Approximating multi-skill blocking systems by HyperExponential Decomposition

Franx, Geert Jan; Koole, Ger; Pot, Auke

doi:10.1016/j.peva.2005.09.001

Cited by 33 publications

(35 citation statements)

References 5 publications

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“…A possible remedy is to use stationary blocking models (Franx et al, 2006) of multi-skill call centers. However, this excludes modeling the carry-over of backlog such as unanswered e-mails or call retrials.…”

Section: Introductionmentioning

confidence: 99%

“…Bhulai et al (2006) present a two-step approach to solve the staffing (Step 1) and shift scheduling (Step 2) problem for multi-skill call centers of a realistic size. In Step 1, stationary blocking models (Franx et al, 2006) of multi-skill call centers are used to determine staffing levels for each interval. Given these required staffing levels, shift schedules are created via integer programming in Step 2 to meet these staffing requirements.…”

Section: Introductionmentioning

confidence: 99%

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Profit-oriented shift scheduling of inbound contact centers with skills-based routing, impatient customers, and retrials

Helber

Henken

2008

OR Spectrum

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract This paper presents a profit-oriented shift scheduling approach for inbound contact centers. The focus is on systems in which multiple agent classes with different qualifications serve multiple customer classes with different needs. We assume that customers are impatient, abandon if they have to wait, and that they may retry. A discrete-time modeling approach is used to capture the dynamics of the system due to time-dependent arrival rates. Staffing levels and shift schedules are simultaneously optimized over a set of different approximate realizations of the underlying stochastic processes to consider the randomness of the system. The numerical results indicate that the presented approach works best for medium-sized and large contact centers with skills-based routing of customers for which stochastic queueing models are rarely applicable. Terms of use: Documents in EconStor may

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Profit-oriented shift scheduling of inbound contact centers with skills-based routing, impatient customers, and retrials

Helber

Henken

2008

OR Spectrum

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“…Hence, approximative methods are needed for performance analysis (see Kelly [7] for a broad overview). Classical approximation techniques such as the equivalent random method and the Hayward-Fredericks method [14], and the recently introduced hyperexponential decomposition (Franx, Koole, and Pot [3]), are based on parametrically modeling the overflow processes from the first layer by simpler processes. These methods have been observed to produce good approximations for many choices of system parameters.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Bounds for Two-Layer Loss Systems

Jonckheere¹,

Leskelä²

2008

Stochastic Models

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This paper studies multiclass loss systems with two layers of servers, where each server at the first layer is dedicated to a certain customer class, while the servers at the second layer can handle all customer classes. The routing of customers follows an overflow scheme, where arriving customers are preferentially directed to the first layer. Stochastic comparison and coupling techniques are developed for studying how the system is affected by packing of customers, altered service rates, and altered server configurations. This analysis leads to computationally fast upper and lower bounds for the performance of the system.

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“…A common problem is then how to meet the service-level agreements while keeping the disturbance of the back office operators to a minimum; see [14] and references therein. Overflow problems are in general difficult to analyze, see [11], because the overflow traffic is not Poisson; the deterministic threshold of this model only adds to this. We believe though that the model is of independent interest and has its applications in other areas where the service level involves the (tail) distribution of the waiting time, as in, for example, telecommunication and production systems, or in supply chains with lead time decisions [20].…”

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confidence: 99%

Queues with waiting time dependent service

Bekker¹,

Koole²,

Nielsen

et al. 2011

Queueing Syst

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Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting-time process of the first customer in line, we derive steady-state waiting-time distributions for both models. The results are illustrated with numerical examples.

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Approximating multi-skill blocking systems by HyperExponential Decomposition

Cited by 33 publications

References 5 publications

Profit-oriented shift scheduling of inbound contact centers with skills-based routing, impatient customers, and retrials

Profit-oriented shift scheduling of inbound contact centers with skills-based routing, impatient customers, and retrials

Stochastic Bounds for Two-Layer Loss Systems

Queues with waiting time dependent service

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