Erlang Library for Excel Function Reference

Contents

ErlbNsrvFromBlockage

Applies to: Excel 2003, Excel 2007, Excel 2010

Returns the number of servers that will experience the specified blockage given a specified offered load

Syntax

ErlbNsrvFromBlockage( blockageFraction, trafficInErlangs)

blockageFraction is the desired probability that all servers are busy.  Can be any number greater than or equal to 0 and less than or equal to 1.

trafficInErlangs is the offered load in erlangs.  Can be any non-negative number.

Examples

Formula Description Return Value
=ErlbNsrvFromBlockage( 0.01, 10) Returns the number of servers which produce a blockage of 0.01 (that is, 1 percent) for 10 erlangs of offered traffic 17.44497
=ErlbNsrvFromBlockage( 0.05, 10) Same as above except the blockage is specified to be 0.05 (that is, 5 percent) 14.30043

VBA Function Declaration

Public Function ErlbNsrvFromBlockage(blockageFraction As Double, trafficInErlangs As Double) As Double

See Also

Remarks

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: Sizing a Trunk Group

In a telephone exchange or pbx, you can use ErlbNsrvFromBlockage to estimate the number of trunks required to drive the blockage down to a specified value, given a specifide offered traffic load in erlangs.  This application is one of the ways that Agner Erlang used his formulas during the early 20th century in the Danish telephone system.

Suppose that for a certain group of trunks, we expect an offered traffic load of 15.7 erlangs, and that we wish no more than 1% of callers to experience a busy signal.  Suppose further that the calls arrive in a Poisson process, that service times are exponentially distributied, and that blocked callers (those who experience a busy signal) go away and never return.  Then the assumptions of the Erlang B queueing system are satisfied, so we may estimate the required number n of trunks as follows:

n = ErlbNsrvFromBlockage( 0.01, 15.7)
   = 24.4889

Since a fractional number of trunks does not make sense here, we conclude that we need 25 trunks to drive the blockage down to 1%. 

(Note that we can compute the actual blockage produced by 25 trunks by means of the ErlbBlockage function.  The blockage b is given by
b = ErlbBlockage( 25, 15.7) = 0.00781705 = 0.78175%)

Abstract Micro Systems, Nashville, Tennessee
Contact Abstract Micro Systems