Dec. 12, 2007 

Erlang Calculator is a tabbed calculator that includes Erlang B, 
Extended Erlang B and Erlang C traffic calculators for dimensioning 
telecommunications trunk groups, calculating Voice over IP bandwidth 
and estimating staffing requirements of a call center. 

*Erlang B is a formula for blocking no retrial sources.
*Extended Erlang B is a formula for blocking retrial sources.
*Erlang C is delay formula for queueing infinite sources.


*Erlang B calculator Ver4.0
                                       Nov. 8, 2007 

Erlang B is a formula for blocking no retrial sources.

High speed Erlang B calculator, calculate Probability of blocking, 
Lines(Number of servers), Traffic mutually by Erlang B Formula.

Lines and Traffic can set more than 10,000,000.

Erlang B Formula
 B = (a^n/n!)/(1+a/1!+a^2/2!+a^3/3!+...+a^n/n!)
  B:Probability of blocking
  a:Traffic
  n:Lines(Number of servers)


*Extended Erlang B calculator Ver2.1
                                       Dec. 12, 2007 

Extended Erlang B is a formula for blocking retrial sources.

Extended Erlang B calculator, calculate Probability of blocking, 
Lines(Number of servers), Traffic mutually by Extended Erlang B.

Lines and Traffic can set more than 10,000,000, but large number 
calculation will need long time.

ERL-B:Probability of blocking by Erlang B ERL-B(a,n) a:Traffic n:Lines

Be:Blocked Erlangs Be=a*ERL-B(a,n)

C:Carried Traffic C=a-Be=a*(1-ERL-B(a,n))

R:Recall Traffic R=Be*r r:Recall factor

B:Overflow Traffic B=Be*(1-r)

a:Traffic a=ao+R

C+B
 -> =ao:Initial Traffic(Offerd Load)
 C+B=a-Be+Be*(1-r)=a-Be*r=a-a*ERL-B(a,n)*r
    =a*(1-ERL-B(a,n)*r)

Calculate a:Traffic which is satisfy C+B=a*(1-ERL-B(a,n)*r) -> =ao.
At that ERL-B(a,n) is Extended Erlang B Probability of blocking.

Erlang B Formula
 B = (a^n/n!)/(1+a/1!+a^2/2!+a^3/3!+...+a^n/n!)
  B:Probability of blocking
  a:Traffic
  n:Lines(Number of servers)


*Erlang C calculator Ver2.1
                                       Nov. 11, 2007 

Erlang C is delay formula for queueing infinite sources.

Erlang C calculator, calculate Probability of a Delay>0, 
Lines(Number of servers), Traffic mutually.

In addition, calculate Wq:Average wait time in queue, Lq:Average number 
of callers in queue, P(>T):Probability of a Delay>T mutually.

Lines and Traffic can set less than 500,000,000.

P(>0):Probability of a Delay>0

P(>0) = (a^n/n!)*n/(n-a)/((1+a/1!+a^2/2!+a^3/3!+©¥+a^(n-1)/(n-1)!)+(a^n/n!)*n/(n-a))
      = 1/((n-a)/n*(n/a+n*(n-1)/a^2+...+n*(n-1)*...2/a^(n-1)+n!/a^n)+1)

Wq:Average wait time in queue =P(0>)*h/(n-a)
Lq:Average number of callers in queue =P(0>)*a/(n-a)
P(>T):Probability of a Delay>T =P(>0)*e^(-(n-a)*T/h)
h:Average call time