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

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

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.