Rekayasa Trafik, Sukiswo Perluasan Erlang Rekayasa Trafik Sukiswo sukiswok@yahoo.com sukiswo@elektro.ft.undip.ac.id Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Outline Erlang B Extended Erlang Erlang C Rekursif Erlang Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Erlang B Erlang B is a formula for blocking no retrial sources The Erlang B distribution is used for dimensioning trunk routes. It is based on the following assumptions: There are an infinite number of sources; Calls arrive at random; Calls are served in order of arrival; Blocked calls are lost; and Holding times are exponentially distributed. Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Erlang B Erlang B is a formula for blocking no retrial sources The Erlang B distribution is used for dimensioning trunk routes. It is based on the following assumptions: There are an infinite number of sources; Calls arrive at random; Calls are served in order of arrival; Blocked calls are lost; and Holding times are exponentially distributed. Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Erlang B where: B=Erlang B loss probability N=Number of trunks in full availability group A=Traffic offered to group in Erlangs Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Erlang B Example I am planning a remote PABX connected by a tieline that will be used for all inbound calls to that PABX which will have 780 active ends. I estimate 30mE of inbound traffic per active end, and GOS should be better than 0.002. How many trunks do I need in the tie line route? Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Extended Erlang B Extended Erlang B is a formula for blocking retrial sources. A traffic engineering model that, like Erlang B, assumes that an offered call is cleared immediately, with no queuing. However, Extended Erlang B assumes that the caller encountering blockage (e.g., busy signal or no dial tone) will hang up and immediately attempt the call again, with no overflowing of calls to more expensive routes. EEB was developed by Jim Jewitt and Jaqueline Shrago of Telco Research ERL-B:Probability of blocking by Erlang B ERL-B(a,n) a:Traffic n:Lines Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Extended Erlang B 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 factorB: Overflow Traffic B=Be*(1-r) a=ao+RC+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) Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Extended Erlang B Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Extended Erlang B Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Erlang C The Erlang C distribution is used for dimensioning server pools where requests for service wait on a first in, first out (FIFO) queue until an idle server is available. The Erlang C formula is used to predict the probability that a call will be delayed, and can be used to predict the probability that a call will be delayed more than a certain time Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Erlang C It is based on the following assumptions: There are an infinite number of sources; Calls arrive at random; Calls are served in order of arrival; Blocked calls are delayed; and Holding times are exponentially distributed. Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Erlang C where:      P(>0)=Probability of delay greater than zero      N=Number of servers in full availability group      A=Traffic offered to group in Erlangs Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Rekursif Erlang A2 2! (n+1)! An+1 En+1(A)= An+1/(n+1)! 1+A+ +…+ = [A/(n+1)] An/n! Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Rekursif Erlang (2) (n+1)! 2! n! En+1(A)= An/n! 1+A+ A2 An +…+ An+1/(n+1)! An+1 A (n+1) 1+ Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Rekursif Erlang (3) 2! En+1(A)= An+1/(n+1)! 1+A+ A2 An n! +…+ A.En(A) (n+1) 1+ A = En(A) Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Rekursif Erlang (4) n + 1 + A.En(A) n + 1 + A.En-1(A) En+1(A)= A.En(A) Jadi atau En (A)= A.En-1(A) Rekayasa Trafik, Sukiswo

Rekayasa Trafik, Sukiswo Rekursif Erlang (5) Misalkan akan dihitung blocking dari suatu sistem dengan A=15,7 Erlang dan N=10 saluran Perhitungannya dimulai dengan N=0 yaitu E0(15,7)=1 dan seterusnya sampai E10(15,7) Rekayasa Trafik, Sukiswo