Introduction to Erlang

Vipul Gupta, Analytics Consultant,

The classical Erlang-C model (also referred to as M/M/n queuing model) is one of the most frequently used tools in workforce management of call centers.

However, the model has a shortcoming when it comes to customer abandonment. This parameter is not a minor aspect of call center operations, as higher abandonment percentage would adversely impact the reputation of the client, as well as that of the call center.

The abandonment phenomenon is a complex one, and a lot of current research effort worldwide is targeted at developing mathematical models to predict customer abandonment behavior. An effort in this direction, the Erlang-A model (A here is for abandonment) is an extension of existing the Erlang-C model, and offers a simple way to model abandonment.

In the Erlang A model, an exponentially distributed patience time is associated with each arriving caller. The arriving caller encounters an offered waiting time, which is defined as the time that this person would have to wait (given that the patience is infinite). If the offered wait exceeds the customer’s patience time, the call is then abandoned, otherwise the customer awaits service. The caller patience parameter here is also referred to as the individual abandonment rate.

Comparison between Erlang-C and Erlang-A

50 Agents, 2880 calls per hour, 1 min. average service time, 2 min. average patience


For a variable number of agents, while keeping other parameters same (2880 calls per hour, 1 min. service time and 2 min. average patience parameters), the following graphs depict the service level, probability to wait and wait time (s).

For a given target service level, the Erlang-A model required lower number of agents compared to Erlang-C. Since personnel costs are the major operational costs of running call centers, even a small reduction in personnel is economically significant.

Also, note that the Erlang-C is stable only with 49 or more agents, while Erlang-A is always stable.

Based on these calculations, it can be inferred that the Erlang-A model is an efficient method to predict customer abandonment behavior. In call centers, Erlang-A can be used to support solutions of the staffing problem, for a given service level goal. Although exact formulae for the Erlang-A method are available, they are fairly complicated for providing guidelines and insights to call center researchers and managers. Consequently, some useful and insightful approximations have been developed by researchers, and can be utilized to construct black-box models for call center analytics.

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Research Sources:
1. The Palm/Erlang-A Queue, with Applications to Call Centers” by Avishai Mandelbaum and Sergey Zeltyn,

2. Faculty of Industrial Engineering & Management Technion, Haifa 32000, Israel

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