Erlang C Forcing versus IRENE's Scheduling Algorithms

Dr. Leonard J. Forys
ISC Algorithm Specialist

The Erlang C approach to determining force requirements for contact centers has been used for many decades. I first became acquainted with its use in the late 1970s when I became responsible for the algorithms used to engineer and force call centers in all of the then Bell System. It became evident that although the Erlang C formula was easy to use and widely available, it had serious defects. These defects were apparent from repeated complaints from the field, which challenged the accuracy of the Erlang C results.

At that time I began an exhaustive study of the assumptions behind the Erlang C formula and what could be done to overcome these deficiencies. The result of over 25 years of research has produced the algorithms used in IRENE.

There are a number of basic problems with Erlang C which have been verified with decades of field data:

1. Erlang C assumes that the calls arriving in a given forcing interval arrive at a constant rate, and in a specified manner (Poisson arrivals). In practice, this is almost never met. Arrival patterns ebb and peak throughout the day. The result is that when a ramp up of traffic occurs, Erlang C will underestimate the required number of agents. When a ramp down of traffic occurs, Erlang C will overestimate the required number of agents.
2. Erlang C assumes that the number of agents arriving in a given forcing interval is fixed. In practice, this almost never occurs. Agents can take breaks during forcing intervals, connect late to their positions, disconnect early from their positions, etc. As a result, Erlang C nearly always underestimates the number of agents required.
3. Erlang C assumes that the time a customer engages an agent follows a very specific statistical pattern (exponential hold times). This is rarely true in practice. Many situations occur where there are a mixture of calls e.g. some of which are nearly always shorter, others which are nearly always longer. The more variations there are in call mixtures, the more inaccurate Erlang C can be. Situations with wide variability in customer hold times cause Erlang C to underestimate the number of agents required. Situations with narrow variations in customer hold times cause Erlang C to overestimate the number of agents required.
4. Erlang C can only be used for an integer number of agents. To insure that the quality of service objectives can be met, the number of agents is usually "rounded up." This produces a net bias of providing too many agents.
5. Erlang C assumes that there is no priority on the types of calls served. If priority is given to calls which tend to be shorter than average, then Erlang C will provide too many agents. The reverse occurs when priority is given to calls which are longer than average.

This is merely a summary of the problems encountered with using Erlang C. All of these situations have repeatedly occurred in practice. With new modern approaches to skill-based call assignments and inventive ways of handling a mixture of email calls and normal traffic, Erlang C is even more inaccurate.

Based on our experiences with these problems, we have developed an approach that is far more accurate than Erlang C and its variant, the Merlang approach.

Our experience has shown us that each contact center is unique and that one set of parameters will not be adequate.

Our approach is unique because we not only take into account static situations, but we also apply adaptive techniques so that the IRENE algorithms can optimally "learn" the right parameters.

Contact centers amass enormous quantities of service data each day. Yet, no one in the industry outside of IRENE has used this data to optimally determine force requirement based on observations of service data quality.

This approach guarantees that there is no more accurate force determination than that produced by IRENE. It optimally matches the quality of service data.

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