1. Calculation functions
2. All functions
3. Call center planning functions
4. ERLANGC

The ERLANGC function determines the probability of a request being placed in a queue given a specified number of servers, arrival rate of requests, and the average duration to process requests.

For example, you can use the ERLANGC function to ensure that a certain percentage do not enter a queue.

## Syntax

ERLANGC(Number of servers, Arrival rate, Average duration)

## Arguments

 Argument Data type Description Number of servers Number The number of servers (for example, call center agents) available to process requests. Arrival rate Number The interval between the arrival of each request. Average duration Number The average duration it takes to process each request.

The ERLANGC function returns a number, which is the probability a request is placed in an infinite queue.

### How Erlang C is calculated

Erlang C is the solution to this equation:

$ERLANGC(x,y,z) = \dfrac{\frac{a^x}{x!(1-p)}}{\sum \frac{k = x-1}{k!} \frac{a^x}{x!(1-p)}}$

In this equation:

• x is the Number of servers.
• y is the Arrival rate.
• z is the Average duration.
• a is the offered load, which is y multiplied by z.
• p is the offered load per server, which is a divided by x.

## Constraints

### Time unit for arguments

The Arrival rate and Average duration arguments do not have to use a specific time unit. For example, they can be seconds or minutes. However, both arguments must use the same time unit.

### Maximum number of servers

The maximum number you can use for the Number of servers argument is five million.

## Calculation engine functionality differences

Call center planning functions are unavailable in Polaris. Learn more about the differences between Anaplan calculation engines.

## Examples

In this example, the Call Centers list is on columns, and line items on rows. The first three line items contain the scheduled number of servers, arrival rate of requests, and average duration to fulfil requests. The fourth line item, Queuing Possibility calculates the possibility of a call entering a queue using a formula.

The final two line items are a numeric line item, Extra Agents, to adjust the number of servers, and a formula that displays the blocking possibility after adjustment. This can be used to adjust the number of servers until the desired blocking possibility is reached (in this case, less than 15%).

Both of the line items that contain formulas use the Percentage format with two decimal places to display the possibility as a percentage.

 Call Center 1 Call Center 2 Call Center 3 Call Center 4 Scheduled Number of Agents 33 50 55 40 Request Arrival Rate 0.76 0.87 1.35 2.81 Average Duration 19.25 52.9 34.9 13.1 Queuing Possibility ERLANGC(Scheduled Number of Agents, Request Arrival Rate, Average Duration) 0.00% 46.04% 18.93% 50.41% Extra Agents -13 5 1 5 Amended Queuing Possibility ERLANGC(Scheduled Number of Agents + Extra Agents, Request Arrival Rate, Average Duration) 13.26% 13.93% 14.65% 13.48%

Disclaimer

We may update our documentation occasionally, but will only do so in a way that does not negatively affect the features and functionality of the Anaplan service.