Scilab Textbook Companion for Digital Telephony by J. C. Bellamy 1

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1 Scilab Textbook Companion for Digital Telephony by J. C. Bellamy Created by Harish Shenoy B.Tech Electronics Engineering NMIMS, MPSTME College Teacher Not decided Cross-Checked by TechPassion May 0, 06 Funded by a grant from the National Mission on Education through ICT, This Textbook Companion and Scilab codes written in it can be downloaded from the Textbook Companion Project section at the website

2 Book Description Title: Digital Telephony Author: J. C. Bellamy Publisher: Wiley India (P.) Ltd., New Delhi Edition: 3 Year: 000 ISBN:

3 Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular Example of the above book) For example, Exa 3.5 means solved example 3.5 of this book. Sec.3 means a scilab code whose theory is explained in Section.3 of the book.

4 Contents List of Scilab Codes 4 3 Voice Digitization 5 5 Digital Switching 8 6 Digital Modulation and Radio Systems 3 7 Network Synchronization Control and Management 5 8 Fiber Optic Transmission System 8 9 Digital Mobile Telephony 5 0 Data and Asynchronous Transfer Mode Network 7 Digital Subscriber Access 30 Traffic Analysis 33 3

5 List of Scilab Codes Exa 3. Exa 3. Exa 3.4 Exa 5. Exa 5. Exa 5.3 Exa 5.5 Exa 6.4 Exa 7. Exa 7.3 Exa 8. Exa 8. Exa 8.3 Exa 8.4 Program to calculate quantization interval and bits needed to encode each sample Program to calculate the minimum bit rate for a PCM encoder must provide for high fidelity Program to calculate how many bits per sample can be saved by using DPCM Program to find the idle path in a three stage 89 line switch Program to determine the implementaton complexity of the TS switch Program to determine the implementaton complexity of a 048 channel Program to determine the implementaton complexity of a 307 channel Program to determine system gain of 0Mbps Ghz digital microwave repeater using 4 PSK modulation... 3 Program to determine relative accuracy of maintaining a mutual slip rate ojective of one slip in 0hrs Program to determine the minimum and maximum input channel rate accommodated by an M multiplexer 6 Program to determine the loss limit and the multimode dispersion limit of a graded index FOC Program to determine the loss limit and the chromatic dispersion limit of a high performance SMF FOC... 9 Program to determine the BDP of SMF system and DS SMF system using DFB LD Program to determine the difference in wavelength of two optical signal

6 Exa 8.5 Program to determine the system gain Exa 8.6 Program to determine the range of SPE data rates that can be accomodated by the byte stuffing operation.. 3 Exa 9. Progam to determine the probability of maximum interference of a 64 channel CDMA system Exa 0. Program to determine the amount of transmission capacity Exa 0.3 Program to determine the probability that the delay of an ATM voice cell Exa. Program to determine the distance limit imposed by the need to echo E bit in a BRI ST interface Exa. Program to determine the theoretical maximum data rate of a prefectly equalized voiceband modem Exa. Program to calculate how often do two calls arrive with less than milisec between them Exa. Program to calculate the probability that eight or more arrivals occur in an chosen 30 sec Exa.3 Program to calculate the probability that a 000 bit data block experiences exaclty 4 errors while being transmitted over a link having error Exa.4 Program to calculate the percentage of total traffic carried by first five ckt and traffic carried by all other remaining Exa.5 Program to calculate how much traffic can the trunk group carry

7 Chapter 3 Voice Digitization Scilab code Exa 3. Program to calculate quantization interval and bits needed to encode each sample 3 // Example // Page sqr =30 //SQR=30dB 8 9 q =*0^[ -( sqr -7.78) /0] 0 disp ( Thus 3 q u a n t i z a t i o n i n t e r v a l s a r e r needed f o r each p o l a r i t y f o r a t o t a l o f 6 i n t e r v a l s i n a l l. The number o f b i t z r e q u i r e d a r e d e t e r m i n e d as ) 3 N= log (6) 4 5 // R e s u l t 6 7 // q = V 8 6

