WEEK 8 (24-28 MAY)

Erlang algorithm is a common algorithm used in Workforce prediction in a contact center environment. This week I learnt about Erlang. Basically, erlang is a unit of traffic density in a telecommunications system. One erlang is the equivalent of one call (including call attempts and holding time) in a specific channel for 3600 seconds in an hour. The 3600 seconds need not be, and generally are not, in a contiguous block. Erlang is divided into 3 which are Erlang A, Erlang B and Erlang C.

In call centers, Erlang A is used, to support solutions of the staffing problem, such as how many agents should be answering calls during a specified time period. In order to apply Erlang A, it is necessary to input values for its four parameters: λ, μ, θ and n. Parameters λ and μ are calculated for every hourly interval. We also calculate each hour’s average number of agents n. Because the resulting n’s need not be integral, we apply a continuous extrapolation of the Erlang-A formulae, obtained from relationships developed in. Finally, for θ we use the formula P{Ab} = _ • E[W].

A traffic engineering model that assumes that an offered call is cleared immediately, with no queuing. In other words, Erlang B assumes that a call encountering blockage will not appear again. Either the caller will hang up and not attempt to place the call again, or the call will automatically be routed over another circuit if one exists, even if the use of that circuit is more expensive. 

Erlang B is the formula to use when a blocked call is really blocked. For example, when somebody calls your phone number and gets a busy signal or tries to access a tie trunk and finds it in use. It is built around three variables which are Servers, Traffic, and Grade of Service.

The most common traffic engineering problem involves sizing a trunk group. For example, how many trunks are needed to carry your toll-free calls, how many tie trunks between two offices, how many ports into your voice mail system, or some similar question. Erlang B handles that relatively easily, in four steps:

1. Collect traffic data
2. Determine the Average Busy Hour
3. Choose a target Grade of Service
4. Use Erlang B

Example of Erlang B

Erlang B Formula 

Erlang C formula is used when a blocked call is delayed. For example, when someone calls your call centre and must wait for an agent to take the call. It uses the same three variables, plus the average length of each call, to calculate the probability of being delayed and how long the delay is likely to be.

Because Erlang B is so simple to use (insert two numbers, it calculates the third), many people assume that Erlang C will be similarly easy. But it is not true, even basic Erlang C calculations are difficult, and more complex ones can be daunting indeed. Erlang C is most commonly used to calculate how long callers will have to wait before being connected to a human in a call centre or similar situation.

Erlang C Formula

After learning about Erlangs, I searched for erlang sample excel sheet calculations and formula to test it out. Firstly, I searched Erlang B.

Example of Excel Function for Erlang B:

ErlbBlockage(nsrv,trafficInErlangs) returns the Erlang B blockage for a specified number of servers and specified offered traffic. The nsrv is the number of servers (can be any non-negative number) and traffic in Erlangs is the offered traffic in erlangs (can be any non-negative number). For example, =ErlbBlockage(3,10.4) returns Erlang B blockage for 3 servers and 10.4 erlangs of offered traffic. This then returns the value 0.7411421.

Besides that, there are more functions for Erlang B in excel such as ErlbNsrvFromBlockage and ErlbTrafFromBlockage.

Example of Excel Function for Erlang C:

ErlcFractionDelayed(nsrv, trafficInErlangs) returns the probability that a customer arriving at the queuing facility will experience a delay before beginning service. For example, =ErlcFractionDelayed(11,10.1) returns the probability that a customer will experience a wait, when there are 11 servers and 10.1 erlangs of offered traffic. This then returns the value 0.71095477.

Besides that, there are more functions for Erlang C in excel such as ErlcFractionOk, ErlcNsrvFromFractionOk,  ErlcWait and ErlcNsrvFromWait.