CSIS 625 1

CSIS 625 Week 4

Statistical TDM, Traffic Engineering,

Error Detection & Correction

Data Link LayerCopyright 2001 - Dan Oelke

For use by students of CSIS 625 for purposes of this class only.

CSIS 625 2

Overview

• Statistical TDM

• Traffic Engineering

• Error Detection

• Error Correction

• Data Link Layer– Line Discipline– Flow Control– Error Control

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Statistical Time Division Multiplexing

• With Synchronous TDM, if an input has nothing to send, that timeslot is wasted.

• With Statistical TDM you are betting that at any given time only some of the inputs want to send data

• The sum of the input bit rates to the MUX may exceed the output bit rate of the MUX

• If you are “unlucky” some data may be delayed or discarded by the MUX

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Statistical TDM

• Delaying data because others are using the line requires additional buffers at the MUX

• A burst of high speed data at the DEMUX may require the DEMUX to buffer data until the lower speed output can accept it

• Timeslots can be borrowed

• Some inputs can have priority over others

• Some systems have variable length timeslots

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Statistical TDM

• Additional framing overhead required– Just knowing the timeslots is not enough– Each packet of data in a statistical TDM system

must have overhead labeling its source or destination

– It is best to have relatively large timeslots to minimize overhead relative to data carried

• Almost all data systems today use statistical TDM at some point.

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Traffic Engineering

• In telephony networks, not all phones are in use at the same time, so trunks between central offices are over-subscribed– This is a form of statistical TDM

• Agner Krarup Erlang (1878-1929)– developed equations on how the blocking

probability relates to the amount of traffic and number of lines.

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Traffic Engineering Definitions

• Trunk - a communication line between two switching systems

• Poisson Distribution - A mathematical formula that defines the probability of x events occurring in a certain time

• Busy Hour - The one hour during the day or year that has the most traffic

• CCS - Centum Call Seconds - amount of traffic offered on a line.– 60 * 60 = 3600 seconds or 36 CCS

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Traffic Engineering

• Amount of traffic offered can be calculated from the average number of calls and average length.– For example: 2 calls / hour * 3 minutes / call =

2 * 180 = 360 call seconds = 3.6 CCS– If one phone offers 3.6CCS, then 100 phones

offer 360 CCS

• Often Erlangs are used in describe the amount of traffic offered.– 36 CCS = 1 Erlang

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Different Traffic Engineering models

• Poisson distribution - simplest – Assumes that blocked calls are held.– Infinite number of sources

• Erlang B – Assumes that blocked calls never return

• Used originally for blocked calls that went to higher cost lines.

– Infinite number of sources

• Extended Erlang B– Has a retry probability

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Different Traffic Engineering models

• Erlang C– Assumes that blocked calls are delayed– Infinite number of sources– Used for Call Center applications

• “Trunks” are service people

• There are models for Finite number of sources, but they are used much less often.– Even if they should be used - people don’t

• Equations given are nice, but either look up tables, or calculators are really used.

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Poisson Distribution

• Poisson assumes that blocked calls wait forever.– This will tend to over estimate the number of

trunks needed– Equation for Poisson

• N = Number of events to occur in a unit time (Number of trunks)

• A = Average number of events occuring per unit time (Traffic in Erlangs)

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Erlang B

• Erlang B assumes that blocked calls never retry– This will tend to under estimate the number of

trunks needed– Equation for Erlang B

• N = Number of trunks

• A = Traffic offered in Erlangs

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Traffic Engineering example problem

– Given • 100 homes, with average 1.5 phones / home

• First line of a home has 3.5CCS

• Second line of a home has 30CCS

• 50% of blocked calls retry immediately

– Calculate number of trunks to serve these homes with a blocking probability of 0.02

• 100 * 3.6 CCS = 360CCS

• 50 * 30 CCS = 1500CCS

• 360 CCS + 1500 CCS = 51.67 Erlangs

• From Extended Erlang B calculator - 63 trunks

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Traffic Engineering Web pages

– http://www.erlang.com/calculator/– http://www.iinet.net.au/~clark

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Error Detection

• Errors always occur during transmission

• Bit Error - an error that changes only one bit

• Burst Error - an error that changes several adjacent bits.

• Coding Violations - When the line coding mechanism tells us of an error. – Need to use something like Bipolar-AMI,

8b10b, etc.

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Error Detection - Parity Bits

• Parity Bit - an extra bit of data sent with every data packet.