8 9 //N = 4. 7 = 5 b i t s per sample Scilab code Exa 3. Program to calculate the minimum bit rate for a PCM encoder must provide for high fidelity 3 // Example // Page dr =40 // dynamic range =400dB 8 9 SNR =50 // s i g n a l to n o i s e r a t i o =5 0dB 0 SQR =dr+snr 3 n =[( SQR -.76) /6.0] 4 5 disp ( This can be approximated to 5 b i t s per sample ) 6 7 disp ( Assuming e x c e s s sampling f a c t o r u s i n g D type channel, we c h o o s e sampling r a t e as 48KHz ) 8 9 disp ( T h e r e f o r e r e q u i r e d b i t r a t e i s ) 0 5* // R e s u l t 4 5 // 70 kbps 7

9 Scilab code Exa 3.4 Program to calculate how many bits per sample can be saved by using DPCM 3 // Example // Page w =800 // Omega=800Hz 8 9 // x ( t )=A s i n ( p i. wt ), e q u a t i o n f o r s i n e wave with maximum a m p l i t u d e 0 //x ( t )=A( p i ). w. c o s ( p i. wt ), d i f f w. r. t time 3 (* %pi ) *800*(/8000) 4 5 // a, x ( t ) max 6 7 disp ( s a v i n g s i n the b i t s per sample can be d e t e r m i n e d as ) 8 9 log (/0.68) 0 // R e s u l t 3 // b i t s 8

10 Chapter 5 Digital Switching Scilab code Exa 5. Program to find the idle path in a three stage 89 line switch 3 // Example // Page // R e f e r to t a b l e 5. on page disp ( From the t a b l e, s p a c e e x p a n s i o n f a c t o r o f i s Hence the u t i l i z a t i o n o f each i n t e r s t a g e i s g i v e n by ) 0 0./ p = -[( -0.47) ^] // p r o b a b i l i t y t h a t one o f two l i n k s i n s e r i e s i s busy 4 5 disp ( T h e r e f o r e, the e x p e c t e d number o f paths to be t e s t e d are, ) 6 9

11 7 Np =[ -(0.67) ^5]/( -0.67) 8 9 // R e s u l t 0 // Only 3 o f the 5 paths s h o u l d be t e s t e d b e f o r e an i d l e path i s found Scilab code Exa 5. Program to determine the implementaton complexity of the TS switch 3 // Example // Page // R e f e r to f i g u r e 5. 9 on page N =80 //Number o f l i n k s 0 Nc =4 //Number o f c o n t r o l words 3 Nb =7 //Number o f b i t s per c o n t r o l word 4 5 Nb =5 //Number o f b i t s per c o n t r o l word 6 7 disp ( The number o f c r o s s p o i n t s i n the s p a c e s t a g e i s ) 8 9 Nx=N^ 0 disp ( The t o t a l number o f memory b i t s f o r the s p a c e s t a g e c o n t r o l s t o r e i s ) 3 Nbx =N*Nc*Nb 0

12 4 5 disp ( The t o t a l number o f memory b i t s f o r the time s t a g e i s ) 6 7 Nbt =(N*Nc *8) +(N*Nc*Nb ) 8 9 disp ( Thus the i m p l e m e n t a t i o n c o m p l e x i t y i s ) 30 3 Cmplx =Nx +[( Nbx + Nbt ) /00] 3 33 // R e s u l t // Complexity i s 6784 e q u i v a l e n t c r o s s p o i n t. Scilab code Exa 5.3 Program to determine the implementaton complexity of a 048 channel 3 4 // Example // Page k=7 // from e q u a t i o n 5. 4 on page disp ( Using the v a l u e o f k ) disp ( Using the v a l u e o f k, the number o f c r o s s p o i n t d e t e r m i n e d a r e ) 3 4 *7*6 5 6 disp ( The number o f b i t s o f memory can be d e t e r m i n e d a r e )

