Error/Flow Control Modeling (ARQ Modeling)

© Tallal Elshabrawy 2

Data Link Layer

Data Link Layer provides a service for Network Layer (transfer of data from the network layer of a sender to the network layer of a receiver)

Data Link Layer uses the Physical Layer to transmit bits of Data Link Frames over the physical medium

LLC

MAC

Network

Physical

© Tallal Elshabrawy 3

Data Link Layer Functions

Framing (Grouping Bits into Frames)

Error Control

Flow Control

Medium Access Control

© Tallal Elshabrawy 4

Bit Errors in Communication Systems

At the physical layer, bit errors are inevitable to occur with small but non zero probability, example: Bit error probability in the order of 10-6 for systems using copper

wires Bit error probability in the order of 10-9 for modern optical fiber

systems High bit error probability in the order of 10-3 for wireless

transmission systems

Some services are tolerant to relatively high bit error rates such as digital speech transmission

Some applications must experience error-free communications such as electronic funds transfer

© Tallal Elshabrawy 5

Error Control

Error Control is a system to deal with errors that occur due to disturbances on the physical channel.

Components of an error control system: Error Correction and

Detection

Acknowledgement (ACK) & Non- Acknowledgement Control Messages (NAK)

Timers

Sender Receiver

00

Data Frame

ACK

No Errors

11

Errors

11

ACK

No Errors

Timer

Frame is Good

Frame is Good

Detection/Correction

Detection/Correction

Detection/Correction

© Tallal Elshabrawy 6

Error Control Mechanisms

Forward Error Correction (FEC) Detection of erroneous frames or packets Processing of received frame bits in attempt to correct

the errors

Automatic Retransmission reQuest (ARQ) Detection of erroneous frames or packets Retransmission of erroneous frames with the hope that

no errors would occur in the next attempt

© Tallal Elshabrawy 7

Automatic Repeat reQuest (ARQ) Protocols

Purpose: to ensure a sequence of information packets is delivered in order and without errors or duplications despite transmission errors & losses (Error Control & Flow Control)

Modeling of Stop and Wait Protocol

© Tallal Elshabrawy 9

Stop-and-Wait ARQ

Stop after Transmitting a Packet Wait for an Acknowledgement

Transmitter Receiver

Packet

H

CRCH

Error Free Packet

ACK

Information Frame CRC

Transmitter Receiver

Packet

H

CRCH

Error Free Packet

ACK

Information Frame CRC

H : HeaderCRC : Cyclic Redundancy Check (Error Detection)

© Tallal Elshabrawy 10

Stop-and-Wait ARQ Operation

Machine A Machine B

Physical Channel

First Packet-Bit enters

ChannelsLast Packet-Bit

enters Channels

First Packet-Bit arrives at B

Last Packet-Bit arrives at B

Last ACK-Bit Arrives at A

Processing Time for Error

Detection

Channel is Idle

© Tallal Elshabrawy 11

Stop-and-Wait ARQ Operation

Machine A Machine B

Physical Channel

 

 

 

 

 

 

 

 

 

© Tallal Elshabrawy

Stop-and-Wait ARQ Modeling

12

Machine A Machine B

Physical Channel

 

 

 

 

Assumptions

Forward Channel BER

Backward Channel (i.e., ACK/NAK) is Error Free

Infinite number of retransmissions

© Tallal Elshabrawy

Stop-and-Wait ARQ Markov Model

13

              

 

     

 

 

 

Model DetailsState corresponds to

retransmissions of a given packet

The time step is equal to

Transition probabilities are governed by probability of packet error

ForDefine as the probability of Define as the transition

probability from to

© Tallal Elshabrawy

Stop-and-Wait ARQ Markov Model

14

              

 

     

 

 

 

 

𝚫=[ (𝟏−𝒑𝒆 ) 𝒑𝒆 𝟎 𝟎 …

(𝟏−𝒑𝒆 ) 𝟎 𝒑𝒆 𝟎 …

(𝟏−𝒑𝒆 ) 𝟎 𝟎 𝒑𝒆 …

⋮ ⋮ ⋮ ⋮ ⋱]

At steady State

With boundary condition

Solving:

© Tallal Elshabrawy

Stop-and-Wait ARQ Performance

15

              

 

     

  

Average number of retransmissions per packet

© Tallal Elshabrawy

Stop-and-Wait ARQ Efficiency

16

              

 

     

 

Efficiency Decreases with: Increase in BER Increase in Packet Size

Efficiency measures number of transmissions required to send one packet

For

Notes The efficiency is expressed in terms of the time step The closed form solution presents a simple equation in terms of ,

© Tallal Elshabrawy

Stop-and-Wait ARQ Throughput

17

              

 

     

 

Throughput measures the percentage of time slots that are utilized for successful transmissions

Notes Throughput does not care how many attempts have been done to successfully

transmit a packet Throughput measures the channel utilization for successful transmission Efficiency rather measures the delay of a given packet Both efficiency and throughput represent two faces of the same coin

© Tallal Elshabrawy

Stop-and-Wait ARQ Simplified Model

18

State corresponds to new transmission and State corresponds to a retransmission state.

At steady State

With boundary condition

Solving:

𝑠𝑟𝑡

𝟏−𝒑𝒆

𝟏−𝒑𝒆

𝒑𝒆

𝒑𝒆

𝚷=[𝝅𝟎 𝝅𝒓𝒕 ]

𝚫=[𝟏−𝒑𝒆 𝒑𝒆

𝟏−𝒑𝒆 𝒑𝒆]

𝑠0