provided an apt model for such a setting, with a two way communication retrial queue. However, by assuming a classical (proportional) retrial rate for the incoming calls, the outgoing call activity is largely blocked when many incoming calls are in orbit, which may be unwanted, especially when outgoing calls are vital to the service offered.In this paper, we assume a balanced way of call blending, through a retrial queue with constant retrial rate for incoming calls. For the single server case (one operator), a generating functions approach enables deriving explicit formulas for the joint stationary distribution of the number of incoming calls and the system state, and also for the factorial moments. This is complemented with a stability analysis, expressions for performance measures, and also recursive formulas, allowing reliable numerical calculation. For the multiserver case (multiple operators), we provide a quasi-birth-and-death process formulation, enabling deriving a sufficient and necessary condition for stability in this case, as well as a numerical recipe to obtain the stationary distribution.

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“…Milner and Olsen (2008) explore the role that service level constraints in outsourcing contracts play in settings where the contractor firm has both contractual and non-contractual customers. Another paper that consider a similar idea of contract and noncontract customers is Bhulai and Koole (2003). For a detailed survey of relevant papers considering the optimal control of the V-model, we refer the reader to Gurvich (2004).…”

Section: Literature Reviewmentioning

confidence: 99%

Online scheduling policies for multiclass call centers with impatient customers

Jouini¹,

Pot²,

Koole³

et al. 2010

European Journal of Operational Research

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We consider a call center with two classes of impatient customers: premium and regular classes. Modeling our call center as a multiclass GI/GI/s + M queue, we focus on developing scheduling policies that satisfy a target ratio constraint on the abandonment probabilities of premium customers to regular ones. The problem is inspired by a real call center application in which we want to reach some predefined preference between customer classes for any workload condition. The motivation for this constraint comes from the difficulty of predicting in a quite satisfying way the workload. In such a case, the traditional routing problem formulation with differentiated service levels for different customer classes would be useless. For this new problem formulation, we propose two families of online scheduling policies: queue joining and call selection policies. The principle of our policies is that we adjust their routing rules by dynamically changing their parameters. We then evaluate the performance of these policies through a numerical study. The policies are characterized by simplicity and ease of implementation.

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Queueing model for call blending in call centers

Cited by 93 publications

References 7 publications

Service-Level Differentiation in Call Centers with Fully Flexible Servers

Service-Level Differentiation in Call Centers with Fully Flexible Servers

Two Way Communication Retrial Queues with Balanced Call Blending

Online scheduling policies for multiclass call centers with impatient customers

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