13 7 8 N =[*7* 8*4]+[7* 8*8]+[7* 8*7] 9 0 // R e s u l t // The c o m p o s i t e i m p l e m e n t a t i o n c o m p l e c i t y i s 430 e q u i v a l e n t c r o s s p o i n t s. Scilab code Exa 5.5 Program to determine the implementaton complexity of a 307 channel 3 4 // Example // Page n =3 // b i n a r y w. r. t (N/) ˆ k =7 // d e t e r m i n e d as a b l o c k i n g p r o b a b i l i t y o f // R e f e r e q u a t i o n s 5. 8 and Nx =[*04*7]+[7+(3^) ] 7 8 Nx =[*04*7]+[7*(3^) ] 9 0 Nbx =[*7*8*3*5]+{7*8*3*5} Nbt =[*04*8*8] 3 4 Nbtc =[*04*8*7]

14 5 6 cmplx =[ Nx +{( Nbx + Nbt + Nbtc ) /00}] 7 8 // R e s u l t 9 30 // Complexity i s 38,854 e q u i v a l e n t c r o s s p o i n t. 3

15 Chapter 6 Digital Modulation and Radio Systems Scilab code Exa 6.4 Program to determine system gain of 0Mbps Ghz digital microwave repeater using 4 PSK modulation 3 // Example // Page // R e f e r to f i g u r e 6. 7 on page disp ( SNR d e t e c t o r i s 3dB h i g h e r than Eb/N0, t h e r e f o r e ) snr =3.7 //SNR=3.7dB 3 4 disp ( S i n c e 4 PSK modulation p r o v i d e s bps /Hz, the s a m p l i n g r a t e i s 5 MHz, which i s Nqyuist r a t e, t h e r e f o r e ) 5 4

16 6 a =0* log0 ( ) 7 8 a =0* log0 (.3) 9 0 A0=a a disp ( At a c a r r i e r f r e q u e n c y o f GHz, the wavelength i s ) 3 4 (3*0^8) /(*0^9) 5 6 FM =6+60+0* log0 (0.5) -5-0* log0 (4* %pi *5*0^4) // Fade Margin can be found by Equation // R e s u l t 9 //A0 = 6dB 30 // wavelength = 0. 5 m 3 // Fade Margin = db 5

17 Chapter 7 Network Synchronization Control and Management Scilab code Exa 7. Program to determine relative accuracy of maintaining a mutual slip rate ojective of one slip in 0hrs 3 // Example // Page df =(/0*60*60) 9 0 df =[/(0*60*60) ] disp ( S i n c e t h e r e a r e 8000 frame per second, the r e l a t i v e a c c u r a c y i s d e t e r m i n e d as ) 3 4 ans =[ df /8000] 5 6 // R e s u l t 7 6

18 8 // Hence the c l o c k must be a c c u r a t e to. 7 p a r t s i n 0 ˆ 9. Scilab code Exa 7.3 Program to determine the minimum and maximum input channel rate accommodated by an M multiplexer 3 // Example // Page disp ( The maximum i n f o r m a t i o n r a t e per c h a n n e l i s d e t e r m i n e d as ) 8 9 Imax =[(6.3*88) /76] 0 disp ( The minimum i n f o r m a t i o n r a t e per c h a n n e l i s d e t e r m i n e d as ) 3 Imin =[(6.3*87) /76] 4 5 disp ( S i n c e t h e r e a r e t h r e e p o s s i b l e c o m b i n a t i o n s o f two e r r o r s i n the C b i t s, the p r o b a b i l i t y o f m i s i n t e r p r e t i n g an S b i t i s ) 6 7 3*(0^ -6) ^ /6.3 // d u r a t i o n o f each master frame 0 [(3*0^ -) /(86*0^ -6) ] 3 // R e s u l t 4 5 // ˆ 6 m i s f r a m e s per second 7

