P RINCIPLES OF S WITCHING Professor Saad Haj Bakry, PhD, CEng, FIEE N ETWORK A RCHITECTURE

C ONTENTS Saad Haj Bakry Network ArchitectureSwitching C IRCUIT S WITCHING M ULTIPLEXING S TORE & F ORWARD S UGGESTED W ORK

M ULTIPLEXING Saad Haj Bakry Network ArchitectureSwitching / Multiplexing T IME D IVISION: TDM P RINCIPLES F REQUENCY D IVISION: FDM P ROBLEM

P RINCIPLES Saad Haj Bakry Network ArchitectureSwitching / Multiplexing O BJECTIVE: Enabling “ N ” Signals to Share a Channel C ONCEPT: Dividing the Channel into “ N ” Sub-channels F IXED D IVISION: S PACE D IVISION ( “ N ” Physical Links into One Conduit) F REQUENCY D IVISION T IME D IVISION D YNAMIC D IVISION: C ONCENTRATION ( S & F )

F REQUENCY D IVISION M ULTIPLEXING Saad Haj Bakry Network ArchitectureSwitching / Multiplexing FDM 1 1 N N IIII f2f2 f1f1 f3f3 fNfN F = f 1 + f 2 + f f N = N.f F : Bandwidth of Shared Channel fi: Bandwidth for “ i = N ” f: Average / Fixed Bandwidth per Subchannel Shared Channel

T IME D IVISION M ULTIPLEXING Saad Haj Bakry Network ArchitectureSwitching / Multiplexing TDM 1 1 IIII N N Shared Channel 3 3 N N S S Frame of “ Slots ”, where a user is regularly assigned the same sequenced slot in each frame. Time Frame S: Sync

P ROBLEM Saad Haj Bakry Network ArchitectureSwitching / Multiplexing U SE: Suitable for Continuous Use, Not for Burst / Random Use M AIN P ROBLEM: Sub-channels of the Shared Channels are Reserved to Users on “ Fixed ” Basis Not on “ Dynamic / Demand ” Basis. Sub-channels are “ Wasted ” when their Users are “ Not Active ”. S OLUTION: Use of “ Circuit Switching ”

C IRCUIT S WITCHING Saad Haj Bakry Network ArchitectureSwitching / Circuit P RINCIPLES E RLANG- B F ORMULA T ELEPHONE O PERATION T ELEPHONE T RAFFIC

P RINCIPLES: 1/2 Saad Haj Bakry Network ArchitectureSwitching / Circuit O BJECTIVE: Enabling Sub-channels to be Assigned to Users “ Dynamically ” on Demand (Not on Fixed Basis) U SE: Suitable for Burst / Random Use C ONCEPT: Sub- channels Assigned on Demand for Active Use and Released when Activity is Completed

Saad Haj Bakry Network ArchitectureSwitching / Circuit P RINCIPLES: 2/2 TDM / FDM C IRCUIT S WITCHING USERSUSERS USERSUSERS Users Generating Demands Dynamic Assignment / Release on Demand “ N ” Sub-Channels Channel Sharing Shared Channel

T ELEPHONE O PERATION Saad Haj Bakry Network ArchitectureSwitching / Circuit 1. D IAL- U P 3. C ALL P ROGRESS 4. C ALL T ERMINATION 2. S IGNALLING / R OUTING / A SSIGNMENT 5. R ELEASE

T ELEPHONE T RAFFIC: 1/3 Saad Haj Bakry Network ArchitectureSwitching / Circuit T WO R ANDOM P ROCESSES C ALL A RRIVALS: Random Distribution (Poisson Process) C ALL D URATION: Random Distribution (Negative Exponential Distribution / Related to Poisson Process)

T ELEPHONE T RAFFIC: 2/3 Saad Haj Bakry Network ArchitectureSwitching / Circuit R [Calls / Time Unit]: Rate of Generated Calls D [Time Unit]: Average Call Duration A [Erlang]: A = R.D B USY H OUR P RINCIPLE E RLANG: “ 1 ” Erlang is Full Channel Occupancy For “ 1 ” Time Unit

T ELEPHONE T RAFFIC: 3/3 Saad Haj Bakry Network ArchitectureSwitching / Circuit “ 1 ” E RLANG R = 1 [Calls / Hour] D = 60 [Minutes] A = 1 [Erlang] R = 4 [Calls / Hour] D = 15 [Minutes] A = 1 [Erlang] R = 12 [Calls / Hour] D = 5 [Minutes] A = 1 [Erlang]

