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Erlang-C公式介绍

(2009-06-05 12:51:20)
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The Erlang-C Formula

The widely-used Erlang-C formula is given here for people who want to see the actual mathematical definition.


The Erlang-C calculations are described step by step below, using and example of 360 calls per half hour, with an average call duration of 4 minutes, and 55 agents. The target answer time for service level is 15 seconds.

(1) Specify Call Arrival Rate

The first parameter needed is the average customer arrival rate. It doesn't matter what time unit is used to specify the arrival rate, as long as the same time unit is used for the average call duration. Also, the results we shall get for waiting times will be in these same time units. Generally, for call-center applications of Erlang-C, the best time unit to use is seconds.

Erlang-C公式介绍 Erlang-C公式介绍

(2) Specify Call Duration

The second factor to be specified is the average call duration. This must be expressed in the same time unit used for the call arrival rate.

Erlang-C公式介绍 Erlang-C公式介绍

(3) Specify Number of Agents

The third factor is the number of agents available.

Erlang-C公式介绍 Erlang-C公式介绍

(4) Calculate Traffic Intensity

The term "traffic intensity" comes from the original application of Erlang-C, which was for telephone networks, and the volume of calls was described as the "traffic". We need to calculate the traffic intensity as a preliminary step to the main Erlang-C formula, but traffic intensity can be interpreted in several useful ways.

Erlang-C公式介绍 Erlang-C公式介绍

(5) Calculate Agent Occupancy

The agent occupancy, or utilisation, is now calculated by dividing the traffic intensity by the number of agents. The agent occupancy will be between 0 and 1. If it is not less than 1 then the agents are overloaded, and the Erlang-C calculations cannot be done. For reporting results we ususually quote occupancy as a percentage, so we multiply by 100% to get the agent occupancy as a percentage.

Erlang-C公式介绍 Erlang-C公式介绍

(6) Calculate the Erlang-C Formula

Now we can calculate the main Erlang-C formula. This formula looks complicated, but is straightforward to calculate with a few lines of programming. The value of EC(m,u) is needed to calculate the answers we actually want.

Erlang-C公式介绍

(7) Calculate Probability A Call Waits

EC(m,u) is the probability that a call is not answered immediately, and has to wait. This is a probability between 0 and 1, and to express it as a percentage of calls we multiply by 100%.

Erlang-C公式介绍 Erlang-C公式介绍

(8) Calculate Average Speed Of Answer

Having calculated EC(m,u) it is quite easy to calculate the average waiting time for a call, which is often referred to as the "Average Speed of Answer" or ASA. We have to remember the time units we used for arrival rate and call duration, since this calcualtion gives the result in the same time units. This is the reason that the best time unit to use is seconds.

Erlang-C公式介绍 Erlang-C公式介绍

(9) Calculate Service Level

Frequently we want to calculate the probability that a call will be answered in less than a target waiting time. The formula for this is given here. Remember that, again, the probability will be on the scale 0 to 1 and should be multiplied by 100% to get a percentage.

Erlang-C公式介绍 Erlang-C公式介绍

(10) Calculate Agents Needed

If the service level is specified and you want to calculate the number of agents needed, then you must do a bit of (intelligent) trial and error. You have to find the number of agents that will just achieve the service-level you want. A good approach is to start with u, the traffic intensity, as the number of agents. If u is fractional then take the next highest integer. You will need at least this number of agents to avoid overload. Calculate the service-level you will get with this number of agents, then increase by one agent at a time until you just get the service-level you want.

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