19 8

20 Chapter 8 Fiber Optic Transmission System Scilab code Exa 8. Program to determine the loss limit and the multimode dispersion limit of a graded index FOC // Caption : Program to d e t e r m i n e the l o s s l i m i t and the multimode d i s p e r s i o n l i m i t o f a graded i n d e x FOC 3 4 // Example // Page // R e f e r to f i g u r e 8. on page Pin =4 // i n p u t power = 4dB 3 A=3 // a t t e n u a t i o n 4 5 LL =( Pin /A) // Loss Limit 6 9

21 7 disp ( Using Gbps km as t y p i c a l BDP o f graded i n d e x multimode f i b e r, the multimode d i s p e r s i o n d i s t a n c e i s d e t e r m i n e d as ) 8 9 Dl =(000/90) // D i s p e r s i o n l i m i t 0 // R e s u l t 3 // Loss Limit = 4 km 4 5 // D i s p e r s i o n Limit =. km Scilab code Exa 8. Program to determine the loss limit and the chromatic dispersion limit of a high performance SMF FOC 3 // Example // Page // R e f e r f i g u r e 8. on page disp ( The a t t e n u a t i o n o f s i n g l e mode f i b r e o p e r a t i n g at 300nm i s a p p r o x i m a t e l y db/km. Thus, ) 0 Pin =4 // i n p u t power = 4dB 3 A = LL =( Pin /A) // Loss Limit 6 7 disp ( Using 50 Gbps km as BDP o f a s i l i c a s i n g l e mode f i b e r, the c h r o m a t i c d i s p e r s i o n l i m i t i s d e t e r m i n e d as ) 0

22 8 9 Cd =(50000/47) // Chromatic d i s p e r s i o n l i m i t 0 // R e s u l t 3 // Loss Limit = 0 km 4 5 // Chromatic D i s p e r s i o n Limit = = 600 km Scilab code Exa 8.3 Program to determine the BDP of SMF system and DS SMF system using DFB LD 3 4 // Example // Page // R e f e r to t a b l e 8. on page 39, a l s o to f i g u r e 8. 6 on page smf =6 smf =6 // d i s p e r s i o n co e f f i c i e n t o f SMF at 550nm 3 4 sw =0.4 // s p e c t r a l width o f the s o u r c e 5 6 BDP =[50/( smf *sw)] // assuming l i n e code as NRZ 7 8 disp ( The BDP o f the DS SMF system i s d e t e r m i n e d as ) 9 0 smf =3.5 // d i s p e r s i o n co e f f i c i e n t o f DS SMF at 550nm

23 BDP =[50/( smf *sw)] // assuming l i n e code as NRZ 3 4 // R e s u l t 5 6 //BDP = 39 Gbps=km (SMF) 7 8 //BDP = 79 Gbps km (DS SMF) Scilab code Exa 8.4 Program to determine the difference in wavelength of two optical signal 3 // Example // Page c =3*0^8 // speed o f l i g h t 8 9 wl =500*0^ -9 // wavlength =500nm 0 f =[(3*0^8) /wl] 3 disp ( Thus the upper and l o w e r f r e q u e n c i e s a r e d e t e r m i n e d as 00,00 and 99,999 GHz r e s p e c t i v e l y. The c o r r e s p o n d i n g w a v e l e n g t h s a r e ) 4 5 lam =[ c /(99999*0^9) ] 6 7 lam =[ c /(0000*0^9) ] 8 9 // R e s u l t 0 // The d i f f e r e n c e i n w a v e l e n g h t s i s nm

24 Scilab code Exa 8.5 Program to determine the system gain 3 // Example // Page // R e f e r to t a b l e 8. and f i g u r e 8. 8 on page dr =565 // data r a t e 0 wl =550*0^ -9 // wavelength 3 disp ( The use o f 5B6B l i n e code i m p l i e s the l i n e data r a t e i s, ) *(6/5) 6 7 // 678 Mbps 8 9 disp ( The r e c e i v e r s e n s i t i v i t y f o r 678 Mbps i s d e t e r m i n e d from f i g 8. 8 or t a b l e 8. as ) 0 rsen = A=( -5 - rsen ) // system g a i n 4 5 BDP =[500/(7*0.4) ] 6 7 BDPs =[73.6/0.678] 8 9 lossp =(0.+0.) *(65) 30 3

