Perluasan Erlang Rekayasa Trafik Sukiswo sukiswokyahoo com sukiswoelektro

Perluasan Erlang Rekayasa Trafik Sukiswo sukiswok@yahoo. com sukiswo@elektro. ft. undip. ac. id Rekayasa Trafik, Sukiswo 1

Outline 4 Erlang B 4 Extended Erlang 4 Erlang C 4 Rekursif Erlang Rekayasa Trafik, Sukiswo 2

Erlang B 4 Erlang B is a formula for blocking no retrial sources 4 The Erlang B distribution is used for dimensioning trunk routes. It is based on the following assumptions: – – – There 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 3

Erlang B 4 Erlang B is a formula for blocking no retrial sources 4 The Erlang B distribution is used for dimensioning trunk routes. 4 It is based on the following assumptions: – – – There 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 4

Erlang B 4 where: 4 B=Erlang B loss probability N=Number of trunks in full availability group A=Traffic offered to group in Erlangs Rekayasa Trafik, Sukiswo 5

Erlang B Example 4 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 30 m. E of inbound traffic per active end, and GOS should be better than 0. 002. 4 How many trunks do I need in the tie line route? Rekayasa Trafik, Sukiswo 6

Extended Erlang B 4 Extended Erlang B is a formula for blocking retrial 4 4 4 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 7

Extended Erlang B 4 Be: Blocked Erlangs 4 Be=a * ERL-B(a, n) 4 C: Carried Traffic 4 C=a-Be=a * (1 -ERL-B(a, n)) 4 R: Recall Traffic R=Be*r 4 r: Recall factor. B: Overflow Traffic B=Be*(1 -r) 4 a=ao+RC+B 4 ao: Initial Traffic(Offerd Load) 4 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 8

Extended Erlang B Rekayasa Trafik, Sukiswo 9

Extended Erlang B Rekayasa Trafik, Sukiswo 10

Erlang C 4 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. 4 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 11

Erlang C 4 It is based on the following assumptions: – There 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 12

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 13

Rekursif Erlang En+1(A)= = An+1/(n+1)! 2 n+1 A A 1+A+ +…+ 2! (n+1)! [A/(n+1)] An/n! 2 n+1 A A 1+A+ +…+ 2! (n+1)! Rekayasa Trafik, Sukiswo 14

Rekursif Erlang (2) A En+1(A)= An/n! 2 A 1+A+ +…+ 2! (n+1) 1+ An n! An+1/(n+1)! 2 n+1 A A 1+A+ +…+ 2! (n+1)! Rekayasa Trafik, Sukiswo 15

Rekursif Erlang (3) A. En(A) En+1(A)= (n+1) 1+ = An+1/(n+1)! A 2 A (n+1) 1+A+ +…+ 2! An n! A. En(A) (n+1) 1+ A (n+1) Rekayasa Trafik, Sukiswo En(A) 16

Rekursif Erlang (4) Jadi En+1(A)= A. En(A) n + 1 + A. En(A) atau En (A)= A. En-1(A) n + 1 + A. En-1(A) Rekayasa Trafik, Sukiswo 17

Rekursif Erlang (5) 4 Misalkan akan dihitung blocking dari suatu sistem dengan A=15, 7 Erlang dan N=10 saluran 4 Perhitungannya dimulai dengan N=0 yaitu E 0(15, 7)=1 dan seterusnya sampai E 10(15, 7) Rekayasa Trafik, Sukiswo 18