E RLANG- B F ORMULA: 1/4 Saad Haj Bakry Network ArchitectureSwitching / Circuit T YPICAL / S IMPLE C ASE S TUDY S YSTEM: “ N ” (Sub) Channels Fully Available to All Call D EMANDS / T RAFFIC O FFERED BY ALL U SERS : “ A ” [Erlang] P ERFORMANCE / G RADE OF S ERVICE / B LOCKING P ROBABILITY “ B ”

E RLANG- B F ORMULA: 2/4 Saad Haj Bakry Network ArchitectureSwitching / Circuit B = (A N / N!) / (A i / i!) B = 1 / (N! / (A i (N - i)!))

E RLANG- B F ORMULA: 3/4 Saad Haj Bakry Network ArchitectureSwitching / Circuit O THER I MPORTANT F ACTORS T RAFFIC C ARRIED / S ERVICED: K = A (1 - B) T RAFFIC C ARRIED / S ERVICED: K = A (1 - B) A VERAGE C HANNEL U TILIZATION / O CCUPANCY: Q = K / N A VERAGE C HANNEL U TILIZATION / O CCUPANCY: Q = K / N

E RLANG- B F ORMULA: 4 /4 Saad Haj Bakry Network ArchitectureSwitching / Circuit P OSSIBLE U SE S YSTEM E VALUATION: Given: N / A Find: B / K / Q S YSTEM E VALUATION: Given: N / A Find: B / K / Q S YSTEM C APACITY: Given: N / B Find: A / K / Q S YSTEM C APACITY: Given: N / B Find: A / K / Q S YSTEM D ESIGN: Given: A / B / K Find: N / Q S YSTEM D ESIGN: Given: A / B / K Find: N / Q

S TORE & F ORWARD Saad Haj Bakry Network ArchitectureSwitching / S&F C ONCENTRATION P ERFORMANCE T RAFFIC A NALYSIS M ESSAGE / P ACKET / F RAME / C ELL ( S WITCHING / R ELAY)

C ONCENTRATION: 1/2 Saad Haj Bakry Network ArchitectureSwitching / S&F I 2 2 N N IIII P P MM S HARED C HANNEL B UFFER P ROCESSOR S TORE & F ORWARD c c c [bps] c C [bps] Dynamic Channel Assignment (Active Users Only) / Efficiency USERS > N Where N = C/c

Saad Haj Bakry Network ArchitectureSwitching / S&F C ONCENTRATION: 2/2 B URST U SE U SE L OSS S ENSITIVE I NFORMATION: “ D ATA / T EXT ” N O D ELAY S ENSITIVE I NFORMATION: “ V OICE / P ICTURE ” ; E XCEPT IN H IGH S PEED

Saad Haj Bakry Network ArchitectureSwitching / S&F M ESSAGE M ESSAGE: An Information Signal Sent by a Single User Physical Block (Basic Name: for M / P / F / C) M ESSAGE: An Information Signal Sent by a Single User Physical Block (Basic Name: for M / P / F / C) P ROBLEM: Fluctuating Size Need for Size Control “ P / F / C ” (Logical Units) Providing Better Sharing P ROBLEM: Fluctuating Size Need for Size Control “ P / F / C ” (Logical Units) Providing Better Sharing

Saad Haj Bakry Network ArchitectureSwitching / S&F P ACKET / F RAME / C ELL: 1 / 3 P ACKET: X.25 / 64 kbps Variable Size H: 8 bytes F RAME: T-1 / E-1 Variable Size H: 2 bytes I NFORMATION H EADER H EADER: S OURCE / D ESTINATION / C ONTROL I NFORMATION: C ONTROLLED S IZE C ELL / ATM : OC-3 / OC-12 Fixed: 48 Bytes H: 5 bytes

Saad Haj Bakry Network ArchitectureSwitching / S&F P ACKET / F RAME / C ELL: 2 / 3 D ATAGRAM : Logical Units (Packets) are Routed Independently Through the Network from Source to Destination V IRTUAL C IRCUIT: Physical Units (Messages) Sent from Source to Destination Look as if they Passed Through a Circuit Example: DATAGRAM with the Packets of a Message Reassembled at Destination V IRTUAL C IRCUIT: Physical Units (Messages) Sent from Source to Destination Look as if they Passed Through a Circuit Example: DATAGRAM with the Packets of a Message Reassembled at Destination