25 3 lossm =A- lossp 3 33 // R e s u l t // System g a i n = 9. 5 db //BDP = Gbps //BDP s p a c i n g = 09 km 40 4 // Path Loss = 6 db 4 43 // Loss Margin = 3. 5 db Scilab code Exa 8.6 Program to determine the range of SPE data rates that can be accomodated by the byte stuffing operation // Example // Page frames =4*9*87 // Four SPE f r a m e s 7 8 rate =8* frames *000 // normal r a t e SPE 9 0 Rmin =8*33*000 // minimum SPE r a t e 3 4 disp ( When n e g a t i v e byte s t u f f i n g i s used to accomodate a f a s t incoming SPE r a t e, 333 b y t e s o f data a r e t r a n s m i t t e d i n f o u r f r a m e s. Thus, the h i g h e s t s l i p r a t e i s ) 5 4

26 6 Rmax =8*333*000 //maximum SPE r a t e 7 8 // R e s u l t 9 0 // Normal SPE r a t e = 5 0. Mbps //Minimum SPE r a t e = Mbps 3 4 //Maximum SPE r a t e = Mbps 5

27 Chapter 9 Digital Mobile Telephony Scilab code Exa 9. Progam to determine the probability of maximum interference of a 64 channel CDMA system 3 // Example // Page disp ( The p r o b a b i l i t y o f 63 d e s t r u c t i v e i n t e r f e r e r s i s merely the p r o b a b i l i t y o f o c c u r e n c e o f 63 e q u a l l y l i k e l y b i n a r y e v e nts, ) 8 9 Pmax =(0.5) ^63 //maximum p r o b a b i l i t y 0 disp ( The v a l u e o f a d e s i r e d r e c e i v e s i g n a l i s the a u t o c o r r e l a t i o n o f a codeword with i t s e l f and can t h e r e f o r e be r e p r e s e n t e d as a v a l u e o f 6 4. ) 3 disp ( The mean and v a r i e n c e o f a sum o f 63 such v a r i a b l e a r e 0 and 63, r e s p e c t i v e l y. The s i g n a l to i n t e r f e r e n c e r a t i o i s now d e t e r m i n e d as, ) 4 6

28 5 a =[(64^) /63] 6 7 SIR =0* log0 (a) 8 9 // R e s u l t 0 // S i g n a l to i n t e r f e r e n c e r a t i o = 8. db 7

29 Chapter 0 Data and Asynchronous Transfer Mode Network Scilab code Exa 0. Program to determine the amount of transmission capacity 3 // Example // Page // ( a ) With l i n k by l i n k 8 9 frame =000*0^ -8 0 disp ( The e x p e c t e d number o f b i t s o f t r a n s m i s s i o n c a p a c i t y r e q u i r e d to r e t r a n s m i t i s ) 3 frame * // ( b ) With end to end 6 7 frames =0*0^ -5 // c o r r u p t e d frame 8

30 8 9 disp ( The e x p e c t e d number o f b i t s o f t r a n s m i s s i o n c a p a c i t y r e q u i r e d i s ) 0 frames *000 3 // ( c ) With b i t e r r o r 0ˆ ans =000*0^ ans =000*0^ -5* ans =0*0^ -* // R e s u l t 3 33 // ( a ) 0. 0 b i t / l i n k // ( b ) 0. b i t / l i n k // ( c ). 0 b i t s / l i n k // ( c ). 00 b i t s / l i n k Scilab code Exa 0.3 Program to determine the probability that the delay of an ATM voice cell 3 // Example // Page disp ( Assuming the a c c e s s l i n k i s 90% u t i l i z e d on a v e r a g e. ) 9

