Erlang Library for Excel Function Reference

Contents

ErlcFractionOk


Applies to: Excel 2003, Excel 2007, Excel 2010

Returns the fraction of customers who begin service after waiting no longer than the specified number of seconds, for the given number of servers, traffic load, and average handle time.

Syntax

ErlcFractionOk( nsrv, trafficInErlangs, ahtSeconds, okWaitSeconds)

nsrv is the number of servers.

trafficInErlangs is the offered traffic load in erlangs.

ahtSeconds is the Average Handle Time (average duration of service) in seconds.

okWaitSeconds is the maximum acceptable wait time in seconds.  (Used to define the "service level".)

Examples

Formula Description Return Value
=ErlcFractionOk(100,97.5,180, 15) Returns the fraction of customers who wait less than 15 seconds before beginning service, number of servers=100, offered traffic=97.5 erlangs, average handle time = 180 seconds. 0.411537
=ErlcFractionOk(100,97.5,180, 50) Same as the preceding, except okWaitSeconds = 50. 0.638087
=ErlcFractionOk(100.7,97.5,180, 50) Same as the preceding, except number of servers= 100.7.  Illustrates the fact that nsrv does not have to be an integer. 0.729022

VBA Function Declaration

Public Function ErlcFractionOk(nsrv As Double, trafficInErlangs As Double, ahtSeconds As Double, okWaitSeconds As Double)

See Also

ErlcNsrvFromFractionOk  ErlcNsrvFromFractionOk5

Remarks

This function, ErlcFractionOk, is the cumulative distribution function for customer wait time in the Erlang C queueing model.  The return value is the probability that an arriving customer will experience a wait no greater than okWaitSeconds.  Some call centers designate a specific value for okWaitSeconds, for example, 10 seconds, to be used in "Service Level" computations.  The return value from ErlcFractionOk is then called the Service Level, and is usually formatted as a percent.  See the Case Study below.

If this function is not available, and returns the #NAME? error, then you must install and load the Erlang Library for Excel from Abstract Micro Systems.

How?

Case Study: Estimating Service Level in a Call Center

A certain call center has a policy of trying to achieve a Service Level of 90% of calls answered with 10 seconds.  During a certain period of the day, the following traffic parameters have been forecasted:

  Maximum number of calls that can be waiting:  Very large
  Period length:  30 minutes
   
  Number of agents:  103
  Incoming calls offered during the period:  1000
  Average handle time:  3 minutes

Will desired the service level be achieved?  First, we compute the offered traffic load trafficInErlangs as

trafficInErlangs = 1000 * 180 / 1800 = 100.0 erlangs.

Then we compute Service Level, or fractionOk, by means of ErlcFractionOk as follows:

fractionOk = ErlcFractionOk( 103, 100.0, 180, 10)
       = 0.423717
       = 42.3717 %

Conclusion: the desired service level of 90% of calls answered within 10 seconds will not be met because only about 42% of calls will be answered within 10 seconds.  The call center is understaffed: we will have to increase the number of agents in order to achieve the desired quality of service.  The specific number of agents that we need may be estimated by using ErlcNsrvFromFractionOk or ErlcNsrvFromFractionOk5.

 

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