Saad Haj Bakry Network ArchitectureSwitching / S&F P ACKET / F RAME / C ELL: 3 / 3 P ACKET: Point-to- Point & End-to- End F RAME: End-to-End Only E RROR C ONTROL C ELL / ATM : End-to-End (Header Only) L OW N OISE: Eases Error Control Protocols. H IGHER S PEED: Reduces Delay and Helps Information Integration (Data / Voice / Picture)

P ERFORMANCE: D ELAY (1/3) Saad Haj Bakry Network ArchitectureSwitching / S&F P P MM M [bits] N EXT N OD E D ELAY E LEMENTS P ROCESSING D ELAY “ p ” Q UEUING D ELAY “ q ” T RANSMISSION D ELAY “ s ” P ROPAGATION D ELAY “ g ” pq sg M ESSAGE D ELAY: d = p + q + s + g C [bps] l [km] v [km/s] / Sec.

P ERFORMANCE: D ELAY (2/3) Saad Haj Bakry Network ArchitectureSwitching / S&F P ROCESSING D ELAY: Processing Dependent Traffic Independent Q UEUING D ELAY: Traffic / Capacity (System) Dependent Analysis Required T RANSMISSION D ELAY: s = M / C Message / Capacity (System) Dependent Independent of Traffic Volume / Fluctuation P ROPAGATION D ELAY: g = l / v Channel / Distance Dependent Traffic / Capacity Independent

Saad Haj Bakry Network ArchitectureSwitching / S&F P ERFORMANCE: D ELAY (3/3) P ROCESSING D ELAY: Significant in High Speed Links Q UEUING D ELAY: An Essential Element, as it is Associated with the Capacity / “ System ”, and Traffic Volume / Fluctuation / “ Demands ” T RANSMISSION D ELAY: An Essential Element, as it is Associated with the Capacity / “ System ”, and the Message Length / “ Demands ” P ROPAGATION D ELAY: Significant in Satellites g = 36 / 300 = 0.12 sec

Saad Haj Bakry Network ArchitectureSwitching / S&F T RAFFIC: 1/2 T WO R ANDOM P ROCESSES M ESSAGE A RRIVALS : Poisson Process M ESSAGE L ENGTH: Negative Exponential Distribution / Fixed Size Messages (Deterministic)

T RAFFIC: 2/2 Saad Haj Bakry Network ArchitectureSwitching / S&F R [Messages / Sec]: Rate of Generated Messages M [Bits] : Average / Fixed Message Length B USY H OUR P RINCIPLE T RAFFIC R ATE: A [bps] = R. M

A NALYSIS: 1/4 Saad Haj Bakry Network ArchitectureSwitching / S&F Q UEUING D ELAY: Variable Message Length q v = (RM / C) / ( (C/M) - R) Fixed Message Length q f = (1/2). qv Q UEUING D ELAY: Variable Message Length q v = (RM / C) / ( (C/M) - R) Fixed Message Length q f = (1/2). qv

A NALYSIS: 2/4 Saad Haj Bakry Network ArchitectureSwitching / S&F E SSENTIAL D ELAY E LEMENTS: d = q v + s = 1 / ( (C/M) - R) L IMITATION: RM < C U TILIZATION / O CCUPANCY: U = (RM) / C

A NALYSIS: 3/4 Saad Haj Bakry Network ArchitectureSwitching / S&F D: N ORMALIZED D ELAY: ( M ESSAGE T RANSMISSION TIME “ s ” ) IN T ERMS OF U TILIZATION “ U ” : D = d / s = 1 / (1 - U) D [Unit-less] : Number of Messages in the System (queued & transmitted)

A NALYSIS: 4/4 Saad Haj Bakry Network ArchitectureSwitching / S&F P OSSIBLE U SE S YSTEM E VALUATION: Given: C / M / R Find: d / U / D S YSTEM C APACITY: Given: C / U (d/D) / M Find: R S YSTEM D ESIGN: Given : R / M / U Find : C

S UGGESTED W ORK Saad Haj Bakry Network ArchitectureSwitching: Work G ENERAL: Computations Concerned with “ Circuit Switching ” and “ Store & Forward ” S PECIAL: Investigations of Practical “ CS ” and “ S&F ” Systems