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Rekayasa Trafik, Sukiswo 1 Perluasan Erlang Rekayasa Trafik Sukiswo

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Presentasi berjudul: "Rekayasa Trafik, Sukiswo 1 Perluasan Erlang Rekayasa Trafik Sukiswo"— Transcript presentasi:

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2 Rekayasa Trafik, Sukiswo 1 Perluasan Erlang Rekayasa Trafik Sukiswo

3 Rekayasa Trafik, Sukiswo2 Outline  Erlang B  Extended Erlang  Erlang C  Rekursif Erlang

4 Rekayasa Trafik, Sukiswo3 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.

5 Rekayasa Trafik, Sukiswo4 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.

6 Rekayasa Trafik, Sukiswo5 Erlang B  where:  B=Erlang B loss probability N=Number of trunks in full availability group A=Traffic offered to group in Erlangs

7 Rekayasa Trafik, Sukiswo6 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  How many trunks do I need in the tie line route?

8 Rekayasa Trafik, Sukiswo7 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

9 Rekayasa Trafik, Sukiswo8 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)

10 Rekayasa Trafik, Sukiswo9 Extended Erlang B

11 Rekayasa Trafik, Sukiswo10 Extended Erlang B

12 Rekayasa Trafik, Sukiswo11 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

13 Rekayasa Trafik, Sukiswo12 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.

14 Rekayasa Trafik, Sukiswo13 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

15 Rekayasa Trafik, Sukiswo14 Rekursif Erlang A2A2 2! A2A2 (n+1)! A n+1 (n+1)! A n+1 E n+1 (A)= A n+1 /(n+1)! 1+A++…+ = [A/(n+1)] A n /n! 1+A++…+

16 Rekayasa Trafik, Sukiswo15 Rekursif Erlang (2) (n+1)! 2! n! E n+1 (A)= A n /n! 1+A+ A2A2 AnAn +…+ A n+1 /(n+1)! 1+A+ A2A2 A n+1 +…+ A (n+1)1+

17 Rekayasa Trafik, Sukiswo16 Rekursif Erlang (3) 2! E n+1 (A)= A n+1 /(n+1)! 1+A+ A2A2 AnAn n! +…+ A.E n (A) (n+1) 1+ A (n+1) = E n (A) A.E n (A) (n+1) 1+ A (n+1)

18 Rekayasa Trafik, Sukiswo17 Rekursif Erlang (4) n A.E n (A) n A.E n-1 (A) E n+1 (A)= A.E n (A) Jadi atau E n (A)= A.E n-1 (A)

19 Rekayasa Trafik, Sukiswo18 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 E 0 (15,7)=1 dan seterusnya sampai E 10 (15,7)


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