Error/Flow Control Modeling (ARQ Modeling). Modeling of Go Back N

Error/Flow Control Modeling (ARQ Modeling)

Modeling of Go Back N

© Tallal Elshabrawy 3

Limitation of Stop & Wait Protocol

Inefficiency of Stop-and-Wait because the channel is left idle without use until an acknowledgement is received

Potential Solution: Allowing the transmitter to continue sending enough frames

so that the channel is kept busy while the transmitter is waiting for an acknowledgement

Machine A Machine B

Physical Channel

First Frame-Bit enters Channel

Last Frame-Bit enters Channel

First Frame-Bit arrives at B

Last Frame-Bit arrives at B

Last ACK-Bit Arrives at A

Processing Time

Channel is Idle


Go-Back-N ARQ Protocol Sender Receiver

An outstanding frame:It is a frame that has beentransmitted and is yet to beacknowledged

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3

Fr_3

Fr_4

Fr_5

Fr_6

Fr_7

Fr_8

ACK_4

ACK_5

ACK_6

ACK_7

ACK_8

Example Go Back 4

At this Point there are WS=4 Outstanding Frames. So,GO-BACK-4

Out of Sequence Frames. So, do not accept them


Go-Back-N Basics

Transmit without waiting for ACK

Each frame received correctly is acknowledged with a sequence number corresponding to the NEXT frame expected

The receiver discards all out of sequence packets

If number of outstanding frames is WS: Go-Back-N


What does WS Represent?

WS is called the sending window size

Each frame must be buffered (stored) until a valid ACK arrives (in case retransmission is needed)

WS represents the maximum number of frames that may be outstanding (i.e., stored) simultaneously


Sliding Window Concept

Sender Receiver

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3

Example Go Back 4Sending Window

Frame Sequences that are allowed to be sentOutstanding Frame Sequences

Fr_0

Fr_1

Fr_2

Fr_3

Go Back N is an example of what is called a sliding window protocol

An ACK received means that all previous frames have been received correctly (previous ACKs were lost or receiver chose not to send them)



Sender Receiver

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3



Fr_0

Fr_1

Fr_2

Fr_3





Sender Receiver

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3



Fr_0

Fr_1

Fr_2

Fr_3





Sender Receiver

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3



Fr_0

Fr_1

Fr_2

Fr_3





Sender Receiver

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3



Fr_1

Fr_2

Fr_3

Fr_4





Sender Receiver

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3



Fr_2

Fr_3

Fr_4

Fr_5





Sender Receiver

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3



Fr_3

Fr_4

Fr_5

Fr_6





Sender Receiver

Fr_0

Fr_1

Fr_2

Fr_3

Fr_4

Fr_5

Fr_6

ACK_1

ACK_2

ACK_3



Fr_4

Fr_5

Fr_6

Fr_7ACK_4

Transmitter has nothing to send



© Tallal Elshabrawy

Go-Back-N ARQ Modeling

15

Machine A Machine B

Physical Channel

Assumptions

Forward Channel BER

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

Infinite number of retransmissions


Go-Back-N ARQ Markov Model

16

Model DetailsThe time step is equal to

Probability of packet error

ForDefine as the probability of Define as the transition

probability from to

𝒔𝟏 𝒔𝟐 𝒔𝟑 𝒔𝑵𝟏 𝟏 𝒔𝑵 −𝟏

𝟏

𝟏−𝒑𝒆

𝒑𝒆

𝚷=[𝝅𝟏 𝝅𝟐 𝝅𝟑 … 𝝅𝑵 ]

𝚫=[𝜹𝟏 ,𝟏 𝜹𝟏 ,𝟐 … 𝜹𝟏 ,𝑵 −𝟏 𝜹𝟏,𝑵

𝜹𝟐 ,𝟏 𝜹𝟐 ,𝟐 … 𝜹𝟐 ,𝑵 −𝟏 𝜹𝟐,𝑵

⋮ ⋮ ⋮ ⋮ ⋮𝜹𝑵 −𝟏 ,𝟏 𝜹𝑵−𝟏 ,𝟐 … 𝜹𝑵−𝟏,𝑵 −𝟏 𝜹𝑵 −𝟏 ,𝑵

𝜹𝑵 ,𝟏 𝜹𝑵 ,𝟐 … 𝜹𝑵 ,𝑵−𝟏 𝜹𝑵 ,𝑵

]


Go-Back-N ARQ Markov Model

17

𝚷=[𝝅𝟏 𝝅𝟐 𝝅𝟑 … 𝝅𝑵 ]

𝚫=[𝟎 𝟏 𝟎 … 𝟎 𝟎𝟎 𝟎 𝟏 … 𝟎 𝟎⋮ ⋮ ⋮ ⋮ ⋮ ⋮𝟎 𝟎 𝟎 … 𝟎 𝟏𝒑𝒆 𝟎 𝟎 … 𝟎 𝟏−𝒑𝒆

]At steady State

With boundary condition

Solving:

𝒔𝟏 𝒔𝟐 𝒔𝟑 𝒔𝑵𝟏 𝟏 𝒔𝑵 −𝟏

𝟏

𝟏−𝒑𝒆

𝒑𝒆


Go-Back-N ARQ Throughput

18

Throughput measures the percentage of time slots that are utilized for successful transmissions 𝒔𝟏 𝒔𝟐 𝒔𝟑 𝒔𝑵

𝟏 𝟏 𝒔𝑵 −𝟏𝟏

𝟏−𝒑𝒆

𝒑𝒆


S/W and GBN Comparison

19

0 0.1 0.2 0.3 0.4 0.50.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Throughput of S/W and GBN

Probability of Packet Error pe

Th

rou

gh

pu

t

S/W t0/t

pk=4

S/W t0/t

pk=2

GBN t0/t

pk=4

GBN t0/t

pk=2

Documents

Error/Flow Control Modeling (ARQ Modeling). Modeling of Go Back N