• Even Parity - The extra bit is set so that the number of bits is always even

• Odd Parity - The extra bit is set so that the number of bits is always odd

• Receiver checks parity and discards data if parity is not valid

• Regular parity is also known as Vertical Redundancy Check

• Parity is sometimes mis-used as any redundant bit

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Error Detection - BIP

• BIP-8 - Bit Interleaved Parity - 8 bits– BIP is also known as Longitudinal Redundancy

Check– Takes bytes and calculates a parity bit for each

bit position– Diagram of BIP:– Provides better

1 1 1 1Byte 1: 0 0 0 0

1 1 1 1Byte 2: 1 1 1 1

0 0 0 0Byte 3: 0 0 0 0

1 1 0 0Byte 4: 1 0 0 1

0 0 1 1Byte 5: 0 0 1 1

1 1 1 1BIP-8: 0 1 0 1

protection against burst errors

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Error Detection - Checksum

• Checksum - a byte added to the end of the frame to catch errors

• Simplest form is calculated by adding up all the bytes in the frame

• There are several algorithms - so check specifics on any one algorithm

• BIP-8 is sometimes called a checksum

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Error Detection - CRC

• CRC - Cyclic Redundancy Check

• Catches many errors that Parity or BIP-8 will miss.

• Adds bits to the end of a frame so that it can be evenly divided by a number

• Usually 8, 16, or 32-bit CRC

• Easy to implement in hardware with shift register and feedback xor’s.

• See book for examples

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CRC - Strength

• All bursts of errors r (r = length of CRC)

• All odd number of errors

• Probability of missing error – if burst is r+1 => 0.5r-1 (0.532-1 = 4.6E-10)– if burst is r+1 => 0.5r (0.532 = 2.3E-10)

• CRC’s are considered quite strong

• See also:– http://www.ross.net/crc/

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Error Rates - BER

• BER - Bit Error Rate - the probability of a bit being changed– Used to describe transmission lines– All transmission lines have some non-zero BER– Calculate by counting the number of errors and

dividing by the number of bits• Need to adjust for errors that occur but are not

detected

• For example - an odd number of errors when using parity

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Error Rates - BER

• Normal practice is to measure 10 times the period to report a BER– This means that to state the line has a 1E-10

error rate (or better) you must measure 1E+11 bits

– A T1 would require 18 hours to have 1E+11 bits go through.

• Voice sounds ok at BER of 1E-5– Still intelligible at 1E-3

• Data doesn’t work very well below 1E-7

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FEC - Forward Error Correction

• Sometimes it is advantageous to correct an error instead of just detecting it.

• Brute force is to send data repeatedly– To correct n errors, send data 2n+1 times– Not very efficient - there are better ways.

• Hamming codes or Reed-Solomon codes do it much more efficiently

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Hamming Distance

• Hamming distance - the number of bits that have to be changed to go from one valid code to another.– To detect d errors -Hamming distance of d+1

• parity gives a Hamming distance of 2, so it detects up to one bit error

– To correct d errors - Hamming distance of 2d+1• Need to be able to distinguish “closest” valid code

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Hamming Code

• Hamming Code - an error correcting code to correct 1 bit error– For 4 data bits, 3 redundancy bits needed– For 8 data bits, 5 redundancy bits needed

• Rule for Hamming Codes:– (m + r + 1) 2r

• m = message bits

• r = redundant bits

• To handle burst errors, multiple codes can be interleaved.

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Reed-Solomon codes

• Another error correcting code

• Designed to have redundant symbols

• Allows for whole symbols to be errored – It handles bursts of errors

• Common applications– CD Players, – Spacecraft communication– DSL lines

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Reed Solomon Codes

• Notation - RS(NN,KK)• MM - the code symbol size in bits

• NN - the block size in symbols (2**MM - 1)

• KK - the number of data symbols per block– KK < NN

• Can correct (NN-KK)/2 errors per block

• If known that there are missing symbols, then RS can correct NN-KK “erasures”

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Common Reed Solomon Codes

• RS (255,223) – Sends 255 8 bit characters, 223 of them are data

and 32 are parity– Can correct 16 errors or 32 erasures

• RS(204,188) - Used in Digital Video– Sends 204 8 bit characters, 188 of them are data

and 16 are parity– Can correct 8 symbol errors

• Can be done on other than 8-bit characters

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More on FEC

• FEC is often used to improve the BER of lines.– Can be more cost effective than boosting the

power sent over the line– Retransmission at higher levels may not be

practical

• Error Correcting web pages• http://www.piclist.com/techref/method/errors.htm

• http://people.qualcomm.com/karn/code/fec/

• http://www.engelschall.com/u/sb/hamming/

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Line Discipline

• Line Discipline defines who can send and when they can send.

• Simplex system– Who is always known– When is usually any time

• In a duplex system, the sender should send only when it knows that the receiver is ready.– This is in theory, but in practice it only

sometimes works this way

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Line Discipline

• Three phases of communication– Establishment of communication

• Determines who is sending to whom

– Data transfer• Moving the data

– Termination• Tying up loose ends

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ENQ/ACK system

• Process• Sender sends a ENQ (Enquiry) to the intended

receiver.

