Maximizing a Live Chat Call Center with the Erlang Formula

Last Updated: May 6th, 2006
WebsiteAlive Editor Christin Gulick contributed to this article.

In the quest for efficiency and productivity, managers and supervisors have a mathematical way to track the success of their telephone business. In 1909, Danish engineer A.K. Erlang invented a unit of measure aptly named the ‘Erlang.’ This unit describes the total telephone traffic volume for one hour on any given network. This same measurement can be used for determining the same volume on live chat networks. First, however, let’s understand how to calculate an Erlang.

Take, for example, a set of callers that makes twenty calls in one hour with each call averaging roughly seven minutes. We can calculate the Erlangs as such:

Minutes of traffic per hour = duration x number of calls

Minutes of traffic in the hour = 7 x 20

Minutes of traffic in the hour = 140

Hours of traffic in the hour = 140/60

Hours of traffic in the hour = 2.33

Traffic Figure: 2.33 Erlangs

This figure can then be used as the foundation for more complicated equations to predict and understand traffic patterns over a given telephone (or, in our case, LiveChat) network. Managers can then use this number to determine how many personnel they need to adequately support their call volume.

Live chat support software companies can therefore determine how many representatives will be needed to effectively offer sales and support at the best price. Before we make the actual calculations, however, let us first look at a few of the equations. The formulas can be a bit complicated.

Erlang B

from http://en.wikipedia.org/wiki/Erlang_unit

where:

• Eb is the probability of blocking
• r is the number of resources (eg. servers or circuits in a group).
• t is the amount of traffic offered in Erlangs.

Erlang C
from http://en.wikipedia.org/wiki/Erlang_unit 

where:

• A is the total traffic units offered in Erlangs
• N is the number of servers in a full availability environment
• P(>0) probability that delay is greater than 0
• P is the probability of loss

Fortunately for the not-so-math-minded, several websites offer free automated calculators for the purpose of determining these useful numbers. There are free and paid for versions depending on the complexity of the calculations the business may require. A list of available calculators can be seen at the Erlang.com website at http://www.erlang.com/calculator. In particular you can use one of these calculators to derive the number of representatives you may need based upon the number of calls you receive per hour. The “Call Center Calculator,” available at http://www.erlang.com/calculator/call, offers some great information, a few slight adjustments need to be made to compensate for the differences between traditional phone based systems and the live chat systems. For this translation we recommend substituting the “number or calls” with the number of chat requests received over a period of one month plus the number of proactive sales inquiries the business is willing to extend to site visitors.

The average chat session can run between 10-20 minutes or longer depending on the complexity of the questions being asked. Fortunately during this time the live chat aspect of the program allows the representative to multi-task between service/sales chats as well as other smaller projects simultaneously. Here again we can see by the Erlang numbers that the use of Live Chat software for sales and support is much more efficient than the traditional call center telephone operator. If you were to compare a traditional phone operator and a Live Chat operator you could easily see that the Live Chat operator is going to be more efficient as they perform multiple tasks at one time. It also means, as the Erlang numbers show, that a company needs a much smaller staff to answer the same number of ‘calls’ (online chat sessions versus phone calls).

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