31 8 9 disp ( The queuing t h e o r y i s p r o v i d e d i n Chapter. I t i n v o l v e s d e t e r m i n i n g the p r o b a b i l i t y t h a t the DSI a c c e s s queue c o n t a i n s enough c e l l s to r e p r e s e n t 0 msec o f t r a n s m i s s i o n time ) 0 tm =[(53*8) /(9*8000) ] 3 disp ( T h e r e f o r e, 0 msec d e l a y r e p r e s e n t s 0 / = 3 6. c e l l t i m e s. ) 4 5 p =(0.9) *{ %e ^[ -( -0.9) *36.]} // R e f e r to e q u a t i o n. 5 i n chap 6 7 disp ( R e s u l t ) 8 9 disp ( P(& gt ; 0 msec ) =. 5% d e l a y w i l l be d i s p l a y e d by more than 0 msec ) 30

32 Chapter Digital Subscriber Access Scilab code Exa. Program to determine the distance limit imposed by the need to echo E bit in a BRI ST interface // Example. 3 4 // Page // R e f e r to f i g u r e. 5 on page disp ( By s e e i n g the f i g u r e, i t can be s e e n t h a t the minimum d e l a y between a t e r m i n a l t r a n s m i t t i n g D b i t and r e c e i v i n g i t back i n the f o l l o w i n g E b i t i s s e v e n b i t t i m e s ) 9 0 disp ( At a 9 kbps data r a t e the d u r a t i o n o f b i t i s 5. u s e c. Thus, the t o t a l round t r i p p r o p a g a t i o n time i s ) 7*5. // u s e c 3 4 disp ( Assuming no a p p r e c i a b l e c i r c u i t r y d e l a y s i n the NT, ) 3

33 5 6 c =3*0^8 // speed o f l i g h t 7 8 Lmax =(36.4*0^ -6) *(/3) * c 9 0 disp ( Because round t r i p p r o p a g a t i o n i n v o l v e s both d i r e c t i o n o f t r a n s m i s s i o n ) Dmax =(/) * Lmax 3 4 disp ( R e s u l t ) 5 6 disp ( Maximum l e n g t h o f w i r e ( Lmax ) = 3640 m = km ) 7 8 disp ( Maximum d i s t a n c e (Dmax)= 80 m =. 8 km ) Scilab code Exa. Program to determine the theoretical maximum data rate of a prefectly equalized voiceband modem // Example. 3 4 // Page disp ( The s i g n a l to q u a n t i z i n g n o i s e r a t i o (SQR) i s g i v e n i n chap3 to be on the o r d e r o f 36dB, which c o r r e s p o n d s to power r a t i o o f ) 7 8 disp ( Using t h i s v a l u e i n Shannon theorem f o r the t h e o r e t i c a l c a p a c i t y o f a c h a n n e l y i e l d, ) 9 0 SNR =398 C =300*[ log (+ SNR )] 3

34 3 4 disp ( R e s u l t ) 5 6 disp ( data r a t e = 37 kbps ) 33

35 Chapter Traffic Analysis Scilab code Exa. Program to calculate how often do two calls arrive with less than milisec between them // Example. 3 4 // Page disp ( The a v e r a g e a r r i v a l r a t e i s ) 7 8 lam =(3600/0000) // a r r i v a l s per s e c 9 0 disp ( From e q u a t i o n., the p r o b a b i l i t y on a r r i v a l i n 0.0 s e c i n t e r v a l i s ) // e q u a t i o n on page 54 P0 =( %e ^ ) 3 4 disp ( Thus. 7% a r r i v a l s o c c u r w i t h n i n 0. 0 s e c o f the p e r v i o u s a r r i v a l. S i n c e the a r r i v a l r a t e i s. 7 8 a r r i v a l s per second, the r a t e o f o c c u r r e n c e o f i n t e r v a r r i v a l time l e s s than 0. 0 s e c i s ) *