• Receiver sends back an ACK (Acknowledgement) when it is ready to receive

• Sender sends data

• Sender sends EOT (End of Transmission) when done sending.

• Receiver may send a NAK (Negative Acknowledgement) if it isn’t ready.

• Used in point to point systems

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ENQ/ACK system

• Common to have one node a primary and another a secondary– Primary is responsible for initiating

communication

• Some systems have nodes as peers– Either can initiate a transfer

• In full-duplex system, data and control messages can be sent simultaneously

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Poll & Select system

• Always has a primary and secondary nodes

• Process - Poll– Primary node requests data from the secondary– If no data, secondary responds with a NAK– Otherwise secondary responds with the data

• Process - Select– Primary node selects a secondary node and

sends data to it– Secondary responds with ACK after successful

transfer of data

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Network Addresses

– In a multi-point system, addresses needed so that nodes know who is talking to who

– Simple in some systems where physical position or dip-switch sets it.

– Ethernet defines that all manufactures of devices include a unique 48-bit (6-byte) address in every device.

– Polling 2^48 devices isn’t practical• at 10Mbps, with a 60 byte poll it would take

– 2^24 / 10Mbps * 60 * 8 bytes = 1.35E+10 seconds

– or about 428 years

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Media Access Control

• MAC - Media access Control

• A multipoint network with no clear master and slave. – master == primary– slave == secondary

• In this system, there needs to be more complicated protocol than ENQ/ACK or select/poll to figure out who sends when

• Next week’s lecture…..

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Flow Control

• Flow control - a protocol to ensure that the sender does not overwhelm a receiving station

• Incoming data must be checked and processed before it can be used– This is often slower than the transmission rate– Receivers need to buffer received data until it is

processed– Buffers are always limited

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Flow Control - Stop-n-Wait

• Stop and Wait flow control is simplest form of flow control

• Process– Sender sends one frame of data– Sender waits for ACK before sending more – Receiver can slow down process by waiting to

send ACK

• May be simple - but it is inefficient

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Stop-n-Wait efficiency

– Entire set of data is divided into n frames

– tprop = time to go from sender to receiver • depends on distance and medium

– tframe = time to send one data frame• depends on bit rate

– TD = n(2 tprop + tframe) = Time to send data

– Actual transmission of data is n* tframe

– Efficiency is (n* tframe )/ n(2 tprop + tframe)

– = 1 / (1 +2(tprop / tframe))

– If tprop is small and tframefor frame is large, it approaches 100%, but never reaches it.

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Sliding Window Protocol

• Sliding Window flow control allows for more than one frame to be sent before an acknowledgement is received

• frames are numbered from 0 to n-1• Sender sends frames up until it has sent n-1

frames• Receiver sends back an ACK with the number

of the next frame it expects• Sender can now send up to this new number • Maximum window size is n-1 frames

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Figure 10-14

WCB/McGraw-Hill The McGraw-Hill Companies, Inc., 1998

Sliding Window Example

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Sliding Window Efficiency

• If the sliding window is big enough, and the receiver is fast enough, then 100% efficiency can be achieved

• To get 100% - – tprop ((n - 1) * tframe )

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Error Control

• Error detection and retransmission

• Error detection is detection is achieved using parity, checksums, CRC, etc– Extra data added to each frame

• ARQ - Automatic Repeat Request– This abbreviation isn’t really used much

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Stop-n-Wait Error Control

• Extension of Stop-n-Wait flow control– When a good frame is received, an ACK sent

back to originator.– When a damaged frame is received, a NAK is

sent back to originator– When a NAK is received, the same frame is

retransmitted

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Stop-n-Wait Error Control

• Any frame may be dropped - data or NAK or ACK.– If ACK isn’t received after some time, a NAK

is assumed– If a NAK is lost - timeout and retransmission – If a ACK is lost timeout and retransmission

• Frames must be numbered so receiver can throw away duplicates

– If data is lost - timeout and retransmission

• Has same efficiency issues

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Go-back-N Error Control

• Uses a Sliding window

• If a NAK is received or an ACK timeout occurs– all data since last ACK received is resent– This may be several frames

• ACKs contain next expected frame number

• NAKs contain errored frame number

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Selective-Reject Error Control

• Uses a Sliding window– If a NAK is received, only the damaged frame is

resent

• Selective Reject is more complicated to implement – Receiver must contain the sorting logic to enable it to reorder frames

– Sending device must contain searching mechanism to enable it to find and select only the requested frame for retransmission

– Buffer in the receiver must keep all previously received frames on hold until all retransmissions have been sorted, duplicates identified and discarded

– ACK numbers must refer to the frame received instead of next frame expected

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Selective-Reject Error Control

• More efficient as it resends less data – If errors don’t occur very often - there isn’t a

big difference in efficiency

• Selective Reject is rarely implemented over Go-back-N method