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The "sensitive" Markovian queueing system and its application for a call center problem

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Kanavetas, Odysseas and Balcıoğlu, Ahmet Barış The "sensitive" Markovian queueing system and its application for a call center problem. Annals of Operations Research . ISSN 0254-5330 (Print) 1572-9338 (Online) Published Online First http://dx.doi.org/10.1007/s10479-018-2802-6

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Official URL: http://dx.doi.org/10.1007/s10479-018-2802-6

Abstract

In this paper, we study the M_n/M_n/c/K+M_n queueing system where customers arrive according to a Poisson process with state-dependent rates. Moreover, the rates of the exponential service times and times-to-abandonment of the queued customers can also change whenever the system size changes. This implies that a customer may experience different service rates throughout the time she is being served. Similarly, a queued customer can change her patience time limits while waiting in the queue. Thus, we refer to the analyzed system as the ``sensitive" Markovian queue. We conduct an exact analysis of this system and obtain its steady-state performance measures. The steady-state system size distribution yields itself via a birth-death process. The times spent in the queue by an arbitrary or an eventually served customer are represented as the times until absorption in two continuous-time Markov chains and follow Phase-type distributions with which the queueing time distributions and moments are obtained. Then, we demonstrate how the M_n/M_n/c/K+M_n queue can be employed to approximately yet accurately estimate the performance measures of the M_n/GI/c/K+GI type call center.

Item Type:Article
Subjects:Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
ID Code:35268
Deposited By:Barış Balcıoğlu
Deposited On:31 Jul 2018 16:33
Last Modified:25 Jul 2019 16:06

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