36 7 8 disp ( R e s u l t ) 9 0 disp ( t i m e s / s e c ) Scilab code Exa. Program to calculate the probability that eight or more arrivals occur in an chosen 30 sec // Example. 3 4 // Page disp ( The a v e r a g e number o f a r r i v a l s i n a 30 s e c i n t e r v a l i s, ) 7 8 lamt =4*(30/60) 9 0 disp ( The p r o b a b i l i t y o f e i g h t or more a r r i v a l s i s, ) P0 = 3 4 P =[(^) /() ] 5 6 P =[(^) /(*) ] 7 8 P3 =[(^3) /(**3) ] 9 0 P4 =[(^4) /(**3*4) ] P5 =[(^5) /(**3*4*5) ] 3 4 P6 =[(^6) /(**3*4*5*6) ] 5 35

37 6 P7 =[(^7) /(**3*4*5*6*7) ] 7 8 i= -{( %e ^ -) *[ P0+P+P+P3+P4+P5+P6+P7 ]} 9 30 disp ( R e s u l t ) 3 3 disp ( P ( ) = ) Scilab code Exa.3 Program to calculate the probability that a 000 bit data block experiences exaclty 4 errors while being transmitted over a link having error 3 // Example // Page disp ( Assuming i n p e n d e n t e r r o r, we can o b t a i n the p r o b a b i l i t y o f e x a c t l y 4 e r r o r s d i r e c t l y from the P o i s s o n d i s t r i b u t i o n. The a v e r a g e number o f e r r o r s i s, ) 8 9 lamt =[(0^3) *(0^ -5) ] 0 disp ( Thus, ) 3 P4 ={[(0.0^4) /(**3*4) ]* %e ^ -0.0} 4 5 disp ( R e s u l t ) 6 7 disp ( P ( 4 ) = 4.5 0ˆ 0 ) 36

38 Scilab code Exa.4 Program to calculate the percentage of total traffic carried by first five ckt and traffic carried by all other remaining 3 // Example // Page disp ( The T r a f f i c i n t e n s i t y o f system i s, ) 8 9 A =* 0 disp ( The r a f f i c i n t e n s i t y c a r r i e d by i a c t i v e c k t i s e x a c t l y i e r l a n g s. Hence the t r a f f i c c a r r i e d by s t 5 c k t i s, ) 3 P =[(*^) /() ] 4 5 P =[(*^) /(*) ] 6 7 P3 =[(3*^3) /(**3) ] 8 9 P4 =[(4*^4) /(**3*4) ] 0 P5 =[(5*^5) /(**3*4*5) ] 3 A5 ={( %e ^ -) *[ P+P+P3+P4+P5 ]} 4 5 disp ( A l l o f r e m a i n i n g c k t s c a r r y, ) 6 7 Ar = disp ( R e s u l t ) 30 3 disp ( A( 5 ) =. 8 9 e r l a n g s ) 3 33 disp ( A( r e m a i n i n g ) = 0. e r l a n g s ) 37

39 Scilab code Exa.5 Program to calculate how much traffic can the trunk group carry 3 // Example // Page // R e f e r f i g u r e. 5 on page disp ( From f i g, i t can be t h a t the output c i r c u i t u t i l i z a t i o n f o r B=0. and N=4 i s ) 0 N =4 3 op = disp ( Thus the c a r r i e d t r a f f i c i n t e n s i t y i s ) 6 7 N*op 8 9 disp ( S i n c e the b l o c k i n g p r o b a b i l i t y i s 0., the maximum l e v e l o f o f f e r e d t r a a f f i c i s, ) 0 A =[9./( -0.) ] 3 disp ( R e s u l t ) 4 5 disp ( A =. 3 e r l a n g s ) 38

Scilab Textbook Companion for Wireless Communications Principles and Practices by T. S. Rappaport 1

Scilab Textbook Companion for Wireless Communications Principles and Practices by T. S. Rappaport 1 Created by Priyanka Gavadu Patil Wireless communication Others Pillai HOC College Of Engineering & Technology