Generally telecommunication system can classify as loss system or waits system (delay system). This matter happens because total customer that connected to network usually more than total server, so that shaping network that causes the happening of blocking. As finally, be produced overflow traffic in network.
In loss system, overflow traffic will refuse. In this case, there is 3 point may be happen in overflow traffic, that is:
Overflow traffic that refuse by a switching device, there is possibility can be accommodated by other switching device that found in network. This condition is called as LCC (Lost Call Cleared).
Refuse traffic will try to do recalling after a few moments. This condition is called LCR (Lost Call Returned).
Traffic that held by device and then served (proceed) after there is empty server and can be occupied. This condition is called as LCH (Lost Call Held).
Erlang distribution, this distribution is got from condition as follows:
- Infinite calling source
- Average incoming call rate: a (constant)
- Total server (line) that processing is limited
- Incoming calls when all servers busy, refused (LCC system).
Distribution with above condition usually used to analyze traffic in trunk transmission system. Usually in a network found several group of trunk that connects between one switching device (central) with another switching device.
When a group trunk that connect direct between two busy switching devices (all occupied), so make possible to shift traffic pass other switching device that use different group trunk. In this way, callings that experience blocking at a group trunk the service is shifted to other group trunk
LCC traffic analysis condition, first time is done by A.K. Erlang in the year 1917. The aim principal from that analysis is to estimate blocking probability and grade of service (GOS). In this case, to express offered traffic, can be used equation:
A = a.tr
Where a, be Poisson average incoming call rate that the value is equivalent with C (average incoming call rate).
When all servers in a busy state, incoming traffic will be refused by system. Because the traffic loss is occurring, so be produced different incoming rate, called as effective incoming call rate. We are notation average effective incoming call rate as C0, and effective incoming rate in I condition is as Ci. System stay in j condition when is there j busy server. Along all idle servers, so every incoming traffic that can process by network. When all servers is busy, so incoming traffic will be refused. Traffic at one network that follow the limitation, is known as Erlang traffic or pure chance traffic (type 1). In this case at can:
Ci = a untuk 0 £ I < cn =" 0" c0 =" ∑" i="0" pn =" 1" c0 =" a" y =" C0" tr =" a" a =" a." y =" A" pn =" A" gos =" Pn," dn =" n.s" pn =" 0" 1 =" (A"> 0
P1 = A P0 for n = 0
for n = 1, got :
P2 = (A P1 + P1 – AP0) / 2
Substitution for P1
P2 = A2 P0 / 2
With same technique for n = 2, got :
P3 = (A P2 + 2P2 – AP1) / 3 = A3 P0 / (3x2) = A3 P0 / 3!
So that generally got,
Pj = Aj P0 / j!
P0 + AP0 + ….. + AN P0 / N! = 1
P0 = 1 / {1 + A + A2/2! + ….. + AN/N!}
And
Pn = An/n!
1 + A + A2/2! + ….. + AN/N!
For n = N :
Pn = AN/N!
1 + A + A2/2! + ….. + AN/N!
Above equation known as Erlang Loss Equation (Erlang B formula). Where Pn be probability all busy servers and also is blocking probability from system (GOS).
Condition diagram for Erlang distribution showed in figure 4.2, where balanced still occur until n = N - 1.
Figure 4.2 Condition Diagram for Erlang distribution.
