Evaluating the Performance of the Erlang Models for Call Centers

Abstract

In this paper we evaluate two queuing models used to analyze call centers; the Erlang C and Erlang A models. The Erlang C is a simple model that ignores caller abandonment and is the most commonly used model. The Erlang A model allows for abandonment, but performance measures are more difficult to calculate. We compare the theoretical performance predictions of these models to a steady state simulation model where many of the simplifying assumptions used in standard analytical models are relaxed. Our findings support the assertion that the Erlang A model is more accurate, but we find that in contrast to the Erlang C model, Erlang A tends to be optimistically biased. Our findings indicate that neither model clearly dominates the other in all situations and that care must be taken to select the correct model based on call center conditions and the intended purpose of the model.

Applications of artificial neural networks for calculation of the Erlang B formula and its inverses

“…The Erlang B formula determines the probability of blocking for a given offered traffic in the system with the given number of channels, while the Erlang C formula determines the probability that a call request will be on hold for the considered value of the offered traffic 2 . The Erlang's formulas, aimed at the beginning to be used for performance calculation in public telephone networks, over the years have been applied in systems where the resources are limited, such as in mobile communication systems, VoIP (Voice over Internet Protocol) systems, computer networks, call centers, and electric vehicle power systems 3–12 …”

“…2 The Erlang's formulas, aimed at the beginning to be used for performance calculation in public telephone networks, over the years have been applied in systems where the resources are limited, such as in mobile communication systems, VoIP (Voice over Internet Protocol) systems, computer networks, call centers, and electric vehicle power systems. [3][4][5][6][7][8][9][10][11][12] During planning and design of trunking and queuing systems and evaluating their performance, in addition to determining the probability of blocking and the probability of call waiting, which are the basis for estimating the quality of the service, it is also necessary to solve the inverse problem, that is, to determine the traffic intensity or the number of required channels (resources) for a given probability that corresponds to the desired GOS (Grade of Service) value. Given the nature of Erlang formulas, there is no inverse function of these formulas in a closed form.…”