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1 Pilsung B Taegyun Fathur B fif Hari Gary Dhika B pril B Mulya B Yusuf B nin Rizka B Dion B Siska B Mirel B Hani B irita B
2 Blocking Probability Course Number : TTH CLO : Week : 9 ext
3 Time Switch and Space Switch F F TB T TB T B B FB FB Time Switch Exchange TS in the same frame Space Switch Exchange same-number TS but in different frame In small SN (<) we use single stage time switch (T) or space switch (S) In large SN (>) we use multistage Switching, for example: stages STS or TST 5 stage STSTS or TSTST Larger SN = more stages = faster switching rate
4 Space Switch Explained 8 bit PCM word 4 B C C 4 C 8 bit PCM word 4 B 4 C B B t4 t t t & & & Periode s B 4 B B B & & & C 4 C C C t4 t t t Periode s & & & connection memory connection memory connection memory Control ddress (number of incoming highway)
5 write read write read write read write read Time Switch Explained Speech Memory ts : 4 B C D Cell content Cell address ts : 4 D C B D Frame C B 4 write address read address (TS) Counter (TS) (TS) cyclic time slot Frame acyclic (TS4) Speech Memory (SM) Connection Memory (CM) Counter : stores content of TS : controls read sequence from SM : control write sequence into SM
6 Multi Stage Switch N/n array n.k k array N/n.N/n N/n array k.n Multi stage switch has blocking probability due to the shared cross points To provide lower blocking probability, numbers of matrix in center stage play significant role: N inlet n.k N/n.N/n k.n N outlet k n k ( n ) ( n ) n (min.) n.k N/n.N/n k.n Replacing k in (): N X N X N n N N N n k k n k N Nk k n N X = total number of cross points N = number of inlet/outlet n = size of every switch block inlet/outlet k = number of center stage n n n () N N(n ) (n ) n N X () / dn X 0 dn N N x n () () () Number of minimum cross point : 4N( N )
7 S-T-S 0 B SM-B B 45 C CM-B B SM-B 0 B SM-B 0 CM-B CM-B 0 45 B B 45 C C CM- CM CM-C CM-C CM- CM-C bove figure explains interconnection from /TS0 to C/TS45
8 T-S-T 0 SM- SM- SM- 0 CM- 4 0 CM- 4 CM- 4 SM- C SM- C SM- C CM- C 45 CM- C CM- C 4 C C C 4 00 CM- B CM- B CM- B bove figure explains interconnection from /TS0 to C/TS45.
9 Comparison Single stage Space (S) switch is inapplicable due to its high blocking probability Single stage Time (T) switch may be used as non-blocking switch block with low capacity (50 lines) T-S or S-T configuration may be used in small to medium capacity, due to its blocking probability increases with the Time Switch size The size of Space Switch increases in square function with the number of input/output bus, while the size of time switch increases in linear with the increment of time slot number For exchanges with large capacity, we may use from SSTSS, TSST, to TSSST configuration
10 Blocking Probability
11 Blocking Probability in STS. STS Switch Block ssumptions : - Space switch non-blocking - Time switch non-blocking - (STS) individual non-blocking Lee Graph p p' p' p' p' p p' p' k N N x k N x k P = P(n/k) q = P = p/b k = number of Time switch matrix B = k/n (concentration factor) k Blocking Probability: B = ( ( p/b) ) ) k
12 Blocking Probability in TST. TST Switch Block ssumptions : - Space switch non-blocking - Time switch non-blocking - (TST) individual non-blocking Lee Graph P P P P inlet memory outlet memory l N inlet memory inlet memory Space Switch outlet memory outlet memory N B = ( q ) l q = P = P/a a = time expansion ( l/c) l = number of time slot at space stage c = number of time slot per frame at input TST is non-blocking when l = c -
13 Blocking Probability in TSSST. TSSST Switch Block Lee Graph P P K B P P inlet time stage space stage space stage space stage outlet time stage k 8 TSM TSM TSM TSM N x k N x k N N x n n N N x n n k x N k x N TSM TSM TSM TSM l P P = P/a P = P/(ab) a = l/c b = k/n Blocking Probability: B = { (q ( ( q ) k ) } K P B where: q = P = P/a q = P = P/ab
14 Lee Graph * C. Y. Lee
15 Lee Graph Theory (/) non-blocking switching is where everyone can call everyone, at anytime It is perfect, needed, but non efficient For economics reason, capacity is limited especially at peak hours C. Y. Lee provides a concept and how to calculate blocking probability This method based on linear graph approach, and uses: nodes to describe switching stage arcs to describe link between stages Linier graph explains the possibility of a path to be taken from inlet to outlet (point to point)
16 Lee Graph Theory (/) Lee Graph is applicable for any type of switching structure Lee Graph calculates blocking probability by using link usage percentage p describes busy link probability at any time frame, while q describes idle link probability (q = p)
17 Erlang The erlang (E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on telephone switching equipment For example, a single circuit has the capacity to be used for 60 minutes in one hour. If 00 x six-minute calls are received on a group of such circuits, then assuming no other calls are placed for the rest of the hour, the total traffic in that hour will be six hundred minutes, or 0 erlangs.[] In 946, the CCITT named the international unit of telephone traffic the erlang in honor of gner Krarup Erlang
18 Lee Graph Theory on Single Link p If link carries a Erlang, then busy link probability (p) = a, and idle link probability (q) = p = a Blocking probability (B) = p = a (single link)
19 Lee Graph Theory on Parallel Link p If each link carries a Erlang, then busy probability for each link (p) = a, and busy probability for both link (B) = p x p = p idle probability for any link (q) = B = p For N parallel link, B = p N p
20 Lee Graph Theory on Serial Link X p q = p p q = p Y If each link carries a Erlang, then busy probability for each link (p) = a, and idle probability for both link (Q) = q x q = (-p) x (-p) Blocking probability (B) = Q For N serial link, B = - q N
21 See you on next class
Pilsung B Taegyun Fathur B fif Hari Gary Dhika B pril B Mulya B Yusuf B nin Rizka B Dion B Siska B Mirel B Hani B irita B Digital Switch Course umber : TTH CLO : Week : 9 Inside the Digital Local Exchange
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